diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 650 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1396 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1320 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8932 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30579 |
5 files changed, 21439 insertions, 21438 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 4296fdaf..32e96ba4 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2284982 . 3453990495) +(2285080 . 3454219022) (-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 -2386) +(-32 R -2371) ((|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 -1038) (QUOTE (-566))))) @@ -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 -2386 UP UPUP -2468) +(-40 -2371 UP UPUP -3930) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) -(-41 R -2386) +((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2809 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2809 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2809 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2809 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) +(-41 R -2371) ((|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 (-454))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -432) (|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."))) ((-4414 . T) (-4415 . T)) -((-2805 (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|))))))) +((-2809 (-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|))))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2386) +(-54 |Base| R -2371) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) -(-61 -2639) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +(-61 -2640) ((|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 -2639) +(-62 -2640) ((|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 -2639) +(-63 -2640) ((|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 -2639) +(-64 -2640) ((|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 -2639) +(-65 -2640) ((|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 -2639) +(-66 -2640) ((|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 -2639) +(-67 -2640) ((|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 -2639) +(-68 -2640) ((|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 -2639) +(-69 -2640) ((|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 -2639) +(-70 -2640) ((|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 -2639) +(-71 -2640) ((|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 -2639) +(-72 -2640) ((|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 -2639) +(-73 -2640) ((|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 -2639) +(-74 -2640) ((|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 -2639) +(-77 -2640) ((|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 -2639) +(-78 -2640) ((|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 -2639) +(-79 -2640) ((|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 -2639) +(-80 -2640) ((|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 -2639) +(-81 -2640) ((|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 -2639) +(-82 -2640) ((|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 -2639) +(-83 -2640) ((|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 -2639) +(-84 -2640) ((|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 -2639) +(-85 -2640) ((|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 -2639) +(-86 -2640) ((|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 -2639) +(-87 -2640) ((|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 -2639) +(-88 -2640) ((|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 -2639) +(-89 -2640) ((|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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) +((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2809 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (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 -2386 UP) +(-115 -2371 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}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-909))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1022))) (|HasCategory| (-116 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-116 |#1|) (QUOTE (-820))) (|HasCategory| (-116 |#1|) (QUOTE (-850)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-1150))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (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 (-547))) (|HasCategory| (-116 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-909))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-116 |#1|) (QUOTE (-1022))) (|HasCategory| (-116 |#1|) (QUOTE (-820))) (-2809 (|HasCategory| (-116 |#1|) (QUOTE (-820))) (|HasCategory| (-116 |#1|) (QUOTE (-850)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-1150))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (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 (-547))) (|HasCategory| (-116 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-909)))) (|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"))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2805 (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099)))) (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) +((-2809 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2809 (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-129) (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099)))) (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4416 "*") . T)) NIL -(-135 |minix| -4225 S T$) +(-135 |minix| -2420 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -4225 R) +(-136 |minix| -2420 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 @@ -489,13 +489,13 @@ NIL NIL NIL (-140) -((|parents| (((|List| (|ConstructorCall|)) $) "\\spad{parents(c)} returns the list of all category forms directly extended by the category \\spad{`c'}.")) (|principalAncestors| (((|List| (|ConstructorCall|)) $) "\\spad{principalAncestors(c)} returns the list of all category forms that are principal ancestors of the the category \\spad{`c'}.")) (|exportedOperators| (((|List| (|OperatorSignature|)) $) "\\spad{exportedOperators(c)} returns the list of all operator signatures exported by the category \\spad{`c'},{} along with their predicates.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: December 20,{} 2008. Date Last Updated: February 16,{} 2008. Basic Operations: coerce Related Constructors: Also See: Type") (((|CategoryConstructor|) $) "\\spad{constructor(c)} returns the category constructor used to instantiate the category object \\spad{`c'}."))) +((|parents| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{parents(c)} returns the list of all category forms directly extended by the category \\spad{`c'}.")) (|principalAncestors| (((|List| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{principalAncestors(c)} returns the list of all category forms that are principal ancestors of the the category \\spad{`c'}.")) (|exportedOperators| (((|List| (|OperatorSignature|)) $) "\\spad{exportedOperators(c)} returns the list of all operator signatures exported by the category \\spad{`c'},{} along with their predicates.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: December 20,{} 2008. Date Last Updated: February 16,{} 2008. Basic Operations: coerce Related Constructors: Also See: Type") (((|CategoryConstructor|) $) "\\spad{constructor(c)} returns the category constructor used to instantiate the category object \\spad{`c'}."))) NIL NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) ((-4414 . T) (-4404 . T) (-4415 . T)) -((-2805 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2809 (-12 (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-370))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|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{\\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{\\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."))) ((-4411 . T)) NIL -(-148 -2386 UP UPUP) +(-148 -2371 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 -2386) +(-158 R -2371) ((|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 (-909))) (|HasCategory| |#2| (QUOTE (-547))) (|HasCategory| |#2| (QUOTE (-1002))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasCategory| |#2| (QUOTE (-1059))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4410)) (|HasAttribute| |#2| (QUOTE -4413)) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558)))) (-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})"))) -((-4407 -2805 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4410 |has| |#1| (-6 -4410)) (-4413 |has| |#1| (-6 -4413)) (-3661 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-4407 -2809 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4410 |has| |#1| (-6 -4410)) (-4413 |has| |#1| (-6 -4413)) (-3638 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . 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}."))) -((-4407 -2805 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4410 |has| |#1| (-6 -4410)) (-4413 |has| |#1| (-6 -4413)) (-3661 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|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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T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|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| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-370)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-828)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1022)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-1199)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1199)))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-2809 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| |#1| (QUOTE (-1059))) (-12 (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-1199)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasAttribute| |#1| (QUOTE -4410)) (|HasAttribute| |#1| (QUOTE -4413)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|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 @@ -660,8 +660,8 @@ NIL ((|constructor| (NIL "This package provides tools for working with cyclic streams.")) (|computeCycleEntry| ((|#2| |#2| |#2|) "\\spad{computeCycleEntry(x,{}cycElt)},{} where \\spad{cycElt} is a pointer to a node in the cyclic part of the cyclic stream \\spad{x},{} returns a pointer to the first node in the cycle")) (|computeCycleLength| (((|NonNegativeInteger|) |#2|) "\\spad{computeCycleLength(s)} returns the length of the cycle of a cyclic stream \\spad{t},{} where \\spad{s} is a pointer to a node in the cyclic part of \\spad{t}.")) (|cycleElt| (((|Union| |#2| "failed") |#2|) "\\spad{cycleElt(s)} returns a pointer to a node in the cycle if the stream \\spad{s} is cyclic and returns \"failed\" if \\spad{s} is not cyclic"))) NIL NIL -(-183) -((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") (((|Constructor|) $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) +(-183 C) +((|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments(t)} returns the list of syntax objects for the arguments used to invoke the constructor.")) (|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain") ((|#1| $) "\\spad{constructor(t)} returns the name of the constructor used to make the call."))) NIL NIL (-184 S) @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2386) +(-188 R -2371) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2386 UP UPUP R) +(-215 -2371 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 -2386 FP) +(-216 -2371 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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) +((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2809 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2386) +(-219 R -2371) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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}."))) ((-4411 . T)) NIL -(-224 R -2386) +(-224 R -2371) ((|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}."))) -((-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-3628 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . 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{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{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*\\%\\spad{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*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{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}"))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-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 -4225 R) +(-237 S -2420 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 (-793))) (|HasCategory| |#3| (QUOTE (-848))) (|HasAttribute| |#3| (QUOTE -4411)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (QUOTE (-726))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (QUOTE (-1099)))) -(-238 -4225 R) +(-238 -2420 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"))) ((-4408 |has| |#2| (-1049)) (-4409 |has| |#2| (-1049)) (-4411 |has| |#2| (-6 -4411)) ((-4416 "*") |has| |#2| (-172)) (-4414 . T)) NIL -(-239 -4225 A B) +(-239 -2420 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 -4225 R) +(-240 -2420 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."))) ((-4408 |has| |#2| (-1049)) (-4409 |has| |#2| (-1049)) (-4411 |has| |#2| (-6 -4411)) ((-4416 "*") |has| |#2| (-172)) (-4414 . T)) -((-2805 (-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 (-726))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (-2805 (-12 (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-365))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1049)))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365)))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-793))) (-2805 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-848)))) (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (QUOTE (-726))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-1049)))) (|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE 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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}"))) ((-4415 . T) (-4414 . 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(|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 @@ -919,9 +919,9 @@ 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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-909))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-248) -((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\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|) $) "\\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'}."))) +((|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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(|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-726))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-848))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-2809 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (|HasCategory| |#3| (QUOTE (-726))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1175)))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-2809 (|HasCategory| |#3| (QUOTE (-1049))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#3| (QUOTE (-1099)))) (-2809 (|HasAttribute| |#3| (QUOTE -4411)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|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"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#3| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#3| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#3| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#3| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|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 -2386) +(-277 R -2371) ((|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{\\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 -2386) +(-278 R -2371) ((|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{\\spad{ki}} was rewritten as \\spad{\\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 @@ -1053,7 +1053,7 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-365)))) (-281) -((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|ConstructorCall|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) +((|constructor| (NIL "This domains an expresion as elaborated by the interpreter. See Also:")) (|getOperands| (((|Union| (|List| $) "failed") $) "\\spad{getOperands(e)} returns the list of operands in `e',{} assuming it is a call form.")) (|getOperator| (((|Union| (|Identifier|) "failed") $) "\\spad{getOperator(e)} retrieves the operator being invoked in `e',{} when `e' is an expression.")) (|callForm?| (((|Boolean|) $) "\\spad{callForm?(e)} is \\spad{true} when `e' is a call expression.")) (|getIdentifier| (((|Union| (|Identifier|) "failed") $) "\\spad{getIdentifier(e)} retrieves the name of the variable `e'.")) (|variable?| (((|Boolean|) $) "\\spad{variable?(e)} returns \\spad{true} if `e' is a variable.")) (|getConstant| (((|Union| (|SExpression|) "failed") $) "\\spad{getConstant(e)} retrieves the constant value of `e'e.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(e)} returns \\spad{true} if `e' is a constant.")) (|type| (((|Syntax|) $) "\\spad{type(e)} returns the type of the expression as computed by the interpreter."))) NIL NIL (-282 A S) @@ -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| -3418 -3891 |exactQuo|) +(-290 S R |Mod| -3646 -3298 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL @@ -1110,21 +1110,21 @@ NIL NIL (-295 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-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 -2386 S) +(-298 -2371 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 -2386) +(-299 E -2371) ((|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 -2386) +(-311 -2371) ((|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))}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2805 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2809 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1250) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2809 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1250 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|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."))) -((-4411 -2805 (-2447 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2805 (-2447 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4412 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(|HasCategory| |#1| (QUOTE (-1049)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-1049)))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558)))) (-2809 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2809 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2809 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2809 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2809 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| $ (QUOTE (-1049))) (|HasCategory| $ (LIST (QUOTE -1038) (QUOTE (-566))))) +(-318 R -2371) ((|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{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -1941) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3863) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|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."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) -(-329 S -2386) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +(-329 S -2371) ((|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 -2386) +(-330 -2371) ((|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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL @@ -1265,22 +1265,22 @@ NIL NIL NIL (-334) -((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall|)) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) +((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL (-335 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|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 -2386 UP UPUP R) +(-336 S -2371 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 -2386 UP UPUP R) +(-337 -2371 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 -2386 UP UPUP R) +(-338 -2371 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 -2386 UP UPUP) +(-343 S -2371 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(\\spad{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 -2386 UP UPUP) +(-344 -2371 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(\\spad{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."))) ((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . 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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) +((-2809 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2809 (|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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2809 (|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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-352 R UP -2386) +(-352 R UP -2371) ((|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{\\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{\\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{\\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{\\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{\\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{\\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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) +((-2809 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2809 (|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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2809 (|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}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#1|) (QUOTE (-145)))) +((-2809 (|HasCategory| (-910 |#1|) (QUOTE (-145))) (|HasCategory| (-910 |#1|) (QUOTE (-370)))) (|HasCategory| (-910 |#1|) (QUOTE (-147))) (|HasCategory| (-910 |#1|) (QUOTE (-370))) (|HasCategory| (-910 |#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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -2386 GF) +((-2809 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +(-358 -2371 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 -2386 FP FPP) +(-360 -2371 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 \\spad{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}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2809 (|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{\\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}."))) -((-4397 . T) (-4405 . T) (-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-4397 . T) (-4405 . T) (-3628 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . 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}."))) @@ -1504,7 +1504,7 @@ 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 -(-394 -2386 UP UPUP R) +(-394 -2371 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 @@ -1528,11 +1528,11 @@ 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 -(-400 -2639 |returnType| -3072 |symbols|) +(-400 -2640 |returnType| -3218 |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 -(-401 -2386 UP) +(-401 -2371 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1554,7 +1554,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4397)) (|HasAttribute| |#1| (QUOTE -4405))) (-406) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-3628 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-407 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."))) @@ -1567,7 +1567,7 @@ NIL (-409 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."))) ((-4401 -12 (|has| |#1| (-6 -4412)) (|has| |#1| (-454)) (|has| |#1| (-6 -4401))) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2805 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2809 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-547))) (-12 (|HasAttribute| |#1| (QUOTE -4412)) (|HasAttribute| |#1| (QUOTE -4401)) (|HasCategory| |#1| (QUOTE (-454)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-410 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1588,11 +1588,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-415 R -2386 UP A) +(-415 R -2371 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4411 . T)) NIL -(-416 R -2386 UP A |ibasis|) +(-416 R -2371 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 -1038) (|devaluate| |#2|)))) @@ -1611,7 +1611,7 @@ NIL (-420 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."))) ((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1218))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1218)))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-454)))) +((|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -310) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -287) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-1218))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1218)))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-454)))) (-421 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 @@ -1640,7 +1640,7 @@ 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4414 . T) (-4404 . T) (-4415 . T)) NIL -(-428 R -2386) +(-428 R -2371) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1648,7 +1648,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4401 -12 (|has| |#1| (-6 -4401)) (|has| |#2| (-6 -4401))) (-4408 . T) (-4409 . T) (-4411 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4401)) (|HasAttribute| |#2| (QUOTE -4401)))) -(-430 R -2386) +(-430 R -2371) ((|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 @@ -1658,17 +1658,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (-432 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| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|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}."))) -((-4411 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-558)) (-4406 |has| |#1| (-558))) +((-4411 -2809 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-558)) (-4406 |has| |#1| (-558))) NIL -(-433 R -2386) +(-433 R -2371) ((|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 -(-434 R -2386) +(-434 R -2371) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-435 R -2386) +(-435 R -2371) ((|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 @@ -1676,7 +1676,7 @@ 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 -(-437 R -2386 UP) +(-437 R -2371 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 -1038) (QUOTE (-48))))) @@ -1708,7 +1708,7 @@ 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 -(-445 R UP -2386) +(-445 R UP -2371) ((|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 @@ -1755,7 +1755,7 @@ NIL (-456 |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"))) (((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-909))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-457 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 @@ -1820,7 +1820,7 @@ 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 -(-473 |lv| -2386 R) +(-473 |lv| -2371 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 @@ -1835,11 +1835,11 @@ NIL (-476 |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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . 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T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099)))) (-478 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)}"))) ((-4415 . T) (-4414 . T)) @@ -1855,7 +1855,7 @@ NIL (-481 |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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-482) ((|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 @@ -1863,11 +1863,11 @@ NIL (-483 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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|#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-485) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\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| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1875,8 +1875,8 @@ NIL (-486 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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) -(-487 -2386 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +(-487 -2371 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 @@ -1887,7 +1887,7 @@ NIL (-489) ((|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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) +((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2809 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) (-490 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1912,7 +1912,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-496 -2386 UP |AlExt| |AlPol|) +(-496 -2371 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 @@ -1923,16 +1923,16 @@ NIL (-498 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-499 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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-500 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 -(-501 R UP -2386) +(-501 R UP -2371) ((|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{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\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{\\spad{mi}} is given by \\spad{\\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{\\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{\\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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1952,7 +1952,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-506 -2386 |Expon| |VarSet| |DPoly|) +(-506 -2371 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-1175))))) @@ -2003,7 +2003,7 @@ NIL (-518 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-519) ((|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 @@ -2011,15 +2011,15 @@ NIL (-520 |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}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((-2805 (|HasCategory| (-583 |#1|) (QUOTE (-145))) (|HasCategory| (-583 |#1|) (QUOTE (-370)))) (|HasCategory| (-583 |#1|) (QUOTE (-147))) (|HasCategory| (-583 |#1|) (QUOTE (-370))) (|HasCategory| (-583 |#1|) (QUOTE (-145)))) +((-2809 (|HasCategory| (-583 |#1|) (QUOTE (-145))) (|HasCategory| (-583 |#1|) (QUOTE (-370)))) (|HasCategory| (-583 |#1|) (QUOTE (-147))) (|HasCategory| (-583 |#1|) (QUOTE (-370))) (|HasCategory| (-583 |#1|) (QUOTE (-145)))) (-521 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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-522 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."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-523 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 @@ -2031,7 +2031,7 @@ NIL (-525 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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-526) ((|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 @@ -2064,7 +2064,7 @@ 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 -(-534 K -2386 |Par|) +(-534 K -2371 |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 @@ -2088,7 +2088,7 @@ 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 -(-540 K -2386 |Par|) +(-540 K -2371 |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 @@ -2139,12 +2139,12 @@ NIL (-552 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) -(-553 R -2386) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +(-553 R -2371) ((|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 -(-554 R0 -2386 UP UPUP R) +(-554 R0 -2371 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 @@ -2154,7 +2154,7 @@ NIL NIL (-556 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."))) -((-3651 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-3628 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-557 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."))) @@ -2164,7 +2164,7 @@ 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."))) ((-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-559 R -2386) +(-559 R -2371) ((|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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{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 @@ -2176,7 +2176,7 @@ 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 -(-562 R -2386 L) +(-562 R -2371 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -656) (|devaluate| |#2|)))) @@ -2184,11 +2184,11 @@ 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 -(-564 -2386 UP UPUP R) +(-564 -2371 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 -(-565 -2386 UP) +(-565 -2371 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 @@ -2200,15 +2200,15 @@ 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 -(-568 R -2386 L) +(-568 R -2371 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,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 -656) (|devaluate| |#2|)))) -(-569 R -2386) +(-569 R -2371) ((|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 -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1138)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-629))))) -(-570 -2386 UP) +(-570 -2371 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,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{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 @@ -2216,27 +2216,27 @@ 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 -(-572 -2386) +(-572 -2371) ((|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,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{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 (-573 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."))) -((-3651 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-3628 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-574) ((|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 \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-575 R -2386) +(-575 R -2371) ((|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 -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-285))) (|HasCategory| |#2| (QUOTE (-629))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-285)))) (|HasCategory| |#1| (QUOTE (-558)))) -(-576 -2386 UP) +(-576 -2371 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' + +/[\\spad{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(+,{}[\\spad{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(+,{}[\\spad{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 -(-577 R -2386) +(-577 R -2371) ((|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 @@ -2268,15 +2268,15 @@ 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 -(-585 R -2386) +(-585 R -2371) ((|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 -(-586 E -2386) +(-586 E -2371) ((|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 -(-587 -2386) +(-587 -2371) ((|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}."))) ((-4409 . T) (-4408 . T)) ((|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175))))) @@ -2307,7 +2307,7 @@ NIL (-594 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2805 (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2809 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2809 (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-595 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 @@ -2315,7 +2315,7 @@ NIL (-596 |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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-566)) (|devaluate| |#1|)))) (|HasCategory| (-566) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-566)))))) (-597 |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}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} 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.}"))) ((-4409 |has| |#1| (-558)) (-4408 |has| |#1| (-558)) ((-4416 "*") |has| |#1| (-558)) (-4407 |has| |#1| (-558)) (-4411 . T)) @@ -2328,7 +2328,7 @@ 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 -(-600 R -2386 FG) +(-600 R -2371 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{\\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{\\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 @@ -2339,7 +2339,7 @@ NIL (-602 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-603 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2358,12 +2358,12 @@ NIL NIL (-607 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4411 -2805 (-2447 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) -((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4411 -2809 (-2432 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) +((-2809 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-608 |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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-609 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 @@ -2388,7 +2388,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-615 -2386 UP) +(-615 -2371 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2416,7 +2416,7 @@ 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}."))) ((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-848)))) -(-622 R -2386) +(-622 R -2371) ((|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 @@ -2448,18 +2448,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-630 R -2386) +(-630 R -2371) ((|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{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\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 -(-631 |lv| -2386) +(-631 |lv| -2371) ((|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 (-632) ((|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."))) ((-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 (-52))) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -3867) (QUOTE (-52))))))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 (-52))) (QUOTE (-1099)))) (-633 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| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2470,8 +2470,8 @@ NIL NIL (-635 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4411 -2805 (-2447 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) -((-2805 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) +((-4411 -2809 (-2432 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4409 . T) (-4408 . T)) +((-2809 (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (LIST (QUOTE -419) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -369) (|devaluate| |#1|)))) (-636 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 @@ -2483,7 +2483,7 @@ NIL (-638 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 -((-2436 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-2418 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) (-639 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4411 . T)) @@ -2507,7 +2507,7 @@ NIL (-644 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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()} returns the empty list."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-828))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-645 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2519,7 +2519,7 @@ NIL (-647 S) ((|substitute| (($ |#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."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-648 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 @@ -2536,7 +2536,7 @@ 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 -(-652 R -2386 L) +(-652 R -2371 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 @@ -2556,11 +2556,11 @@ 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}."))) ((-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-657 -2386 UP) +(-657 -2371 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)))) -(-658 A -1554) +(-658 A -3056) ((|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}}"))) ((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) @@ -2596,11 +2596,11 @@ 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}."))) ((-4415 . T) (-4414 . T)) NIL -(-667 -2386) +(-667 -2371) ((|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 -(-668 -2386 |Row| |Col| M) +(-668 -2371 |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 @@ -2611,7 +2611,7 @@ NIL (-670 |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."))) ((-4411 . T) (-4414 . T) (-4408 . T) (-4409 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2805 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-558))) (-2809 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-671) ((|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 @@ -2631,7 +2631,7 @@ NIL (-675 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 -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-676) ((|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 @@ -2687,7 +2687,7 @@ NIL (-689 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."))) ((-4414 . T) (-4415 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-558))) (|HasAttribute| |#1| (QUOTE (-4416 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-690 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 @@ -2696,7 +2696,7 @@ 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 -(-692 S -2386 FLAF FLAS) +(-692 S -2371 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 @@ -2706,8 +2706,8 @@ NIL NIL (-694) ((|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"))) -((-4407 . T) (-4412 |has| (-699) (-365)) (-4406 |has| (-699) (-365)) (-3661 . T) (-4413 |has| (-699) (-6 -4413)) (-4410 |has| (-699) (-6 -4410)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2805 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2805 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2805 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2805 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4413)) (|HasAttribute| (-699) (QUOTE -4410)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) +((-4407 . T) (-4412 |has| (-699) (-365)) (-4406 |has| (-699) (-365)) (-3638 . T) (-4413 |has| (-699) (-6 -4413)) (-4410 |has| (-699) (-6 -4410)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((|HasCategory| (-699) (QUOTE (-147))) (|HasCategory| (-699) (QUOTE (-145))) (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-370))) (|HasCategory| (-699) (QUOTE (-365))) (-2809 (|HasCategory| (-699) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-233))) (-2809 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (LIST (QUOTE -287) (QUOTE (-699)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -310) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-699)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-699) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-699) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (-2809 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-351)))) (|HasCategory| (-699) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-699) (QUOTE (-1022))) (|HasCategory| (-699) (QUOTE (-1199))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1199)))) (-2809 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2809 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-365))) (|HasCategory| (-699) (QUOTE (-909)))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (|HasCategory| (-699) (QUOTE (-547))) (-12 (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-1199)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2809 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2809 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-558)))) (-12 (|HasCategory| (-699) (QUOTE (-233))) (|HasCategory| (-699) (QUOTE (-365)))) (-12 (|HasCategory| (-699) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-699) (QUOTE (-365)))) (|HasCategory| (-699) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-699) (QUOTE (-558))) (|HasAttribute| (-699) (QUOTE -4413)) (|HasAttribute| (-699) (QUOTE -4410)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) (-695 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}."))) ((-4415 . T)) @@ -2720,13 +2720,13 @@ 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 -(-698 OV E -2386 PG) +(-698 OV E -2371 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 (-699) ((|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}"))) -((-3651 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) +((-3628 . T) (-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-700 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."))) @@ -2752,7 +2752,7 @@ 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 -(-706 S -2876 I) +(-706 S -2875 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 @@ -2772,14 +2772,14 @@ 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 -(-711 R |Mod| -3418 -3891 |exactQuo|) +(-711 R |Mod| -3646 -3298 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-712 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4410 |has| |#1| (-365)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-713 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2788,7 +2788,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4409 |has| |#1| (-172)) (-4408 |has| |#1| (-172)) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-715 R |Mod| -3418 -3891 |exactQuo|) +(-715 R |Mod| -3646 -3298 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4411 . T)) NIL @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4409 . T) (-4408 . T)) NIL -(-718 -2386) +(-718 -2371) ((|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]]}."))) ((-4411 . T)) NIL @@ -2836,7 +2836,7 @@ 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 -(-727 -2386 UP) +(-727 -2371 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 @@ -2855,7 +2855,7 @@ NIL (-731 |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."))) (((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-909))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-864 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-732 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 @@ -2988,11 +2988,11 @@ 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 -(-765 -2386) +(-765 -2371) ((|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 -(-766 P -2386) +(-766 P -2371) ((|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 @@ -3000,7 +3000,7 @@ NIL NIL NIL NIL -(-768 UP -2386) +(-768 UP -2371) ((|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{\\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{\\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{\\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{\\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{\\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{\\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 @@ -3016,7 +3016,7 @@ 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."))) (((-4416 "*") . T)) NIL -(-772 R -2386) +(-772 R -2371) ((|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 @@ -3036,7 +3036,7 @@ 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 -(-777 -2386 |ExtF| |SUEx| |ExtP| |n|) +(-777 -2371 |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 @@ -3051,7 +3051,7 @@ NIL (-780 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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . 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|#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175))))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-2418 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-2418 (|HasCategory| |#1| (QUOTE (-547)))) (-2418 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-2418 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-566))))) (-2418 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-2418 (|HasCategory| |#1| (LIST (QUOTE -992) (QUOTE (-566))))))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-781 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 @@ -3059,7 +3059,7 @@ NIL (-782 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)}"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4410 |has| |#1| (-365)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-783 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 @@ -3120,23 +3120,23 @@ 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,{}\\spad{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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4408 . T) (-4409 . T) (-4411 . T)) NIL -(-798 -2805 R OS S) +(-798 -2809 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-799 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2805 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -287) (|devaluate| |#1|) (|devaluate| |#1|))) (-2809 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2809 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (-800) ((|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 -(-801 R -2386 L) +(-801 R -2371 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{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-802 R -2386) +(-802 R -2371) ((|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 @@ -3144,7 +3144,7 @@ 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 -(-804 R -2386) +(-804 R -2371) ((|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 @@ -3152,11 +3152,11 @@ 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 -(-806 -2386 UP UPUP R) +(-806 -2371 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 -(-807 -2386 UP L LQ) +(-807 -2371 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 @@ -3164,38 +3164,38 @@ 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 -(-809 -2386 UP L LQ) +(-809 -2371 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^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{\\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{\\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 \\spad{ai}}} is \\spad{\\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 -(-810 -2386 UP) +(-810 -2371 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 -(-811 -2386 L UP A LO) +(-811 -2371 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 -(-812 -2386 UP) +(-812 -2371 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{\\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 \\spad{ai}}} is \\spad{\\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)))) -(-813 -2386 LO) +(-813 -2371 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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|#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4411)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))))) (-816 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"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-818 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-817 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4416 "*") |has| |#2| (-365)) (-4407 |has| |#2| (-365)) (-4412 |has| |#2| (-365)) (-4406 |has| |#2| (-365)) (-4411 . T) (-4409 . T) (-4408 . T)) @@ -3263,7 +3263,7 @@ NIL (-833 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."))) ((-4411 |has| |#1| (-848))) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) +((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2809 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2809 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-834 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 @@ -3303,12 +3303,12 @@ NIL (-843 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4411 |has| |#1| (-848))) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) +((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2809 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2809 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-844) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-845 -4225 S) +(-845 -2420 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 @@ -3344,11 +3344,11 @@ 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 (-558)))) -(-854 R |sigma| -1545) +(-854 R |sigma| -1695) ((|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."))) ((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-365)))) -(-855 |x| R |sigma| -1545) +(-855 |x| R |sigma| -1695) ((|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}."))) ((-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-365)))) @@ -3415,15 +3415,15 @@ NIL (-871 |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)."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-870 |#1|) (QUOTE (-909))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-147))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-870 |#1|) (QUOTE (-1022))) (|HasCategory| (-870 |#1|) (QUOTE (-820))) (-2805 (|HasCategory| (-870 |#1|) (QUOTE (-820))) (|HasCategory| (-870 |#1|) (QUOTE (-850)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-1150))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-233))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-308))) (|HasCategory| (-870 |#1|) (QUOTE (-547))) (|HasCategory| (-870 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))))) +((|HasCategory| (-870 |#1|) (QUOTE (-909))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-147))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-870 |#1|) (QUOTE (-1022))) (|HasCategory| (-870 |#1|) (QUOTE (-820))) (-2809 (|HasCategory| (-870 |#1|) (QUOTE (-820))) (|HasCategory| (-870 |#1|) (QUOTE (-850)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-1150))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-870 |#1|) (QUOTE (-233))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -310) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (LIST (QUOTE -287) (LIST (QUOTE -870) (|devaluate| |#1|)) (LIST (QUOTE -870) (|devaluate| |#1|)))) (|HasCategory| (-870 |#1|) (QUOTE (-308))) (|HasCategory| (-870 |#1|) (QUOTE (-547))) (|HasCategory| (-870 |#1|) (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-870 |#1|) (QUOTE (-909)))) (|HasCategory| (-870 |#1|) (QUOTE (-145))))) (-872 |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)}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (-2805 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 (-547))) (|HasCategory| |#2| (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-1022))) (|HasCategory| |#2| (QUOTE (-820))) (-2809 (|HasCategory| |#2| (QUOTE (-820))) (|HasCategory| |#2| (QUOTE (-850)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 (-547))) (|HasCategory| |#2| (QUOTE (-850))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-873 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 (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))))) (-874) ((|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 @@ -3479,7 +3479,7 @@ NIL (-887 |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 (-2436 (|HasCategory| |#2| (QUOTE (-1049)))) (-2436 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2436 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) +((-12 (-2418 (|HasCategory| |#2| (QUOTE (-1049)))) (-2418 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2418 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) (-888 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 @@ -3488,7 +3488,7 @@ 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 -(-890 R -2876) +(-890 R -2875) ((|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 @@ -3512,7 +3512,7 @@ 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 -(-896 UP -2386) +(-896 UP -2371) ((|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 @@ -3535,7 +3535,7 @@ NIL (-901 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 (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-902 |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 @@ -3551,7 +3551,7 @@ NIL (-905 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."))) ((-4411 . T)) -((-2805 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) +((-2809 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (-906 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 \\spad{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 @@ -3572,7 +3572,7 @@ 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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-911 R0 -2386 UP UPUP R) +(-911 R0 -2371 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 @@ -3600,7 +3600,7 @@ 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(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{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(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{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 \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{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(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{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 -(-918 -2386) +(-918 -2371) ((|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 @@ -3616,11 +3616,11 @@ 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}."))) (((-4416 "*") . T)) NIL -(-922 -2386 P) +(-922 -2371 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-923 |xx| -2386) +(-923 |xx| -2371) ((|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 @@ -3644,7 +3644,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-929 R -2386) +(-929 R -2371) ((|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 @@ -3656,7 +3656,7 @@ 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 -(-932 S R -2386) +(-932 S R -2371) ((|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 @@ -3676,11 +3676,11 @@ 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 -886) (|devaluate| |#1|)))) -(-937 R -2386 -2876) +(-937 R -2371 -2875) ((|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 -(-938 -2876) +(-938 -2875) ((|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 @@ -3703,7 +3703,7 @@ NIL (-943 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-944 |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 @@ -3728,7 +3728,7 @@ 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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL -(-950 E V R P -2386) +(-950 E V R P -2371) ((|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 @@ -3739,8 +3739,8 @@ NIL (-952 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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-953 E V R P -2386) +((|HasCategory| |#1| (QUOTE (-909))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1175) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-953 E V R P -2371) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-454)))) @@ -3763,12 +3763,12 @@ NIL (-958 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-959) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-960 -2386) +(-960 -2371) ((|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{\\spad{ai} = \\spad{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{\\spad{ai} = \\spad{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 @@ -3783,11 +3783,11 @@ NIL (-963 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}"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4412))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4412))) (-964 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"))) ((-4411 -12 (|has| |#2| (-475)) (|has| |#1| (-475)))) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2805 (-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 (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2805 (-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 (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2809 (-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 (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726))))) (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-370)))) (-2809 (-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 (-475))) (|HasCategory| |#2| (QUOTE (-475)))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-793))) (|HasCategory| |#2| (QUOTE (-793))))) (-12 (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#2| (QUOTE (-726)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-850))))) (-965) ((|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 @@ -3868,7 +3868,7 @@ 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 -(-985 K R UP -2386) +(-985 K R UP -2371) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3927,11 +3927,11 @@ NIL (-999 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.}"))) ((-4407 |has| |#1| (-291)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 -900) (QUOTE (-1175)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2809 (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-291))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -516) (QUOTE (-1175)) (|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 -900) (QUOTE (-1175)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-1059))) (|HasCategory| |#1| (QUOTE (-547)))) (-1000 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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1001 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3940,14 +3940,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1003 -2386 UP UPUP |radicnd| |n|) +(-1003 -2371 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4407 |has| (-409 |#2|) (-365)) (-4412 |has| (-409 |#2|) (-365)) (-4406 |has| (-409 |#2|) (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2805 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2805 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2805 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) +((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2809 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2809 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2809 (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-351))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -639) (QUOTE (-566)))) (-2809 (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 |#2|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-12 (|HasCategory| (-409 |#2|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365))))) (-1004 |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."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2805 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) +((|HasCategory| (-566) (QUOTE (-909))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-566) (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-147))) (|HasCategory| (-566) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-1022))) (|HasCategory| (-566) (QUOTE (-820))) (-2809 (|HasCategory| (-566) (QUOTE (-820))) (|HasCategory| (-566) (QUOTE (-850)))) (|HasCategory| (-566) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-1150))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-566) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-566) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-566) (QUOTE (-233))) (|HasCategory| (-566) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-566) (LIST (QUOTE -516) (QUOTE (-1175)) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -310) (QUOTE (-566)))) (|HasCategory| (-566) (LIST (QUOTE -287) (QUOTE (-566)) (QUOTE (-566)))) (|HasCategory| (-566) (QUOTE (-308))) (|HasCategory| (-566) (QUOTE (-547))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-566) (LIST (QUOTE -639) (QUOTE (-566)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-566) (QUOTE (-909)))) (|HasCategory| (-566) (QUOTE (-145))))) (-1005) ((|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 @@ -3980,19 +3980,19 @@ 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}}"))) ((-4407 . T) (-4412 . T) (-4406 . T) (-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4411 . T)) NIL -(-1013 R -2386) +(-1013 R -2371) ((|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 -(-1014 R -2386) +(-1014 R -2371) ((|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 -(-1015 -2386 UP) +(-1015 -2371 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 -(-1016 -2386 UP) +(-1016 -2371 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 @@ -4027,8 +4027,8 @@ NIL (-1024 |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"))) ((-4407 . T) (-4412 . T) (-4406 . T) (-4409 . T) (-4408 . T) ((-4416 "*") . T) (-4411 . T)) -((-2805 (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566))))) -(-1025 -2386 L) +((-2809 (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-409 (-566)) (LIST (QUOTE -1038) (QUOTE (-566))))) +(-1025 -2371 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{\\spad{fi}} must satisfy \\spad{op \\spad{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 @@ -4064,14 +4064,14 @@ 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 -(-1034 -2386 |Expon| |VarSet| |FPol| |LFPol|) +(-1034 -2371 |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"))) (((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL (-1035) ((|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.}"))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -3867) (QUOTE (-52))))))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1036) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4128,7 +4128,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4411 . T)) NIL -(-1050 |xx| -2386) +(-1050 |xx| -2371) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4147,7 +4147,7 @@ NIL (-1054 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4414 . T) (-4409 . T) (-4408 . T)) -((|HasCategory| |#3| (QUOTE (-172))) (-2805 (-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 (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-558))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862))))) +((|HasCategory| |#3| (QUOTE (-172))) (-2809 (-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 (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-365)))) (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (QUOTE (-308))) (|HasCategory| |#3| (QUOTE (-558))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862))))) (-1055 |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 @@ -4179,7 +4179,7 @@ NIL (-1062) ((|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}"))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2849) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -3867) (QUOTE (-52))))))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1063 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 @@ -4228,11 +4228,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1075 |Base| R -2386) +(-1075 |Base| R -2371) ((|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 -(-1076 |Base| R -2386) +(-1076 |Base| R -2371) ((|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 @@ -4247,7 +4247,7 @@ NIL (-1079 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."))) ((-4407 |has| |#1| (-365)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365))))) (-1080 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 @@ -4275,7 +4275,7 @@ NIL (-1086 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"))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1087 (-1175)) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1087 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 @@ -4335,7 +4335,7 @@ NIL (-1101 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)}}"))) ((-4414 . T) (-4404 . T) (-4415 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1102 |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{\\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 @@ -4379,7 +4379,7 @@ NIL (-1112 |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}."))) 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(QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-848))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2809 (|HasCategory| |#3| (QUOTE (-1049))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#3| (QUOTE (-1099)))) (|HasAttribute| |#3| (QUOTE -4411)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#3| (QUOTE (-1099))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|))))) (-1113 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 @@ -4388,7 +4388,7 @@ 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 -(-1115 R -2386) +(-1115 R -2371) ((|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 @@ -4427,16 +4427,16 @@ NIL (-1124 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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-909))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-365))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1125 |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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) (-1126 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}"))) ((-4415 . T) (-4414 . T)) NIL -(-1127 UP -2386) +(-1127 UP -2371) ((|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 @@ -4491,11 +4491,11 @@ NIL (-1140 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2805 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2809 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) (-1141 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4411 . T) (-4403 |has| |#2| (-6 (-4416 "*"))) (-4414 . T) (-4408 . T) (-4409 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (-2805 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (QUOTE (-308))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-365))) (-2809 (|HasAttribute| |#2| (QUOTE (-4416 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1142 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4515,7 +4515,7 @@ NIL (-1146 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1147 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 @@ -4527,7 +4527,7 @@ NIL (-1149 |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."))) ((-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099)))) (-1150) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4551,7 +4551,7 @@ NIL (-1155 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."))) ((-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1156) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4415 . T) (-4414 . T)) @@ -4559,11 +4559,11 @@ NIL (-1157) NIL ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) +((-2809 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-1158 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#1|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#1|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-1159 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 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,{}\\spad{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 @@ -4594,9 +4594,9 @@ NIL NIL (-1166 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4416 "*") -2805 (-2447 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-820))) (|has| |#1| (-172)) (-2447 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-909)))) (-4407 -2805 (-2447 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-820))) (|has| |#1| (-558)) (-2447 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-909)))) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . 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(|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-1150))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4412)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1172 |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,{}} 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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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . 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(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}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2805 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| (-971) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasAttribute| |#1| (QUOTE -4412))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2809 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| (-971) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasAttribute| |#1| (QUOTE -4412))) (-1178) ((|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 @@ -4679,7 +4679,7 @@ NIL (-1187 |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}"))) ((-4414 . T) (-4415 . T)) -((-12 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2050) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2849) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2004) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3867) (|devaluate| |#2|)))))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2809 (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-1188 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{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4731,7 +4731,7 @@ NIL (-1200 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4415 . T) (-4414 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1201 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4740,7 +4740,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1203 R -2386) +(-1203 R -2371) ((|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 @@ -4748,7 +4748,7 @@ 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 -(-1205 R -2386) +(-1205 R -2371) ((|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 -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -886) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -886) (|devaluate| |#1|))))) @@ -4763,7 +4763,7 @@ NIL (-1208 |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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) (-1209 |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 @@ -4776,7 +4776,7 @@ 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 (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) -(-1212 -2386) +(-1212 -2371) ((|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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(LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2809 (-12 (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-365)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| (-1256 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1229 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4879,7 +4879,7 @@ NIL (-1237 |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}"))) (((-4416 "*") |has| |#2| (-172)) (-4407 |has| |#2| (-558)) (-4410 |has| |#2| (-365)) (-4412 |has| |#2| (-6 -4412)) (-4409 . T) (-4408 . T) (-4411 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2805 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-558)))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-381))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -886) (QUOTE (-566))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566)))))) (-12 (|HasCategory| (-1081) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2809 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2809 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-1150))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4412)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2809 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1238 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 @@ -4895,7 +4895,7 @@ NIL (-1241 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 -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3780) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) +((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1111))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3783) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) (-1242 |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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) @@ -4923,15 +4923,15 @@ NIL (-1248 |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)}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) +((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -1941) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3863) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-1249 |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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4412 |has| |#1| (-365)) (-4406 |has| |#1| (-365)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566))) (|devaluate| |#1|)))) (|HasCategory| (-409 (-566)) (QUOTE (-1111))) (|HasCategory| |#1| (QUOTE (-365))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2809 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -1941) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3863) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1250 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))}."))) (((-4416 "*") |has| (-1249 |#2| |#3| |#4|) (-172)) (-4407 |has| (-1249 |#2| |#3| |#4|) (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-172))) (-2805 (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-558)))) +((|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-172))) (-2809 (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1249 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1249 |#2| |#3| |#4|) (QUOTE (-558)))) (-1251 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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4947,7 +4947,7 @@ NIL (-1254 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3921) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#2| (QUOTE (-959))) (|HasCategory| |#2| (QUOTE (-1199))) (|HasSignature| |#2| (LIST (QUOTE -3863) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1941) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) (-1255 |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."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) @@ -4955,12 +4955,12 @@ NIL (-1256 |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}."))) (((-4416 "*") |has| |#1| (-172)) (-4407 |has| |#1| (-558)) (-4408 . T) (-4409 . T) (-4411 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2805 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -3780) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2805 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -3921) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2608) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2809 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-771)) (|devaluate| |#1|)))) (|HasCategory| (-771) (QUOTE (-1111))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasSignature| |#1| (LIST (QUOTE -3783) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2809 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1199))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasSignature| |#1| (LIST (QUOTE -1941) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3863) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1257 |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 -(-1258 -2386 UP L UTS) +(-1258 -2371 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 (-558)))) @@ -4987,7 +4987,7 @@ NIL (-1264 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."))) ((-4415 . T) (-4414 . T)) -((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2809 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2809 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2809 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-726))) (|HasCategory| |#1| (QUOTE (-1049))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1049)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-1265) ((|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,{}\\spad{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{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\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(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\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 @@ -5020,7 +5020,7 @@ 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 -(-1273 K R UP -2386) +(-1273 K R UP -2371) ((|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{\\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{\\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{\\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{\\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{\\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{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5056,11 +5056,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4407 |has| |#2| (-6 -4407)) (-4409 . T) (-4408 . T) (-4411 . T)) NIL -(-1282 S -2386) +(-1282 S -2371) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1283 -2386) +(-1283 -2371) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4406 . T) (-4412 . T) (-4407 . T) ((-4416 "*") . T) (-4408 . T) (-4409 . T) (-4411 . T)) NIL @@ -5116,4 +5116,4 @@ NIL NIL NIL NIL -((-3 NIL 2284962 2284967 2284972 2284977) (-2 NIL 2284942 2284947 2284952 2284957) (-1 NIL 2284922 2284927 2284932 2284937) (0 NIL 2284902 2284907 2284912 2284917) (-1292 "ZMOD.spad" 2284711 2284724 2284840 2284897) (-1291 "ZLINDEP.spad" 2283755 2283766 2284701 2284706) (-1290 "ZDSOLVE.spad" 2273604 2273626 2283745 2283750) (-1289 "YSTREAM.spad" 2273097 2273108 2273594 2273599) (-1288 "XRPOLY.spad" 2272317 2272337 2272953 2273022) (-1287 "XPR.spad" 2270108 2270121 2272035 2272134) (-1286 "XPOLY.spad" 2269663 2269674 2269964 2270033) (-1285 "XPOLYC.spad" 2268980 2268996 2269589 2269658) (-1284 "XPBWPOLY.spad" 2267417 2267437 2268760 2268829) (-1283 "XF.spad" 2265878 2265893 2267319 2267412) (-1282 "XF.spad" 2264319 2264336 2265762 2265767) (-1281 "XFALG.spad" 2261343 2261359 2264245 2264314) (-1280 "XEXPPKG.spad" 2260594 2260620 2261333 2261338) (-1279 "XDPOLY.spad" 2260208 2260224 2260450 2260519) (-1278 "XALG.spad" 2259868 2259879 2260164 2260203) (-1277 "WUTSET.spad" 2255707 2255724 2259514 2259541) (-1276 "WP.spad" 2254906 2254950 2255565 2255632) (-1275 "WHILEAST.spad" 2254704 2254713 2254896 2254901) (-1274 "WHEREAST.spad" 2254375 2254384 2254694 2254699) (-1273 "WFFINTBS.spad" 2251938 2251960 2254365 2254370) (-1272 "WEIER.spad" 2250152 2250163 2251928 2251933) (-1271 "VSPACE.spad" 2249825 2249836 2250120 2250147) (-1270 "VSPACE.spad" 2249518 2249531 2249815 2249820) (-1269 "VOID.spad" 2249195 2249204 2249508 2249513) (-1268 "VIEW.spad" 2246817 2246826 2249185 2249190) (-1267 "VIEWDEF.spad" 2242014 2242023 2246807 2246812) (-1266 "VIEW3D.spad" 2225849 2225858 2242004 2242009) (-1265 "VIEW2D.spad" 2213586 2213595 2225839 2225844) (-1264 "VECTOR.spad" 2212260 2212271 2212511 2212538) (-1263 "VECTOR2.spad" 2210887 2210900 2212250 2212255) (-1262 "VECTCAT.spad" 2208787 2208798 2210855 2210882) (-1261 "VECTCAT.spad" 2206494 2206507 2208564 2208569) (-1260 "VARIABLE.spad" 2206274 2206289 2206484 2206489) (-1259 "UTYPE.spad" 2205918 2205927 2206264 2206269) (-1258 "UTSODETL.spad" 2205211 2205235 2205874 2205879) (-1257 "UTSODE.spad" 2203399 2203419 2205201 2205206) (-1256 "UTS.spad" 2198188 2198216 2201866 2201963) (-1255 "UTSCAT.spad" 2195639 2195655 2198086 2198183) (-1254 "UTSCAT.spad" 2192734 2192752 2195183 2195188) (-1253 "UTS2.spad" 2192327 2192362 2192724 2192729) (-1252 "URAGG.spad" 2186960 2186971 2192317 2192322) (-1251 "URAGG.spad" 2181557 2181570 2186916 2186921) (-1250 "UPXSSING.spad" 2179200 2179226 2180638 2180771) (-1249 "UPXS.spad" 2176348 2176376 2177332 2177481) (-1248 "UPXSCONS.spad" 2174105 2174125 2174480 2174629) (-1247 "UPXSCCA.spad" 2172670 2172690 2173951 2174100) (-1246 "UPXSCCA.spad" 2171377 2171399 2172660 2172665) (-1245 "UPXSCAT.spad" 2169958 2169974 2171223 2171372) (-1244 "UPXS2.spad" 2169499 2169552 2169948 2169953) (-1243 "UPSQFREE.spad" 2167911 2167925 2169489 2169494) (-1242 "UPSCAT.spad" 2165504 2165528 2167809 2167906) (-1241 "UPSCAT.spad" 2162803 2162829 2165110 2165115) (-1240 "UPOLYC.spad" 2157781 2157792 2162645 2162798) (-1239 "UPOLYC.spad" 2152651 2152664 2157517 2157522) (-1238 "UPOLYC2.spad" 2152120 2152139 2152641 2152646) (-1237 "UP.spad" 2149313 2149328 2149706 2149859) (-1236 "UPMP.spad" 2148203 2148216 2149303 2149308) (-1235 "UPDIVP.spad" 2147766 2147780 2148193 2148198) (-1234 "UPDECOMP.spad" 2146003 2146017 2147756 2147761) (-1233 "UPCDEN.spad" 2145210 2145226 2145993 2145998) (-1232 "UP2.spad" 2144572 2144593 2145200 2145205) (-1231 "UNISEG.spad" 2143925 2143936 2144491 2144496) (-1230 "UNISEG2.spad" 2143418 2143431 2143881 2143886) (-1229 "UNIFACT.spad" 2142519 2142531 2143408 2143413) (-1228 "ULS.spad" 2133071 2133099 2134164 2134593) (-1227 "ULSCONS.spad" 2125465 2125485 2125837 2125986) (-1226 "ULSCCAT.spad" 2123194 2123214 2125311 2125460) (-1225 "ULSCCAT.spad" 2121031 2121053 2123150 2123155) (-1224 "ULSCAT.spad" 2119247 2119263 2120877 2121026) (-1223 "ULS2.spad" 2118759 2118812 2119237 2119242) (-1222 "UINT8.spad" 2118636 2118645 2118749 2118754) (-1221 "UINT64.spad" 2118512 2118521 2118626 2118631) (-1220 "UINT32.spad" 2118388 2118397 2118502 2118507) (-1219 "UINT16.spad" 2118264 2118273 2118378 2118383) (-1218 "UFD.spad" 2117329 2117338 2118190 2118259) (-1217 "UFD.spad" 2116456 2116467 2117319 2117324) (-1216 "UDVO.spad" 2115303 2115312 2116446 2116451) (-1215 "UDPO.spad" 2112730 2112741 2115259 2115264) (-1214 "TYPE.spad" 2112662 2112671 2112720 2112725) (-1213 "TYPEAST.spad" 2112581 2112590 2112652 2112657) (-1212 "TWOFACT.spad" 2111231 2111246 2112571 2112576) (-1211 "TUPLE.spad" 2110715 2110726 2111130 2111135) (-1210 "TUBETOOL.spad" 2107552 2107561 2110705 2110710) (-1209 "TUBE.spad" 2106193 2106210 2107542 2107547) (-1208 "TS.spad" 2104782 2104798 2105758 2105855) (-1207 "TSETCAT.spad" 2091909 2091926 2104750 2104777) (-1206 "TSETCAT.spad" 2079022 2079041 2091865 2091870) (-1205 "TRMANIP.spad" 2073388 2073405 2078728 2078733) (-1204 "TRIMAT.spad" 2072347 2072372 2073378 2073383) (-1203 "TRIGMNIP.spad" 2070864 2070881 2072337 2072342) (-1202 "TRIGCAT.spad" 2070376 2070385 2070854 2070859) (-1201 "TRIGCAT.spad" 2069886 2069897 2070366 2070371) (-1200 "TREE.spad" 2068457 2068468 2069493 2069520) (-1199 "TRANFUN.spad" 2068288 2068297 2068447 2068452) (-1198 "TRANFUN.spad" 2068117 2068128 2068278 2068283) (-1197 "TOPSP.spad" 2067791 2067800 2068107 2068112) (-1196 "TOOLSIGN.spad" 2067454 2067465 2067781 2067786) (-1195 "TEXTFILE.spad" 2066011 2066020 2067444 2067449) (-1194 "TEX.spad" 2063143 2063152 2066001 2066006) (-1193 "TEX1.spad" 2062699 2062710 2063133 2063138) (-1192 "TEMUTL.spad" 2062254 2062263 2062689 2062694) (-1191 "TBCMPPK.spad" 2060347 2060370 2062244 2062249) (-1190 "TBAGG.spad" 2059383 2059406 2060327 2060342) (-1189 "TBAGG.spad" 2058427 2058452 2059373 2059378) (-1188 "TANEXP.spad" 2057803 2057814 2058417 2058422) (-1187 "TABLE.spad" 2056214 2056237 2056484 2056511) (-1186 "TABLEAU.spad" 2055695 2055706 2056204 2056209) (-1185 "TABLBUMP.spad" 2052478 2052489 2055685 2055690) (-1184 "SYSTEM.spad" 2051706 2051715 2052468 2052473) (-1183 "SYSSOLP.spad" 2049179 2049190 2051696 2051701) (-1182 "SYSNNI.spad" 2048359 2048370 2049169 2049174) (-1181 "SYSINT.spad" 2047763 2047774 2048349 2048354) (-1180 "SYNTAX.spad" 2043957 2043966 2047753 2047758) (-1179 "SYMTAB.spad" 2042013 2042022 2043947 2043952) (-1178 "SYMS.spad" 2037998 2038007 2042003 2042008) (-1177 "SYMPOLY.spad" 2037005 2037016 2037087 2037214) (-1176 "SYMFUNC.spad" 2036480 2036491 2036995 2037000) (-1175 "SYMBOL.spad" 2033907 2033916 2036470 2036475) (-1174 "SWITCH.spad" 2030664 2030673 2033897 2033902) (-1173 "SUTS.spad" 2027563 2027591 2029131 2029228) (-1172 "SUPXS.spad" 2024698 2024726 2025695 2025844) (-1171 "SUP.spad" 2021503 2021514 2022284 2022437) (-1170 "SUPFRACF.spad" 2020608 2020626 2021493 2021498) (-1169 "SUP2.spad" 2019998 2020011 2020598 2020603) (-1168 "SUMRF.spad" 2018964 2018975 2019988 2019993) (-1167 "SUMFS.spad" 2018597 2018614 2018954 2018959) (-1166 "SULS.spad" 2009136 2009164 2010242 2010671) (-1165 "SUCHTAST.spad" 2008905 2008914 2009126 2009131) (-1164 "SUCH.spad" 2008585 2008600 2008895 2008900) (-1163 "SUBSPACE.spad" 2000592 2000607 2008575 2008580) (-1162 "SUBRESP.spad" 1999752 1999766 2000548 2000553) (-1161 "STTF.spad" 1995851 1995867 1999742 1999747) (-1160 "STTFNC.spad" 1992319 1992335 1995841 1995846) (-1159 "STTAYLOR.spad" 1984717 1984728 1992200 1992205) (-1158 "STRTBL.spad" 1983222 1983239 1983371 1983398) (-1157 "STRING.spad" 1982631 1982640 1982645 1982672) (-1156 "STRICAT.spad" 1982419 1982428 1982599 1982626) (-1155 "STREAM.spad" 1979277 1979288 1981944 1981959) (-1154 "STREAM3.spad" 1978822 1978837 1979267 1979272) (-1153 "STREAM2.spad" 1977890 1977903 1978812 1978817) (-1152 "STREAM1.spad" 1977594 1977605 1977880 1977885) (-1151 "STINPROD.spad" 1976500 1976516 1977584 1977589) (-1150 "STEP.spad" 1975701 1975710 1976490 1976495) (-1149 "STBL.spad" 1974227 1974255 1974394 1974409) (-1148 "STAGG.spad" 1973302 1973313 1974217 1974222) (-1147 "STAGG.spad" 1972375 1972388 1973292 1973297) (-1146 "STACK.spad" 1971726 1971737 1971982 1972009) (-1145 "SREGSET.spad" 1969430 1969447 1971372 1971399) (-1144 "SRDCMPK.spad" 1967975 1967995 1969420 1969425) (-1143 "SRAGG.spad" 1963072 1963081 1967943 1967970) (-1142 "SRAGG.spad" 1958189 1958200 1963062 1963067) (-1141 "SQMATRIX.spad" 1955805 1955823 1956721 1956808) (-1140 "SPLTREE.spad" 1950357 1950370 1955241 1955268) (-1139 "SPLNODE.spad" 1946945 1946958 1950347 1950352) (-1138 "SPFCAT.spad" 1945722 1945731 1946935 1946940) (-1137 "SPECOUT.spad" 1944272 1944281 1945712 1945717) (-1136 "SPADXPT.spad" 1936411 1936420 1944262 1944267) (-1135 "spad-parser.spad" 1935876 1935885 1936401 1936406) (-1134 "SPADAST.spad" 1935577 1935586 1935866 1935871) (-1133 "SPACEC.spad" 1919590 1919601 1935567 1935572) (-1132 "SPACE3.spad" 1919366 1919377 1919580 1919585) (-1131 "SORTPAK.spad" 1918911 1918924 1919322 1919327) (-1130 "SOLVETRA.spad" 1916668 1916679 1918901 1918906) (-1129 "SOLVESER.spad" 1915188 1915199 1916658 1916663) (-1128 "SOLVERAD.spad" 1911198 1911209 1915178 1915183) (-1127 "SOLVEFOR.spad" 1909618 1909636 1911188 1911193) (-1126 "SNTSCAT.spad" 1909218 1909235 1909586 1909613) (-1125 "SMTS.spad" 1907478 1907504 1908783 1908880) (-1124 "SMP.spad" 1904953 1904973 1905343 1905470) (-1123 "SMITH.spad" 1903796 1903821 1904943 1904948) (-1122 "SMATCAT.spad" 1901906 1901936 1903740 1903791) (-1121 "SMATCAT.spad" 1899948 1899980 1901784 1901789) (-1120 "SKAGG.spad" 1898909 1898920 1899916 1899943) (-1119 "SINT.spad" 1897735 1897744 1898775 1898904) (-1118 "SIMPAN.spad" 1897463 1897472 1897725 1897730) (-1117 "SIG.spad" 1896791 1896800 1897453 1897458) (-1116 "SIGNRF.spad" 1895899 1895910 1896781 1896786) (-1115 "SIGNEF.spad" 1895168 1895185 1895889 1895894) (-1114 "SIGAST.spad" 1894549 1894558 1895158 1895163) (-1113 "SHP.spad" 1892467 1892482 1894505 1894510) (-1112 "SHDP.spad" 1882178 1882205 1882687 1882818) (-1111 "SGROUP.spad" 1881786 1881795 1882168 1882173) (-1110 "SGROUP.spad" 1881392 1881403 1881776 1881781) (-1109 "SGCF.spad" 1874273 1874282 1881382 1881387) (-1108 "SFRTCAT.spad" 1873201 1873218 1874241 1874268) (-1107 "SFRGCD.spad" 1872264 1872284 1873191 1873196) (-1106 "SFQCMPK.spad" 1866901 1866921 1872254 1872259) (-1105 "SFORT.spad" 1866336 1866350 1866891 1866896) (-1104 "SEXOF.spad" 1866179 1866219 1866326 1866331) (-1103 "SEX.spad" 1866071 1866080 1866169 1866174) (-1102 "SEXCAT.spad" 1863622 1863662 1866061 1866066) (-1101 "SET.spad" 1861922 1861933 1863043 1863082) (-1100 "SETMN.spad" 1860356 1860373 1861912 1861917) (-1099 "SETCAT.spad" 1859678 1859687 1860346 1860351) (-1098 "SETCAT.spad" 1858998 1859009 1859668 1859673) (-1097 "SETAGG.spad" 1855519 1855530 1858978 1858993) (-1096 "SETAGG.spad" 1852048 1852061 1855509 1855514) (-1095 "SEQAST.spad" 1851751 1851760 1852038 1852043) (-1094 "SEGXCAT.spad" 1850873 1850886 1851741 1851746) (-1093 "SEG.spad" 1850686 1850697 1850792 1850797) (-1092 "SEGCAT.spad" 1849593 1849604 1850676 1850681) (-1091 "SEGBIND.spad" 1848665 1848676 1849548 1849553) (-1090 "SEGBIND2.spad" 1848361 1848374 1848655 1848660) (-1089 "SEGAST.spad" 1848075 1848084 1848351 1848356) (-1088 "SEG2.spad" 1847500 1847513 1848031 1848036) (-1087 "SDVAR.spad" 1846776 1846787 1847490 1847495) (-1086 "SDPOL.spad" 1844202 1844213 1844493 1844620) (-1085 "SCPKG.spad" 1842281 1842292 1844192 1844197) (-1084 "SCOPE.spad" 1841430 1841439 1842271 1842276) (-1083 "SCACHE.spad" 1840112 1840123 1841420 1841425) (-1082 "SASTCAT.spad" 1840021 1840030 1840102 1840107) (-1081 "SAOS.spad" 1839893 1839902 1840011 1840016) (-1080 "SAERFFC.spad" 1839606 1839626 1839883 1839888) (-1079 "SAE.spad" 1837781 1837797 1838392 1838527) (-1078 "SAEFACT.spad" 1837482 1837502 1837771 1837776) (-1077 "RURPK.spad" 1835123 1835139 1837472 1837477) (-1076 "RULESET.spad" 1834564 1834588 1835113 1835118) (-1075 "RULE.spad" 1832768 1832792 1834554 1834559) (-1074 "RULECOLD.spad" 1832620 1832633 1832758 1832763) (-1073 "RTVALUE.spad" 1832353 1832362 1832610 1832615) (-1072 "RSTRCAST.spad" 1832070 1832079 1832343 1832348) (-1071 "RSETGCD.spad" 1828448 1828468 1832060 1832065) (-1070 "RSETCAT.spad" 1818232 1818249 1828416 1828443) (-1069 "RSETCAT.spad" 1808036 1808055 1818222 1818227) (-1068 "RSDCMPK.spad" 1806488 1806508 1808026 1808031) (-1067 "RRCC.spad" 1804872 1804902 1806478 1806483) (-1066 "RRCC.spad" 1803254 1803286 1804862 1804867) (-1065 "RPTAST.spad" 1802956 1802965 1803244 1803249) (-1064 "RPOLCAT.spad" 1782316 1782331 1802824 1802951) (-1063 "RPOLCAT.spad" 1761390 1761407 1781900 1781905) (-1062 "ROUTINE.spad" 1757253 1757262 1760037 1760064) (-1061 "ROMAN.spad" 1756581 1756590 1757119 1757248) (-1060 "ROIRC.spad" 1755661 1755693 1756571 1756576) (-1059 "RNS.spad" 1754564 1754573 1755563 1755656) (-1058 "RNS.spad" 1753553 1753564 1754554 1754559) (-1057 "RNG.spad" 1753288 1753297 1753543 1753548) (-1056 "RMODULE.spad" 1753053 1753064 1753278 1753283) (-1055 "RMCAT2.spad" 1752461 1752518 1753043 1753048) (-1054 "RMATRIX.spad" 1751285 1751304 1751628 1751667) (-1053 "RMATCAT.spad" 1746818 1746849 1751241 1751280) (-1052 "RMATCAT.spad" 1742241 1742274 1746666 1746671) (-1051 "RLINSET.spad" 1741635 1741646 1742231 1742236) (-1050 "RINTERP.spad" 1741523 1741543 1741625 1741630) (-1049 "RING.spad" 1740993 1741002 1741503 1741518) (-1048 "RING.spad" 1740471 1740482 1740983 1740988) (-1047 "RIDIST.spad" 1739855 1739864 1740461 1740466) (-1046 "RGCHAIN.spad" 1738434 1738450 1739340 1739367) (-1045 "RGBCSPC.spad" 1738215 1738227 1738424 1738429) (-1044 "RGBCMDL.spad" 1737745 1737757 1738205 1738210) (-1043 "RF.spad" 1735359 1735370 1737735 1737740) (-1042 "RFFACTOR.spad" 1734821 1734832 1735349 1735354) (-1041 "RFFACT.spad" 1734556 1734568 1734811 1734816) (-1040 "RFDIST.spad" 1733544 1733553 1734546 1734551) (-1039 "RETSOL.spad" 1732961 1732974 1733534 1733539) (-1038 "RETRACT.spad" 1732389 1732400 1732951 1732956) (-1037 "RETRACT.spad" 1731815 1731828 1732379 1732384) (-1036 "RETAST.spad" 1731627 1731636 1731805 1731810) (-1035 "RESULT.spad" 1729687 1729696 1730274 1730301) (-1034 "RESRING.spad" 1729034 1729081 1729625 1729682) (-1033 "RESLATC.spad" 1728358 1728369 1729024 1729029) (-1032 "REPSQ.spad" 1728087 1728098 1728348 1728353) (-1031 "REP.spad" 1725639 1725648 1728077 1728082) (-1030 "REPDB.spad" 1725344 1725355 1725629 1725634) (-1029 "REP2.spad" 1714916 1714927 1725186 1725191) (-1028 "REP1.spad" 1708906 1708917 1714866 1714871) (-1027 "REGSET.spad" 1706703 1706720 1708552 1708579) (-1026 "REF.spad" 1706032 1706043 1706658 1706663) (-1025 "REDORDER.spad" 1705208 1705225 1706022 1706027) (-1024 "RECLOS.spad" 1703991 1704011 1704695 1704788) (-1023 "REALSOLV.spad" 1703123 1703132 1703981 1703986) (-1022 "REAL.spad" 1702995 1703004 1703113 1703118) (-1021 "REAL0Q.spad" 1700277 1700292 1702985 1702990) (-1020 "REAL0.spad" 1697105 1697120 1700267 1700272) (-1019 "RDUCEAST.spad" 1696826 1696835 1697095 1697100) (-1018 "RDIV.spad" 1696477 1696502 1696816 1696821) (-1017 "RDIST.spad" 1696040 1696051 1696467 1696472) (-1016 "RDETRS.spad" 1694836 1694854 1696030 1696035) (-1015 "RDETR.spad" 1692943 1692961 1694826 1694831) (-1014 "RDEEFS.spad" 1692016 1692033 1692933 1692938) (-1013 "RDEEF.spad" 1691012 1691029 1692006 1692011) (-1012 "RCFIELD.spad" 1688198 1688207 1690914 1691007) (-1011 "RCFIELD.spad" 1685470 1685481 1688188 1688193) (-1010 "RCAGG.spad" 1683382 1683393 1685460 1685465) (-1009 "RCAGG.spad" 1681221 1681234 1683301 1683306) (-1008 "RATRET.spad" 1680581 1680592 1681211 1681216) (-1007 "RATFACT.spad" 1680273 1680285 1680571 1680576) (-1006 "RANDSRC.spad" 1679592 1679601 1680263 1680268) (-1005 "RADUTIL.spad" 1679346 1679355 1679582 1679587) (-1004 "RADIX.spad" 1676247 1676261 1677813 1677906) (-1003 "RADFF.spad" 1674660 1674697 1674779 1674935) (-1002 "RADCAT.spad" 1674253 1674262 1674650 1674655) (-1001 "RADCAT.spad" 1673844 1673855 1674243 1674248) (-1000 "QUEUE.spad" 1673186 1673197 1673451 1673478) (-999 "QUAT.spad" 1671768 1671778 1672110 1672175) (-998 "QUATCT2.spad" 1671387 1671405 1671758 1671763) (-997 "QUATCAT.spad" 1669552 1669562 1671317 1671382) (-996 "QUATCAT.spad" 1667468 1667480 1669235 1669240) (-995 "QUAGG.spad" 1666294 1666304 1667436 1667463) (-994 "QQUTAST.spad" 1666063 1666071 1666284 1666289) (-993 "QFORM.spad" 1665526 1665540 1666053 1666058) (-992 "QFCAT.spad" 1664229 1664239 1665428 1665521) (-991 "QFCAT.spad" 1662523 1662535 1663724 1663729) (-990 "QFCAT2.spad" 1662214 1662230 1662513 1662518) (-989 "QEQUAT.spad" 1661771 1661779 1662204 1662209) (-988 "QCMPACK.spad" 1656518 1656537 1661761 1661766) (-987 "QALGSET.spad" 1652593 1652625 1656432 1656437) (-986 "QALGSET2.spad" 1650589 1650607 1652583 1652588) (-985 "PWFFINTB.spad" 1647899 1647920 1650579 1650584) (-984 "PUSHVAR.spad" 1647228 1647247 1647889 1647894) (-983 "PTRANFN.spad" 1643354 1643364 1647218 1647223) (-982 "PTPACK.spad" 1640442 1640452 1643344 1643349) (-981 "PTFUNC2.spad" 1640263 1640277 1640432 1640437) (-980 "PTCAT.spad" 1639512 1639522 1640231 1640258) (-979 "PSQFR.spad" 1638819 1638843 1639502 1639507) (-978 "PSEUDLIN.spad" 1637677 1637687 1638809 1638814) (-977 "PSETPK.spad" 1623110 1623126 1637555 1637560) (-976 "PSETCAT.spad" 1617030 1617053 1623090 1623105) (-975 "PSETCAT.spad" 1610924 1610949 1616986 1616991) (-974 "PSCURVE.spad" 1609907 1609915 1610914 1610919) (-973 "PSCAT.spad" 1608674 1608703 1609805 1609902) (-972 "PSCAT.spad" 1607531 1607562 1608664 1608669) (-971 "PRTITION.spad" 1606476 1606484 1607521 1607526) (-970 "PRTDAST.spad" 1606195 1606203 1606466 1606471) (-969 "PRS.spad" 1595757 1595774 1606151 1606156) (-968 "PRQAGG.spad" 1595188 1595198 1595725 1595752) (-967 "PROPLOG.spad" 1594483 1594491 1595178 1595183) (-966 "PROPFRML.spad" 1593291 1593302 1594473 1594478) (-965 "PROPERTY.spad" 1592777 1592785 1593281 1593286) (-964 "PRODUCT.spad" 1590457 1590469 1590743 1590798) (-963 "PR.spad" 1588843 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"POLTOPOL.spad" 1556869 1556884 1558111 1558116) (-943 "POINT.spad" 1555707 1555717 1555794 1555821) (-942 "PNTHEORY.spad" 1552373 1552381 1555697 1555702) (-941 "PMTOOLS.spad" 1551130 1551144 1552363 1552368) (-940 "PMSYM.spad" 1550675 1550685 1551120 1551125) (-939 "PMQFCAT.spad" 1550262 1550276 1550665 1550670) (-938 "PMPRED.spad" 1549731 1549745 1550252 1550257) (-937 "PMPREDFS.spad" 1549175 1549197 1549721 1549726) (-936 "PMPLCAT.spad" 1548245 1548263 1549107 1549112) (-935 "PMLSAGG.spad" 1547826 1547840 1548235 1548240) (-934 "PMKERNEL.spad" 1547393 1547405 1547816 1547821) (-933 "PMINS.spad" 1546969 1546979 1547383 1547388) (-932 "PMFS.spad" 1546542 1546560 1546959 1546964) (-931 "PMDOWN.spad" 1545828 1545842 1546532 1546537) (-930 "PMASS.spad" 1544836 1544844 1545818 1545823) (-929 "PMASSFS.spad" 1543801 1543817 1544826 1544831) (-928 "PLOTTOOL.spad" 1543581 1543589 1543791 1543796) (-927 "PLOT.spad" 1538412 1538420 1543571 1543576) (-926 "PLOT3D.spad" 1534832 1534840 1538402 1538407) (-925 "PLOT1.spad" 1533973 1533983 1534822 1534827) (-924 "PLEQN.spad" 1521189 1521216 1533963 1533968) (-923 "PINTERP.spad" 1520805 1520824 1521179 1521184) (-922 "PINTERPA.spad" 1520587 1520603 1520795 1520800) (-921 "PI.spad" 1520194 1520202 1520561 1520582) (-920 "PID.spad" 1519150 1519158 1520120 1520189) (-919 "PICOERCE.spad" 1518807 1518817 1519140 1519145) (-918 "PGROEB.spad" 1517404 1517418 1518797 1518802) (-917 "PGE.spad" 1508657 1508665 1517394 1517399) (-916 "PGCD.spad" 1507539 1507556 1508647 1508652) (-915 "PFRPAC.spad" 1506682 1506692 1507529 1507534) (-914 "PFR.spad" 1503339 1503349 1506584 1506677) (-913 "PFOTOOLS.spad" 1502597 1502613 1503329 1503334) (-912 "PFOQ.spad" 1501967 1501985 1502587 1502592) (-911 "PFO.spad" 1501386 1501413 1501957 1501962) (-910 "PF.spad" 1500960 1500972 1501191 1501284) (-909 "PFECAT.spad" 1498626 1498634 1500886 1500955) (-908 "PFECAT.spad" 1496320 1496330 1498582 1498587) (-907 "PFBRU.spad" 1494190 1494202 1496310 1496315) (-906 "PFBR.spad" 1491728 1491751 1494180 1494185) (-905 "PERM.spad" 1487409 1487419 1491558 1491573) (-904 "PERMGRP.spad" 1482145 1482155 1487399 1487404) (-903 "PERMCAT.spad" 1480697 1480707 1482125 1482140) (-902 "PERMAN.spad" 1479229 1479243 1480687 1480692) (-901 "PENDTREE.spad" 1478568 1478578 1478858 1478863) (-900 "PDRING.spad" 1477059 1477069 1478548 1478563) (-899 "PDRING.spad" 1475558 1475570 1477049 1477054) (-898 "PDEPROB.spad" 1474573 1474581 1475548 1475553) (-897 "PDEPACK.spad" 1468575 1468583 1474563 1474568) (-896 "PDECOMP.spad" 1468037 1468054 1468565 1468570) (-895 "PDECAT.spad" 1466391 1466399 1468027 1468032) (-894 "PCOMP.spad" 1466242 1466255 1466381 1466386) (-893 "PBWLB.spad" 1464824 1464841 1466232 1466237) (-892 "PATTERN.spad" 1459255 1459265 1464814 1464819) (-891 "PATTERN2.spad" 1458991 1459003 1459245 1459250) (-890 "PATTERN1.spad" 1457293 1457309 1458981 1458986) (-889 "PATRES.spad" 1454840 1454852 1457283 1457288) (-888 "PATRES2.spad" 1454502 1454516 1454830 1454835) (-887 "PATMATCH.spad" 1452659 1452690 1454210 1454215) (-886 "PATMAB.spad" 1452084 1452094 1452649 1452654) (-885 "PATLRES.spad" 1451168 1451182 1452074 1452079) (-884 "PATAB.spad" 1450932 1450942 1451158 1451163) (-883 "PARTPERM.spad" 1448294 1448302 1450922 1450927) (-882 "PARSURF.spad" 1447722 1447750 1448284 1448289) (-881 "PARSU2.spad" 1447517 1447533 1447712 1447717) (-880 "script-parser.spad" 1447037 1447045 1447507 1447512) (-879 "PARSCURV.spad" 1446465 1446493 1447027 1447032) (-878 "PARSC2.spad" 1446254 1446270 1446455 1446460) (-877 "PARPCURV.spad" 1445712 1445740 1446244 1446249) (-876 "PARPC2.spad" 1445501 1445517 1445702 1445707) (-875 "PAN2EXPR.spad" 1444913 1444921 1445491 1445496) (-874 "PALETTE.spad" 1443883 1443891 1444903 1444908) (-873 "PAIR.spad" 1442866 1442879 1443471 1443476) (-872 "PADICRC.spad" 1440196 1440214 1441371 1441464) (-871 "PADICRAT.spad" 1438211 1438223 1438432 1438525) (-870 "PADIC.spad" 1437906 1437918 1438137 1438206) (-869 "PADICCT.spad" 1436447 1436459 1437832 1437901) (-868 "PADEPAC.spad" 1435126 1435145 1436437 1436442) (-867 "PADE.spad" 1433866 1433882 1435116 1435121) (-866 "OWP.spad" 1433106 1433136 1433724 1433791) (-865 "OVERSET.spad" 1432679 1432687 1433096 1433101) (-864 "OVAR.spad" 1432460 1432483 1432669 1432674) (-863 "OUT.spad" 1431544 1431552 1432450 1432455) (-862 "OUTFORM.spad" 1420840 1420848 1431534 1431539) (-861 "OUTBFILE.spad" 1420258 1420266 1420830 1420835) (-860 "OUTBCON.spad" 1419256 1419264 1420248 1420253) (-859 "OUTBCON.spad" 1418252 1418262 1419246 1419251) (-858 "OSI.spad" 1417727 1417735 1418242 1418247) (-857 "OSGROUP.spad" 1417645 1417653 1417717 1417722) (-856 "ORTHPOL.spad" 1416106 1416116 1417562 1417567) (-855 "OREUP.spad" 1415559 1415587 1415786 1415825) (-854 "ORESUP.spad" 1414858 1414882 1415239 1415278) (-853 "OREPCTO.spad" 1412677 1412689 1414778 1414783) (-852 "OREPCAT.spad" 1406734 1406744 1412633 1412672) (-851 "OREPCAT.spad" 1400681 1400693 1406582 1406587) (-850 "ORDSET.spad" 1399847 1399855 1400671 1400676) (-849 "ORDSET.spad" 1399011 1399021 1399837 1399842) (-848 "ORDRING.spad" 1398401 1398409 1398991 1399006) (-847 "ORDRING.spad" 1397799 1397809 1398391 1398396) (-846 "ORDMON.spad" 1397654 1397662 1397789 1397794) (-845 "ORDFUNS.spad" 1396780 1396796 1397644 1397649) (-844 "ORDFIN.spad" 1396600 1396608 1396770 1396775) (-843 "ORDCOMP.spad" 1395065 1395075 1396147 1396176) (-842 "ORDCOMP2.spad" 1394350 1394362 1395055 1395060) (-841 "OPTPROB.spad" 1392988 1392996 1394340 1394345) (-840 "OPTPACK.spad" 1385373 1385381 1392978 1392983) (-839 "OPTCAT.spad" 1383048 1383056 1385363 1385368) (-838 "OPSIG.spad" 1382700 1382708 1383038 1383043) (-837 "OPQUERY.spad" 1382249 1382257 1382690 1382695) (-836 "OP.spad" 1381991 1382001 1382071 1382138) (-835 "OPERCAT.spad" 1381455 1381465 1381981 1381986) (-834 "OPERCAT.spad" 1380917 1380929 1381445 1381450) (-833 "ONECOMP.spad" 1379662 1379672 1380464 1380493) (-832 "ONECOMP2.spad" 1379080 1379092 1379652 1379657) (-831 "OMSERVER.spad" 1378082 1378090 1379070 1379075) (-830 "OMSAGG.spad" 1377870 1377880 1378038 1378077) (-829 "OMPKG.spad" 1376482 1376490 1377860 1377865) (-828 "OM.spad" 1375447 1375455 1376472 1376477) (-827 "OMLO.spad" 1374872 1374884 1375333 1375372) (-826 "OMEXPR.spad" 1374706 1374716 1374862 1374867) (-825 "OMERR.spad" 1374249 1374257 1374696 1374701) (-824 "OMERRK.spad" 1373283 1373291 1374239 1374244) (-823 "OMENC.spad" 1372627 1372635 1373273 1373278) (-822 "OMDEV.spad" 1366916 1366924 1372617 1372622) (-821 "OMCONN.spad" 1366325 1366333 1366906 1366911) (-820 "OINTDOM.spad" 1366088 1366096 1366251 1366320) (-819 "OFMONOID.spad" 1362275 1362285 1366078 1366083) (-818 "ODVAR.spad" 1361536 1361546 1362265 1362270) (-817 "ODR.spad" 1361180 1361206 1361348 1361497) (-816 "ODPOL.spad" 1358562 1358572 1358902 1359029) (-815 "ODP.spad" 1348409 1348429 1348782 1348913) (-814 "ODETOOLS.spad" 1346992 1347011 1348399 1348404) (-813 "ODESYS.spad" 1344642 1344659 1346982 1346987) (-812 "ODERTRIC.spad" 1340583 1340600 1344599 1344604) (-811 "ODERED.spad" 1339970 1339994 1340573 1340578) (-810 "ODERAT.spad" 1337521 1337538 1339960 1339965) (-809 "ODEPRRIC.spad" 1334412 1334434 1337511 1337516) (-808 "ODEPROB.spad" 1333669 1333677 1334402 1334407) (-807 "ODEPRIM.spad" 1330943 1330965 1333659 1333664) (-806 "ODEPAL.spad" 1330319 1330343 1330933 1330938) (-805 "ODEPACK.spad" 1316921 1316929 1330309 1330314) (-804 "ODEINT.spad" 1316352 1316368 1316911 1316916) (-803 "ODEIFTBL.spad" 1313747 1313755 1316342 1316347) (-802 "ODEEF.spad" 1309114 1309130 1313737 1313742) (-801 "ODECONST.spad" 1308633 1308651 1309104 1309109) (-800 "ODECAT.spad" 1307229 1307237 1308623 1308628) (-799 "OCT.spad" 1305367 1305377 1306083 1306122) (-798 "OCTCT2.spad" 1305011 1305032 1305357 1305362) (-797 "OC.spad" 1302785 1302795 1304967 1305006) (-796 "OC.spad" 1300284 1300296 1302468 1302473) (-795 "OCAMON.spad" 1300132 1300140 1300274 1300279) (-794 "OASGP.spad" 1299947 1299955 1300122 1300127) (-793 "OAMONS.spad" 1299467 1299475 1299937 1299942) (-792 "OAMON.spad" 1299328 1299336 1299457 1299462) (-791 "OAGROUP.spad" 1299190 1299198 1299318 1299323) (-790 "NUMTUBE.spad" 1298777 1298793 1299180 1299185) (-789 "NUMQUAD.spad" 1286639 1286647 1298767 1298772) (-788 "NUMODE.spad" 1277775 1277783 1286629 1286634) (-787 "NUMINT.spad" 1275333 1275341 1277765 1277770) (-786 "NUMFMT.spad" 1274173 1274181 1275323 1275328) (-785 "NUMERIC.spad" 1266245 1266255 1273978 1273983) (-784 "NTSCAT.spad" 1264747 1264763 1266213 1266240) (-783 "NTPOLFN.spad" 1264292 1264302 1264664 1264669) (-782 "NSUP.spad" 1257338 1257348 1261878 1262031) (-781 "NSUP2.spad" 1256730 1256742 1257328 1257333) (-780 "NSMP.spad" 1252961 1252980 1253269 1253396) (-779 "NREP.spad" 1251333 1251347 1252951 1252956) (-778 "NPCOEF.spad" 1250579 1250599 1251323 1251328) (-777 "NORMRETR.spad" 1250177 1250216 1250569 1250574) (-776 "NORMPK.spad" 1248079 1248098 1250167 1250172) (-775 "NORMMA.spad" 1247767 1247793 1248069 1248074) (-774 "NONE.spad" 1247508 1247516 1247757 1247762) (-773 "NONE1.spad" 1247184 1247194 1247498 1247503) (-772 "NODE1.spad" 1246653 1246669 1247174 1247179) (-771 "NNI.spad" 1245540 1245548 1246627 1246648) (-770 "NLINSOL.spad" 1244162 1244172 1245530 1245535) (-769 "NIPROB.spad" 1242703 1242711 1244152 1244157) (-768 "NFINTBAS.spad" 1240163 1240180 1242693 1242698) (-767 "NETCLT.spad" 1240137 1240148 1240153 1240158) (-766 "NCODIV.spad" 1238335 1238351 1240127 1240132) (-765 "NCNTFRAC.spad" 1237977 1237991 1238325 1238330) (-764 "NCEP.spad" 1236137 1236151 1237967 1237972) (-763 "NASRING.spad" 1235733 1235741 1236127 1236132) (-762 "NASRING.spad" 1235327 1235337 1235723 1235728) (-761 "NARNG.spad" 1234671 1234679 1235317 1235322) (-760 "NARNG.spad" 1234013 1234023 1234661 1234666) (-759 "NAGSP.spad" 1233086 1233094 1234003 1234008) (-758 "NAGS.spad" 1222611 1222619 1233076 1233081) (-757 "NAGF07.spad" 1221004 1221012 1222601 1222606) (-756 "NAGF04.spad" 1215236 1215244 1220994 1220999) (-755 "NAGF02.spad" 1209045 1209053 1215226 1215231) (-754 "NAGF01.spad" 1204648 1204656 1209035 1209040) (-753 "NAGE04.spad" 1198108 1198116 1204638 1204643) (-752 "NAGE02.spad" 1188450 1188458 1198098 1198103) (-751 "NAGE01.spad" 1184334 1184342 1188440 1188445) (-750 "NAGD03.spad" 1182254 1182262 1184324 1184329) (-749 "NAGD02.spad" 1174785 1174793 1182244 1182249) (-748 "NAGD01.spad" 1168898 1168906 1174775 1174780) (-747 "NAGC06.spad" 1164685 1164693 1168888 1168893) (-746 "NAGC05.spad" 1163154 1163162 1164675 1164680) (-745 "NAGC02.spad" 1162409 1162417 1163144 1163149) (-744 "NAALG.spad" 1161944 1161954 1162377 1162404) (-743 "NAALG.spad" 1161499 1161511 1161934 1161939) (-742 "MULTSQFR.spad" 1158457 1158474 1161489 1161494) (-741 "MULTFACT.spad" 1157840 1157857 1158447 1158452) (-740 "MTSCAT.spad" 1155874 1155895 1157738 1157835) (-739 "MTHING.spad" 1155531 1155541 1155864 1155869) (-738 "MSYSCMD.spad" 1154965 1154973 1155521 1155526) (-737 "MSET.spad" 1152907 1152917 1154671 1154710) (-736 "MSETAGG.spad" 1152752 1152762 1152875 1152902) (-735 "MRING.spad" 1149723 1149735 1152460 1152527) (-734 "MRF2.spad" 1149291 1149305 1149713 1149718) (-733 "MRATFAC.spad" 1148837 1148854 1149281 1149286) (-732 "MPRFF.spad" 1146867 1146886 1148827 1148832) (-731 "MPOLY.spad" 1144338 1144353 1144697 1144824) (-730 "MPCPF.spad" 1143602 1143621 1144328 1144333) (-729 "MPC3.spad" 1143417 1143457 1143592 1143597) (-728 "MPC2.spad" 1143059 1143092 1143407 1143412) (-727 "MONOTOOL.spad" 1141394 1141411 1143049 1143054) (-726 "MONOID.spad" 1140713 1140721 1141384 1141389) (-725 "MONOID.spad" 1140030 1140040 1140703 1140708) (-724 "MONOGEN.spad" 1138776 1138789 1139890 1140025) (-723 "MONOGEN.spad" 1137544 1137559 1138660 1138665) (-722 "MONADWU.spad" 1135558 1135566 1137534 1137539) (-721 "MONADWU.spad" 1133570 1133580 1135548 1135553) (-720 "MONAD.spad" 1132714 1132722 1133560 1133565) (-719 "MONAD.spad" 1131856 1131866 1132704 1132709) (-718 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(-399 "FORT.spad" 651915 651923 652976 652981) (-398 "FORTFN.spad" 649085 649093 651905 651910) (-397 "FORTCAT.spad" 648769 648777 649075 649080) (-396 "FORMULA.spad" 646233 646241 648759 648764) (-395 "FORMULA1.spad" 645712 645722 646223 646228) (-394 "FORDER.spad" 645403 645427 645702 645707) (-393 "FOP.spad" 644604 644612 645393 645398) (-392 "FNLA.spad" 644028 644050 644572 644599) (-391 "FNCAT.spad" 642615 642623 644018 644023) (-390 "FNAME.spad" 642507 642515 642605 642610) (-389 "FMTC.spad" 642305 642313 642433 642502) (-388 "FMONOID.spad" 639360 639370 642261 642266) (-387 "FM.spad" 639055 639067 639294 639321) (-386 "FMFUN.spad" 636085 636093 639045 639050) (-385 "FMC.spad" 635137 635145 636075 636080) (-384 "FMCAT.spad" 632791 632809 635105 635132) (-383 "FM1.spad" 632148 632160 632725 632752) (-382 "FLOATRP.spad" 629869 629883 632138 632143) (-381 "FLOAT.spad" 623157 623165 629735 629864) (-380 "FLOATCP.spad" 620574 620588 623147 623152) (-379 "FLINEXP.spad" 620286 620296 620554 620569) (-378 "FLINEXP.spad" 619952 619964 620222 620227) (-377 "FLASORT.spad" 619272 619284 619942 619947) (-376 "FLALG.spad" 616918 616937 619198 619267) (-375 "FLAGG.spad" 613936 613946 616898 616913) (-374 "FLAGG.spad" 610855 610867 613819 613824) (-373 "FLAGG2.spad" 609536 609552 610845 610850) (-372 "FINRALG.spad" 607565 607578 609492 609531) (-371 "FINRALG.spad" 605520 605535 607449 607454) (-370 "FINITE.spad" 604672 604680 605510 605515) (-369 "FINAALG.spad" 593653 593663 604614 604667) (-368 "FINAALG.spad" 582646 582658 593609 593614) (-367 "FILE.spad" 582229 582239 582636 582641) (-366 "FILECAT.spad" 580747 580764 582219 582224) (-365 "FIELD.spad" 580153 580161 580649 580742) (-364 "FIELD.spad" 579645 579655 580143 580148) (-363 "FGROUP.spad" 578254 578264 579625 579640) (-362 "FGLMICPK.spad" 577041 577056 578244 578249) (-361 "FFX.spad" 576416 576431 576757 576850) (-360 "FFSLPE.spad" 575905 575926 576406 576411) (-359 "FFPOLY.spad" 567157 567168 575895 575900) (-358 "FFPOLY2.spad" 566217 566234 567147 567152) (-357 "FFP.spad" 565614 565634 565933 566026) (-356 "FF.spad" 565062 565078 565295 565388) (-355 "FFNBX.spad" 563574 563594 564778 564871) (-354 "FFNBP.spad" 562087 562104 563290 563383) (-353 "FFNB.spad" 560552 560573 561768 561861) (-352 "FFINTBAS.spad" 557966 557985 560542 560547) (-351 "FFIELDC.spad" 555541 555549 557868 557961) (-350 "FFIELDC.spad" 553202 553212 555531 555536) (-349 "FFHOM.spad" 551950 551967 553192 553197) (-348 "FFF.spad" 549385 549396 551940 551945) (-347 "FFCGX.spad" 548232 548252 549101 549194) (-346 "FFCGP.spad" 547121 547141 547948 548041) (-345 "FFCG.spad" 545913 545934 546802 546895) (-344 "FFCAT.spad" 538940 538962 545752 545908) (-343 "FFCAT.spad" 532046 532070 538860 538865) (-342 "FFCAT2.spad" 531791 531831 532036 532041) (-341 "FEXPR.spad" 523500 523546 531547 531586) (-340 "FEVALAB.spad" 523206 523216 523490 523495) (-339 "FEVALAB.spad" 522697 522709 522983 522988) (-338 "FDIV.spad" 522139 522163 522687 522692) (-337 "FDIVCAT.spad" 520181 520205 522129 522134) (-336 "FDIVCAT.spad" 518221 518247 520171 520176) (-335 "FDIV2.spad" 517875 517915 518211 518216) (-334 "FCTRDATA.spad" 516907 516915 517865 517870) (-333 "FCPAK1.spad" 515460 515468 516897 516902) (-332 "FCOMP.spad" 514839 514849 515450 515455) (-331 "FC.spad" 504754 504762 514829 514834) (-330 "FAXF.spad" 497689 497703 504656 504749) (-329 "FAXF.spad" 490676 490692 497645 497650) (-328 "FARRAY.spad" 488822 488832 489859 489886) (-327 "FAMR.spad" 486942 486954 488720 488817) (-326 "FAMR.spad" 485046 485060 486826 486831) (-325 "FAMONOID.spad" 484696 484706 485000 485005) (-324 "FAMONC.spad" 482918 482930 484686 484691) (-323 "FAGROUP.spad" 482524 482534 482814 482841) (-322 "FACUTIL.spad" 480720 480737 482514 482519) (-321 "FACTFUNC.spad" 479896 479906 480710 480715) (-320 "EXPUPXS.spad" 476729 476752 478028 478177) (-319 "EXPRTUBE.spad" 473957 473965 476719 476724) (-318 "EXPRODE.spad" 470829 470845 473947 473952) (-317 "EXPR.spad" 466104 466114 466818 467225) (-316 "EXPR2UPS.spad" 462196 462209 466094 466099) (-315 "EXPR2.spad" 461899 461911 462186 462191) (-314 "EXPEXPAN.spad" 458837 458862 459471 459564) (-313 "EXIT.spad" 458508 458516 458827 458832) (-312 "EXITAST.spad" 458244 458252 458498 458503) (-311 "EVALCYC.spad" 457702 457716 458234 458239) (-310 "EVALAB.spad" 457266 457276 457692 457697) (-309 "EVALAB.spad" 456828 456840 457256 457261) (-308 "EUCDOM.spad" 454370 454378 456754 456823) (-307 "EUCDOM.spad" 451974 451984 454360 454365) (-306 "ESTOOLS.spad" 443814 443822 451964 451969) (-305 "ESTOOLS2.spad" 443415 443429 443804 443809) (-304 "ESTOOLS1.spad" 443100 443111 443405 443410) (-303 "ES.spad" 435647 435655 443090 443095) (-302 "ES.spad" 428100 428110 435545 435550) (-301 "ESCONT.spad" 424873 424881 428090 428095) (-300 "ESCONT1.spad" 424622 424634 424863 424868) (-299 "ES2.spad" 424117 424133 424612 424617) (-298 "ES1.spad" 423683 423699 424107 424112) (-297 "ERROR.spad" 421004 421012 423673 423678) (-296 "EQTBL.spad" 419476 419498 419685 419712) (-295 "EQ.spad" 414269 414279 417068 417180) (-294 "EQ2.spad" 413985 413997 414259 414264) (-293 "EP.spad" 410299 410309 413975 413980) (-292 "ENV.spad" 408951 408959 410289 410294) (-291 "ENTIRER.spad" 408619 408627 408895 408946) (-290 "EMR.spad" 407820 407861 408545 408614) (-289 "ELTAGG.spad" 406060 406079 407810 407815) (-288 "ELTAGG.spad" 404264 404285 406016 406021) (-287 "ELTAB.spad" 403711 403729 404254 404259) (-286 "ELFUTS.spad" 403090 403109 403701 403706) (-285 "ELEMFUN.spad" 402779 402787 403080 403085) (-284 "ELEMFUN.spad" 402466 402476 402769 402774) (-283 "ELAGG.spad" 400409 400419 402446 402461) (-282 "ELAGG.spad" 398289 398301 400328 400333) (-281 "ELABEXPR.spad" 397212 397220 398279 398284) (-280 "EFUPXS.spad" 393988 394018 397168 397173) (-279 "EFULS.spad" 390824 390847 393944 393949) (-278 "EFSTRUC.spad" 388779 388795 390814 390819) (-277 "EF.spad" 383545 383561 388769 388774) (-276 "EAB.spad" 381821 381829 383535 383540) (-275 "E04UCFA.spad" 381357 381365 381811 381816) (-274 "E04NAFA.spad" 380934 380942 381347 381352) (-273 "E04MBFA.spad" 380514 380522 380924 380929) (-272 "E04JAFA.spad" 380050 380058 380504 380509) (-271 "E04GCFA.spad" 379586 379594 380040 380045) (-270 "E04FDFA.spad" 379122 379130 379576 379581) (-269 "E04DGFA.spad" 378658 378666 379112 379117) (-268 "E04AGNT.spad" 374500 374508 378648 378653) (-267 "DVARCAT.spad" 371185 371195 374490 374495) (-266 "DVARCAT.spad" 367868 367880 371175 371180) (-265 "DSMP.spad" 365335 365349 365640 365767) (-264 "DROPT.spad" 359280 359288 365325 365330) (-263 "DROPT1.spad" 358943 358953 359270 359275) (-262 "DROPT0.spad" 353770 353778 358933 358938) (-261 "DRAWPT.spad" 351925 351933 353760 353765) (-260 "DRAW.spad" 344525 344538 351915 351920) (-259 "DRAWHACK.spad" 343833 343843 344515 344520) (-258 "DRAWCX.spad" 341275 341283 343823 343828) (-257 "DRAWCURV.spad" 340812 340827 341265 341270) (-256 "DRAWCFUN.spad" 329984 329992 340802 340807) (-255 "DQAGG.spad" 328152 328162 329952 329979) (-254 "DPOLCAT.spad" 323493 323509 328020 328147) (-253 "DPOLCAT.spad" 318920 318938 323449 323454) (-252 "DPMO.spad" 311146 311162 311284 311585) (-251 "DPMM.spad" 303385 303403 303510 303811) (-250 "DOMTMPLT.spad" 303045 303053 303375 303380) (-249 "DOMCTOR.spad" 302800 302808 303035 303040) (-248 "DOMAIN.spad" 301931 301939 302790 302795) (-247 "DMP.spad" 299189 299204 299761 299888) (-246 "DLP.spad" 298537 298547 299179 299184) (-245 "DLIST.spad" 297116 297126 297720 297747) (-244 "DLAGG.spad" 295527 295537 297106 297111) (-243 "DIVRING.spad" 295069 295077 295471 295522) (-242 "DIVRING.spad" 294655 294665 295059 295064) (-241 "DISPLAY.spad" 292835 292843 294645 294650) (-240 "DIRPROD.spad" 282415 282431 283055 283186) (-239 "DIRPROD2.spad" 281223 281241 282405 282410) (-238 "DIRPCAT.spad" 280165 280181 281087 281218) (-237 "DIRPCAT.spad" 278836 278854 279760 279765) (-236 "DIOSP.spad" 277661 277669 278826 278831) (-235 "DIOPS.spad" 276645 276655 277641 277656) (-234 "DIOPS.spad" 275603 275615 276601 276606) (-233 "DIFRING.spad" 274895 274903 275583 275598) (-232 "DIFRING.spad" 274195 274205 274885 274890) (-231 "DIFEXT.spad" 273354 273364 274175 274190) (-230 "DIFEXT.spad" 272430 272442 273253 273258) (-229 "DIAGG.spad" 272060 272070 272410 272425) (-228 "DIAGG.spad" 271698 271710 272050 272055) (-227 "DHMATRIX.spad" 270002 270012 271155 271182) (-226 "DFSFUN.spad" 263410 263418 269992 269997) (-225 "DFLOAT.spad" 260131 260139 263300 263405) (-224 "DFINTTLS.spad" 258340 258356 260121 260126) (-223 "DERHAM.spad" 256250 256282 258320 258335) (-222 "DEQUEUE.spad" 255568 255578 255857 255884) (-221 "DEGRED.spad" 255183 255197 255558 255563) (-220 "DEFINTRF.spad" 252708 252718 255173 255178) (-219 "DEFINTEF.spad" 251204 251220 252698 252703) (-218 "DEFAST.spad" 250572 250580 251194 251199) (-217 "DECIMAL.spad" 248678 248686 249039 249132) (-216 "DDFACT.spad" 246477 246494 248668 248673) (-215 "DBLRESP.spad" 246075 246099 246467 246472) (-214 "DBASE.spad" 244729 244739 246065 246070) (-213 "DATAARY.spad" 244191 244204 244719 244724) (-212 "D03FAFA.spad" 244019 244027 244181 244186) (-211 "D03EEFA.spad" 243839 243847 244009 244014) (-210 "D03AGNT.spad" 242919 242927 243829 243834) (-209 "D02EJFA.spad" 242381 242389 242909 242914) (-208 "D02CJFA.spad" 241859 241867 242371 242376) (-207 "D02BHFA.spad" 241349 241357 241849 241854) (-206 "D02BBFA.spad" 240839 240847 241339 241344) (-205 "D02AGNT.spad" 235643 235651 240829 240834) (-204 "D01WGTS.spad" 233962 233970 235633 235638) (-203 "D01TRNS.spad" 233939 233947 233952 233957) (-202 "D01GBFA.spad" 233461 233469 233929 233934) (-201 "D01FCFA.spad" 232983 232991 233451 233456) (-200 "D01ASFA.spad" 232451 232459 232973 232978) (-199 "D01AQFA.spad" 231897 231905 232441 232446) (-198 "D01APFA.spad" 231321 231329 231887 231892) (-197 "D01ANFA.spad" 230815 230823 231311 231316) (-196 "D01AMFA.spad" 230325 230333 230805 230810) (-195 "D01ALFA.spad" 229865 229873 230315 230320) (-194 "D01AKFA.spad" 229391 229399 229855 229860) (-193 "D01AJFA.spad" 228914 228922 229381 229386) (-192 "D01AGNT.spad" 224973 224981 228904 228909) (-191 "CYCLOTOM.spad" 224479 224487 224963 224968) (-190 "CYCLES.spad" 221311 221319 224469 224474) (-189 "CVMP.spad" 220728 220738 221301 221306) (-188 "CTRIGMNP.spad" 219218 219234 220718 220723) (-187 "CTOR.spad" 218909 218917 219208 219213) (-186 "CTORKIND.spad" 218512 218520 218899 218904) (-185 "CTORCAT.spad" 217761 217769 218502 218507) (-184 "CTORCAT.spad" 217008 217018 217751 217756) (-183 "CTORCALL.spad" 216588 216596 216998 217003) (-182 "CSTTOOLS.spad" 215831 215844 216578 216583) (-181 "CRFP.spad" 209535 209548 215821 215826) (-180 "CRCEAST.spad" 209255 209263 209525 209530) (-179 "CRAPACK.spad" 208298 208308 209245 209250) (-178 "CPMATCH.spad" 207798 207813 208223 208228) (-177 "CPIMA.spad" 207503 207522 207788 207793) (-176 "COORDSYS.spad" 202396 202406 207493 207498) (-175 "CONTOUR.spad" 201803 201811 202386 202391) (-174 "CONTFRAC.spad" 197415 197425 201705 201798) (-173 "CONDUIT.spad" 197173 197181 197405 197410) (-172 "COMRING.spad" 196847 196855 197111 197168) (-171 "COMPPROP.spad" 196361 196369 196837 196842) (-170 "COMPLPAT.spad" 196128 196143 196351 196356) (-169 "COMPLEX.spad" 190265 190275 190509 190770) (-168 "COMPLEX2.spad" 189978 189990 190255 190260) (-167 "COMPFACT.spad" 189580 189594 189968 189973) (-166 "COMPCAT.spad" 187648 187658 189314 189575) (-165 "COMPCAT.spad" 185444 185456 187112 187117) (-164 "COMMUPC.spad" 185190 185208 185434 185439) (-163 "COMMONOP.spad" 184723 184731 185180 185185) (-162 "COMM.spad" 184532 184540 184713 184718) (-161 "COMMAAST.spad" 184295 184303 184522 184527) (-160 "COMBOPC.spad" 183200 183208 184285 184290) (-159 "COMBINAT.spad" 181945 181955 183190 183195) (-158 "COMBF.spad" 179313 179329 181935 181940) (-157 "COLOR.spad" 178150 178158 179303 179308) (-156 "COLONAST.spad" 177816 177824 178140 178145) (-155 "CMPLXRT.spad" 177525 177542 177806 177811) (-154 "CLLCTAST.spad" 177187 177195 177515 177520) (-153 "CLIP.spad" 173279 173287 177177 177182) (-152 "CLIF.spad" 171918 171934 173235 173274) (-151 "CLAGG.spad" 168403 168413 171908 171913) (-150 "CLAGG.spad" 164759 164771 168266 168271) (-149 "CINTSLPE.spad" 164084 164097 164749 164754) (-148 "CHVAR.spad" 162162 162184 164074 164079) (-147 "CHARZ.spad" 162077 162085 162142 162157) (-146 "CHARPOL.spad" 161585 161595 162067 162072) (-145 "CHARNZ.spad" 161338 161346 161565 161580) (-144 "CHAR.spad" 159206 159214 161328 161333) (-143 "CFCAT.spad" 158522 158530 159196 159201) (-142 "CDEN.spad" 157680 157694 158512 158517) (-141 "CCLASS.spad" 155829 155837 157091 157130) (-140 "CATEGORY.spad" 154919 154927 155819 155824) (-139 "CATCTOR.spad" 154810 154818 154909 154914) (-138 "CATAST.spad" 154428 154436 154800 154805) (-137 "CASEAST.spad" 154142 154150 154418 154423) (-136 "CARTEN.spad" 149245 149269 154132 154137) (-135 "CARTEN2.spad" 148631 148658 149235 149240) (-134 "CARD.spad" 145920 145928 148605 148626) (-133 "CAPSLAST.spad" 145694 145702 145910 145915) (-132 "CACHSET.spad" 145316 145324 145684 145689) (-131 "CABMON.spad" 144869 144877 145306 145311) (-130 "BYTEORD.spad" 144544 144552 144859 144864) (-129 "BYTE.spad" 143969 143977 144534 144539) (-128 "BYTEBUF.spad" 141826 141834 143138 143165) (-127 "BTREE.spad" 140895 140905 141433 141460) (-126 "BTOURN.spad" 139898 139908 140502 140529) (-125 "BTCAT.spad" 139286 139296 139866 139893) (-124 "BTCAT.spad" 138694 138706 139276 139281) (-123 "BTAGG.spad" 137816 137824 138662 138689) (-122 "BTAGG.spad" 136958 136968 137806 137811) (-121 "BSTREE.spad" 135693 135703 136565 136592) (-120 "BRILL.spad" 133888 133899 135683 135688) (-119 "BRAGG.spad" 132812 132822 133878 133883) (-118 "BRAGG.spad" 131700 131712 132768 132773) (-117 "BPADICRT.spad" 129681 129693 129936 130029) (-116 "BPADIC.spad" 129345 129357 129607 129676) (-115 "BOUNDZRO.spad" 129001 129018 129335 129340) (-114 "BOP.spad" 124125 124133 128991 128996) (-113 "BOP1.spad" 121545 121555 124115 124120) (-112 "BOOLEAN.spad" 120977 120985 121535 121540) (-111 "BMODULE.spad" 120689 120701 120945 120972) (-110 "BITS.spad" 120108 120116 120325 120352) (-109 "BINDING.spad" 119519 119527 120098 120103) (-108 "BINARY.spad" 117630 117638 117986 118079) (-107 "BGAGG.spad" 116827 116837 117610 117625) (-106 "BGAGG.spad" 116032 116044 116817 116822) (-105 "BFUNCT.spad" 115596 115604 116012 116027) (-104 "BEZOUT.spad" 114730 114757 115546 115551) (-103 "BBTREE.spad" 111549 111559 114337 114364) (-102 "BASTYPE.spad" 111221 111229 111539 111544) (-101 "BASTYPE.spad" 110891 110901 111211 111216) (-100 "BALFACT.spad" 110330 110343 110881 110886) (-99 "AUTOMOR.spad" 109777 109786 110310 110325) (-98 "ATTREG.spad" 106496 106503 109529 109772) (-97 "ATTRBUT.spad" 102519 102526 106476 106491) (-96 "ATTRAST.spad" 102236 102243 102509 102514) (-95 "ATRIG.spad" 101706 101713 102226 102231) (-94 "ATRIG.spad" 101174 101183 101696 101701) (-93 "ASTCAT.spad" 101078 101085 101164 101169) (-92 "ASTCAT.spad" 100980 100989 101068 101073) (-91 "ASTACK.spad" 100313 100322 100587 100614) (-90 "ASSOCEQ.spad" 99113 99124 100269 100274) (-89 "ASP9.spad" 98194 98207 99103 99108) (-88 "ASP8.spad" 97237 97250 98184 98189) (-87 "ASP80.spad" 96559 96572 97227 97232) (-86 "ASP7.spad" 95719 95732 96549 96554) (-85 "ASP78.spad" 95170 95183 95709 95714) (-84 "ASP77.spad" 94539 94552 95160 95165) (-83 "ASP74.spad" 93631 93644 94529 94534) (-82 "ASP73.spad" 92902 92915 93621 93626) (-81 "ASP6.spad" 91769 91782 92892 92897) (-80 "ASP55.spad" 90278 90291 91759 91764) (-79 "ASP50.spad" 88095 88108 90268 90273) (-78 "ASP4.spad" 87390 87403 88085 88090) (-77 "ASP49.spad" 86389 86402 87380 87385) (-76 "ASP42.spad" 84796 84835 86379 86384) (-75 "ASP41.spad" 83375 83414 84786 84791) (-74 "ASP35.spad" 82363 82376 83365 83370) (-73 "ASP34.spad" 81664 81677 82353 82358) (-72 "ASP33.spad" 81224 81237 81654 81659) (-71 "ASP31.spad" 80364 80377 81214 81219) (-70 "ASP30.spad" 79256 79269 80354 80359) (-69 "ASP29.spad" 78722 78735 79246 79251) (-68 "ASP28.spad" 69995 70008 78712 78717) (-67 "ASP27.spad" 68892 68905 69985 69990) (-66 "ASP24.spad" 67979 67992 68882 68887) (-65 "ASP20.spad" 67443 67456 67969 67974) (-64 "ASP1.spad" 66824 66837 67433 67438) (-63 "ASP19.spad" 61510 61523 66814 66819) (-62 "ASP12.spad" 60924 60937 61500 61505) (-61 "ASP10.spad" 60195 60208 60914 60919) (-60 "ARRAY2.spad" 59555 59564 59802 59829) (-59 "ARRAY1.spad" 58390 58399 58738 58765) (-58 "ARRAY12.spad" 57059 57070 58380 58385) (-57 "ARR2CAT.spad" 52721 52742 57027 57054) (-56 "ARR2CAT.spad" 48403 48426 52711 52716) (-55 "ARITY.spad" 47775 47782 48393 48398) (-54 "APPRULE.spad" 47019 47041 47765 47770) (-53 "APPLYORE.spad" 46634 46647 47009 47014) (-52 "ANY.spad" 45491 45498 46624 46629) (-51 "ANY1.spad" 44562 44571 45481 45486) (-50 "ANTISYM.spad" 43001 43017 44542 44557) (-49 "ANON.spad" 42694 42701 42991 42996) (-48 "AN.spad" 40995 41002 42510 42603) (-47 "AMR.spad" 39174 39185 40893 40990) (-46 "AMR.spad" 37190 37203 38911 38916) (-45 "ALIST.spad" 34602 34623 34952 34979) (-44 "ALGSC.spad" 33725 33751 34474 34527) (-43 "ALGPKG.spad" 29434 29445 33681 33686) (-42 "ALGMFACT.spad" 28623 28637 29424 29429) (-41 "ALGMANIP.spad" 26079 26094 28456 28461) (-40 "ALGFF.spad" 24394 24421 24611 24767) (-39 "ALGFACT.spad" 23515 23525 24384 24389) (-38 "ALGEBRA.spad" 23348 23357 23471 23510) (-37 "ALGEBRA.spad" 23213 23224 23338 23343) (-36 "ALAGG.spad" 22723 22744 23181 23208) (-35 "AHYP.spad" 22104 22111 22713 22718) (-34 "AGG.spad" 20413 20420 22094 22099) (-33 "AGG.spad" 18686 18695 20369 20374) (-32 "AF.spad" 17111 17126 18621 18626) (-31 "ADDAST.spad" 16789 16796 17101 17106) (-30 "ACPLOT.spad" 15360 15367 16779 16784) (-29 "ACFS.spad" 13111 13120 15262 15355) (-28 "ACFS.spad" 10948 10959 13101 13106) (-27 "ACF.spad" 7550 7557 10850 10943) (-26 "ACF.spad" 4238 4247 7540 7545) (-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 2285060 2285065 2285070 2285075) (-2 NIL 2285040 2285045 2285050 2285055) (-1 NIL 2285020 2285025 2285030 2285035) (0 NIL 2285000 2285005 2285010 2285015) (-1292 "ZMOD.spad" 2284809 2284822 2284938 2284995) (-1291 "ZLINDEP.spad" 2283853 2283864 2284799 2284804) (-1290 "ZDSOLVE.spad" 2273702 2273724 2283843 2283848) (-1289 "YSTREAM.spad" 2273195 2273206 2273692 2273697) (-1288 "XRPOLY.spad" 2272415 2272435 2273051 2273120) (-1287 "XPR.spad" 2270206 2270219 2272133 2272232) (-1286 "XPOLY.spad" 2269761 2269772 2270062 2270131) (-1285 "XPOLYC.spad" 2269078 2269094 2269687 2269756) (-1284 "XPBWPOLY.spad" 2267515 2267535 2268858 2268927) (-1283 "XF.spad" 2265976 2265991 2267417 2267510) (-1282 "XF.spad" 2264417 2264434 2265860 2265865) (-1281 "XFALG.spad" 2261441 2261457 2264343 2264412) (-1280 "XEXPPKG.spad" 2260692 2260718 2261431 2261436) (-1279 "XDPOLY.spad" 2260306 2260322 2260548 2260617) (-1278 "XALG.spad" 2259966 2259977 2260262 2260301) (-1277 "WUTSET.spad" 2255805 2255822 2259612 2259639) (-1276 "WP.spad" 2255004 2255048 2255663 2255730) (-1275 "WHILEAST.spad" 2254802 2254811 2254994 2254999) (-1274 "WHEREAST.spad" 2254473 2254482 2254792 2254797) (-1273 "WFFINTBS.spad" 2252036 2252058 2254463 2254468) (-1272 "WEIER.spad" 2250250 2250261 2252026 2252031) (-1271 "VSPACE.spad" 2249923 2249934 2250218 2250245) (-1270 "VSPACE.spad" 2249616 2249629 2249913 2249918) (-1269 "VOID.spad" 2249293 2249302 2249606 2249611) (-1268 "VIEW.spad" 2246915 2246924 2249283 2249288) (-1267 "VIEWDEF.spad" 2242112 2242121 2246905 2246910) (-1266 "VIEW3D.spad" 2225947 2225956 2242102 2242107) (-1265 "VIEW2D.spad" 2213684 2213693 2225937 2225942) (-1264 "VECTOR.spad" 2212358 2212369 2212609 2212636) (-1263 "VECTOR2.spad" 2210985 2210998 2212348 2212353) (-1262 "VECTCAT.spad" 2208885 2208896 2210953 2210980) (-1261 "VECTCAT.spad" 2206592 2206605 2208662 2208667) (-1260 "VARIABLE.spad" 2206372 2206387 2206582 2206587) (-1259 "UTYPE.spad" 2206016 2206025 2206362 2206367) (-1258 "UTSODETL.spad" 2205309 2205333 2205972 2205977) (-1257 "UTSODE.spad" 2203497 2203517 2205299 2205304) (-1256 "UTS.spad" 2198286 2198314 2201964 2202061) (-1255 "UTSCAT.spad" 2195737 2195753 2198184 2198281) (-1254 "UTSCAT.spad" 2192832 2192850 2195281 2195286) (-1253 "UTS2.spad" 2192425 2192460 2192822 2192827) (-1252 "URAGG.spad" 2187058 2187069 2192415 2192420) (-1251 "URAGG.spad" 2181655 2181668 2187014 2187019) (-1250 "UPXSSING.spad" 2179298 2179324 2180736 2180869) (-1249 "UPXS.spad" 2176446 2176474 2177430 2177579) (-1248 "UPXSCONS.spad" 2174203 2174223 2174578 2174727) (-1247 "UPXSCCA.spad" 2172768 2172788 2174049 2174198) (-1246 "UPXSCCA.spad" 2171475 2171497 2172758 2172763) (-1245 "UPXSCAT.spad" 2170056 2170072 2171321 2171470) (-1244 "UPXS2.spad" 2169597 2169650 2170046 2170051) (-1243 "UPSQFREE.spad" 2168009 2168023 2169587 2169592) (-1242 "UPSCAT.spad" 2165602 2165626 2167907 2168004) (-1241 "UPSCAT.spad" 2162901 2162927 2165208 2165213) (-1240 "UPOLYC.spad" 2157879 2157890 2162743 2162896) (-1239 "UPOLYC.spad" 2152749 2152762 2157615 2157620) (-1238 "UPOLYC2.spad" 2152218 2152237 2152739 2152744) (-1237 "UP.spad" 2149411 2149426 2149804 2149957) (-1236 "UPMP.spad" 2148301 2148314 2149401 2149406) (-1235 "UPDIVP.spad" 2147864 2147878 2148291 2148296) (-1234 "UPDECOMP.spad" 2146101 2146115 2147854 2147859) (-1233 "UPCDEN.spad" 2145308 2145324 2146091 2146096) (-1232 "UP2.spad" 2144670 2144691 2145298 2145303) (-1231 "UNISEG.spad" 2144023 2144034 2144589 2144594) (-1230 "UNISEG2.spad" 2143516 2143529 2143979 2143984) (-1229 "UNIFACT.spad" 2142617 2142629 2143506 2143511) (-1228 "ULS.spad" 2133169 2133197 2134262 2134691) (-1227 "ULSCONS.spad" 2125563 2125583 2125935 2126084) (-1226 "ULSCCAT.spad" 2123292 2123312 2125409 2125558) (-1225 "ULSCCAT.spad" 2121129 2121151 2123248 2123253) (-1224 "ULSCAT.spad" 2119345 2119361 2120975 2121124) (-1223 "ULS2.spad" 2118857 2118910 2119335 2119340) (-1222 "UINT8.spad" 2118734 2118743 2118847 2118852) (-1221 "UINT64.spad" 2118610 2118619 2118724 2118729) (-1220 "UINT32.spad" 2118486 2118495 2118600 2118605) (-1219 "UINT16.spad" 2118362 2118371 2118476 2118481) (-1218 "UFD.spad" 2117427 2117436 2118288 2118357) (-1217 "UFD.spad" 2116554 2116565 2117417 2117422) (-1216 "UDVO.spad" 2115401 2115410 2116544 2116549) (-1215 "UDPO.spad" 2112828 2112839 2115357 2115362) (-1214 "TYPE.spad" 2112760 2112769 2112818 2112823) (-1213 "TYPEAST.spad" 2112679 2112688 2112750 2112755) (-1212 "TWOFACT.spad" 2111329 2111344 2112669 2112674) (-1211 "TUPLE.spad" 2110813 2110824 2111228 2111233) (-1210 "TUBETOOL.spad" 2107650 2107659 2110803 2110808) (-1209 "TUBE.spad" 2106291 2106308 2107640 2107645) (-1208 "TS.spad" 2104880 2104896 2105856 2105953) (-1207 "TSETCAT.spad" 2092007 2092024 2104848 2104875) (-1206 "TSETCAT.spad" 2079120 2079139 2091963 2091968) (-1205 "TRMANIP.spad" 2073486 2073503 2078826 2078831) (-1204 "TRIMAT.spad" 2072445 2072470 2073476 2073481) (-1203 "TRIGMNIP.spad" 2070962 2070979 2072435 2072440) (-1202 "TRIGCAT.spad" 2070474 2070483 2070952 2070957) (-1201 "TRIGCAT.spad" 2069984 2069995 2070464 2070469) (-1200 "TREE.spad" 2068555 2068566 2069591 2069618) (-1199 "TRANFUN.spad" 2068386 2068395 2068545 2068550) (-1198 "TRANFUN.spad" 2068215 2068226 2068376 2068381) (-1197 "TOPSP.spad" 2067889 2067898 2068205 2068210) (-1196 "TOOLSIGN.spad" 2067552 2067563 2067879 2067884) (-1195 "TEXTFILE.spad" 2066109 2066118 2067542 2067547) (-1194 "TEX.spad" 2063241 2063250 2066099 2066104) (-1193 "TEX1.spad" 2062797 2062808 2063231 2063236) (-1192 "TEMUTL.spad" 2062352 2062361 2062787 2062792) (-1191 "TBCMPPK.spad" 2060445 2060468 2062342 2062347) (-1190 "TBAGG.spad" 2059481 2059504 2060425 2060440) (-1189 "TBAGG.spad" 2058525 2058550 2059471 2059476) (-1188 "TANEXP.spad" 2057901 2057912 2058515 2058520) (-1187 "TABLE.spad" 2056312 2056335 2056582 2056609) (-1186 "TABLEAU.spad" 2055793 2055804 2056302 2056307) (-1185 "TABLBUMP.spad" 2052576 2052587 2055783 2055788) (-1184 "SYSTEM.spad" 2051804 2051813 2052566 2052571) (-1183 "SYSSOLP.spad" 2049277 2049288 2051794 2051799) (-1182 "SYSNNI.spad" 2048457 2048468 2049267 2049272) (-1181 "SYSINT.spad" 2047861 2047872 2048447 2048452) (-1180 "SYNTAX.spad" 2044055 2044064 2047851 2047856) (-1179 "SYMTAB.spad" 2042111 2042120 2044045 2044050) (-1178 "SYMS.spad" 2038096 2038105 2042101 2042106) (-1177 "SYMPOLY.spad" 2037103 2037114 2037185 2037312) (-1176 "SYMFUNC.spad" 2036578 2036589 2037093 2037098) (-1175 "SYMBOL.spad" 2034005 2034014 2036568 2036573) (-1174 "SWITCH.spad" 2030762 2030771 2033995 2034000) (-1173 "SUTS.spad" 2027661 2027689 2029229 2029326) (-1172 "SUPXS.spad" 2024796 2024824 2025793 2025942) (-1171 "SUP.spad" 2021601 2021612 2022382 2022535) (-1170 "SUPFRACF.spad" 2020706 2020724 2021591 2021596) (-1169 "SUP2.spad" 2020096 2020109 2020696 2020701) (-1168 "SUMRF.spad" 2019062 2019073 2020086 2020091) (-1167 "SUMFS.spad" 2018695 2018712 2019052 2019057) (-1166 "SULS.spad" 2009234 2009262 2010340 2010769) (-1165 "SUCHTAST.spad" 2009003 2009012 2009224 2009229) (-1164 "SUCH.spad" 2008683 2008698 2008993 2008998) (-1163 "SUBSPACE.spad" 2000690 2000705 2008673 2008678) (-1162 "SUBRESP.spad" 1999850 1999864 2000646 2000651) (-1161 "STTF.spad" 1995949 1995965 1999840 1999845) (-1160 "STTFNC.spad" 1992417 1992433 1995939 1995944) (-1159 "STTAYLOR.spad" 1984815 1984826 1992298 1992303) (-1158 "STRTBL.spad" 1983320 1983337 1983469 1983496) (-1157 "STRING.spad" 1982729 1982738 1982743 1982770) (-1156 "STRICAT.spad" 1982517 1982526 1982697 1982724) (-1155 "STREAM.spad" 1979375 1979386 1982042 1982057) (-1154 "STREAM3.spad" 1978920 1978935 1979365 1979370) (-1153 "STREAM2.spad" 1977988 1978001 1978910 1978915) (-1152 "STREAM1.spad" 1977692 1977703 1977978 1977983) (-1151 "STINPROD.spad" 1976598 1976614 1977682 1977687) (-1150 "STEP.spad" 1975799 1975808 1976588 1976593) (-1149 "STBL.spad" 1974325 1974353 1974492 1974507) (-1148 "STAGG.spad" 1973400 1973411 1974315 1974320) (-1147 "STAGG.spad" 1972473 1972486 1973390 1973395) (-1146 "STACK.spad" 1971824 1971835 1972080 1972107) (-1145 "SREGSET.spad" 1969528 1969545 1971470 1971497) (-1144 "SRDCMPK.spad" 1968073 1968093 1969518 1969523) (-1143 "SRAGG.spad" 1963170 1963179 1968041 1968068) (-1142 "SRAGG.spad" 1958287 1958298 1963160 1963165) (-1141 "SQMATRIX.spad" 1955903 1955921 1956819 1956906) (-1140 "SPLTREE.spad" 1950455 1950468 1955339 1955366) (-1139 "SPLNODE.spad" 1947043 1947056 1950445 1950450) (-1138 "SPFCAT.spad" 1945820 1945829 1947033 1947038) (-1137 "SPECOUT.spad" 1944370 1944379 1945810 1945815) (-1136 "SPADXPT.spad" 1936509 1936518 1944360 1944365) (-1135 "spad-parser.spad" 1935974 1935983 1936499 1936504) (-1134 "SPADAST.spad" 1935675 1935684 1935964 1935969) (-1133 "SPACEC.spad" 1919688 1919699 1935665 1935670) (-1132 "SPACE3.spad" 1919464 1919475 1919678 1919683) (-1131 "SORTPAK.spad" 1919009 1919022 1919420 1919425) (-1130 "SOLVETRA.spad" 1916766 1916777 1918999 1919004) (-1129 "SOLVESER.spad" 1915286 1915297 1916756 1916761) (-1128 "SOLVERAD.spad" 1911296 1911307 1915276 1915281) (-1127 "SOLVEFOR.spad" 1909716 1909734 1911286 1911291) (-1126 "SNTSCAT.spad" 1909316 1909333 1909684 1909711) (-1125 "SMTS.spad" 1907576 1907602 1908881 1908978) (-1124 "SMP.spad" 1905051 1905071 1905441 1905568) (-1123 "SMITH.spad" 1903894 1903919 1905041 1905046) (-1122 "SMATCAT.spad" 1902004 1902034 1903838 1903889) (-1121 "SMATCAT.spad" 1900046 1900078 1901882 1901887) (-1120 "SKAGG.spad" 1899007 1899018 1900014 1900041) (-1119 "SINT.spad" 1897833 1897842 1898873 1899002) (-1118 "SIMPAN.spad" 1897561 1897570 1897823 1897828) (-1117 "SIG.spad" 1896889 1896898 1897551 1897556) (-1116 "SIGNRF.spad" 1895997 1896008 1896879 1896884) (-1115 "SIGNEF.spad" 1895266 1895283 1895987 1895992) (-1114 "SIGAST.spad" 1894647 1894656 1895256 1895261) (-1113 "SHP.spad" 1892565 1892580 1894603 1894608) (-1112 "SHDP.spad" 1882276 1882303 1882785 1882916) (-1111 "SGROUP.spad" 1881884 1881893 1882266 1882271) (-1110 "SGROUP.spad" 1881490 1881501 1881874 1881879) (-1109 "SGCF.spad" 1874371 1874380 1881480 1881485) (-1108 "SFRTCAT.spad" 1873299 1873316 1874339 1874366) (-1107 "SFRGCD.spad" 1872362 1872382 1873289 1873294) (-1106 "SFQCMPK.spad" 1866999 1867019 1872352 1872357) (-1105 "SFORT.spad" 1866434 1866448 1866989 1866994) (-1104 "SEXOF.spad" 1866277 1866317 1866424 1866429) (-1103 "SEX.spad" 1866169 1866178 1866267 1866272) (-1102 "SEXCAT.spad" 1863720 1863760 1866159 1866164) (-1101 "SET.spad" 1862020 1862031 1863141 1863180) (-1100 "SETMN.spad" 1860454 1860471 1862010 1862015) (-1099 "SETCAT.spad" 1859776 1859785 1860444 1860449) (-1098 "SETCAT.spad" 1859096 1859107 1859766 1859771) (-1097 "SETAGG.spad" 1855617 1855628 1859076 1859091) (-1096 "SETAGG.spad" 1852146 1852159 1855607 1855612) (-1095 "SEQAST.spad" 1851849 1851858 1852136 1852141) (-1094 "SEGXCAT.spad" 1850971 1850984 1851839 1851844) (-1093 "SEG.spad" 1850784 1850795 1850890 1850895) (-1092 "SEGCAT.spad" 1849691 1849702 1850774 1850779) (-1091 "SEGBIND.spad" 1848763 1848774 1849646 1849651) (-1090 "SEGBIND2.spad" 1848459 1848472 1848753 1848758) (-1089 "SEGAST.spad" 1848173 1848182 1848449 1848454) (-1088 "SEG2.spad" 1847598 1847611 1848129 1848134) (-1087 "SDVAR.spad" 1846874 1846885 1847588 1847593) (-1086 "SDPOL.spad" 1844300 1844311 1844591 1844718) (-1085 "SCPKG.spad" 1842379 1842390 1844290 1844295) (-1084 "SCOPE.spad" 1841528 1841537 1842369 1842374) (-1083 "SCACHE.spad" 1840210 1840221 1841518 1841523) (-1082 "SASTCAT.spad" 1840119 1840128 1840200 1840205) (-1081 "SAOS.spad" 1839991 1840000 1840109 1840114) (-1080 "SAERFFC.spad" 1839704 1839724 1839981 1839986) (-1079 "SAE.spad" 1837879 1837895 1838490 1838625) (-1078 "SAEFACT.spad" 1837580 1837600 1837869 1837874) (-1077 "RURPK.spad" 1835221 1835237 1837570 1837575) (-1076 "RULESET.spad" 1834662 1834686 1835211 1835216) (-1075 "RULE.spad" 1832866 1832890 1834652 1834657) (-1074 "RULECOLD.spad" 1832718 1832731 1832856 1832861) (-1073 "RTVALUE.spad" 1832451 1832460 1832708 1832713) (-1072 "RSTRCAST.spad" 1832168 1832177 1832441 1832446) (-1071 "RSETGCD.spad" 1828546 1828566 1832158 1832163) (-1070 "RSETCAT.spad" 1818330 1818347 1828514 1828541) (-1069 "RSETCAT.spad" 1808134 1808153 1818320 1818325) (-1068 "RSDCMPK.spad" 1806586 1806606 1808124 1808129) (-1067 "RRCC.spad" 1804970 1805000 1806576 1806581) (-1066 "RRCC.spad" 1803352 1803384 1804960 1804965) (-1065 "RPTAST.spad" 1803054 1803063 1803342 1803347) (-1064 "RPOLCAT.spad" 1782414 1782429 1802922 1803049) (-1063 "RPOLCAT.spad" 1761488 1761505 1781998 1782003) (-1062 "ROUTINE.spad" 1757351 1757360 1760135 1760162) (-1061 "ROMAN.spad" 1756679 1756688 1757217 1757346) (-1060 "ROIRC.spad" 1755759 1755791 1756669 1756674) (-1059 "RNS.spad" 1754662 1754671 1755661 1755754) (-1058 "RNS.spad" 1753651 1753662 1754652 1754657) (-1057 "RNG.spad" 1753386 1753395 1753641 1753646) (-1056 "RMODULE.spad" 1753151 1753162 1753376 1753381) (-1055 "RMCAT2.spad" 1752559 1752616 1753141 1753146) (-1054 "RMATRIX.spad" 1751383 1751402 1751726 1751765) (-1053 "RMATCAT.spad" 1746916 1746947 1751339 1751378) (-1052 "RMATCAT.spad" 1742339 1742372 1746764 1746769) (-1051 "RLINSET.spad" 1741733 1741744 1742329 1742334) (-1050 "RINTERP.spad" 1741621 1741641 1741723 1741728) (-1049 "RING.spad" 1741091 1741100 1741601 1741616) (-1048 "RING.spad" 1740569 1740580 1741081 1741086) (-1047 "RIDIST.spad" 1739953 1739962 1740559 1740564) (-1046 "RGCHAIN.spad" 1738532 1738548 1739438 1739465) (-1045 "RGBCSPC.spad" 1738313 1738325 1738522 1738527) (-1044 "RGBCMDL.spad" 1737843 1737855 1738303 1738308) (-1043 "RF.spad" 1735457 1735468 1737833 1737838) (-1042 "RFFACTOR.spad" 1734919 1734930 1735447 1735452) (-1041 "RFFACT.spad" 1734654 1734666 1734909 1734914) (-1040 "RFDIST.spad" 1733642 1733651 1734644 1734649) (-1039 "RETSOL.spad" 1733059 1733072 1733632 1733637) (-1038 "RETRACT.spad" 1732487 1732498 1733049 1733054) (-1037 "RETRACT.spad" 1731913 1731926 1732477 1732482) (-1036 "RETAST.spad" 1731725 1731734 1731903 1731908) (-1035 "RESULT.spad" 1729785 1729794 1730372 1730399) (-1034 "RESRING.spad" 1729132 1729179 1729723 1729780) (-1033 "RESLATC.spad" 1728456 1728467 1729122 1729127) (-1032 "REPSQ.spad" 1728185 1728196 1728446 1728451) (-1031 "REP.spad" 1725737 1725746 1728175 1728180) (-1030 "REPDB.spad" 1725442 1725453 1725727 1725732) (-1029 "REP2.spad" 1715014 1715025 1725284 1725289) (-1028 "REP1.spad" 1709004 1709015 1714964 1714969) (-1027 "REGSET.spad" 1706801 1706818 1708650 1708677) (-1026 "REF.spad" 1706130 1706141 1706756 1706761) (-1025 "REDORDER.spad" 1705306 1705323 1706120 1706125) (-1024 "RECLOS.spad" 1704089 1704109 1704793 1704886) (-1023 "REALSOLV.spad" 1703221 1703230 1704079 1704084) (-1022 "REAL.spad" 1703093 1703102 1703211 1703216) (-1021 "REAL0Q.spad" 1700375 1700390 1703083 1703088) (-1020 "REAL0.spad" 1697203 1697218 1700365 1700370) (-1019 "RDUCEAST.spad" 1696924 1696933 1697193 1697198) (-1018 "RDIV.spad" 1696575 1696600 1696914 1696919) (-1017 "RDIST.spad" 1696138 1696149 1696565 1696570) (-1016 "RDETRS.spad" 1694934 1694952 1696128 1696133) (-1015 "RDETR.spad" 1693041 1693059 1694924 1694929) (-1014 "RDEEFS.spad" 1692114 1692131 1693031 1693036) (-1013 "RDEEF.spad" 1691110 1691127 1692104 1692109) (-1012 "RCFIELD.spad" 1688296 1688305 1691012 1691105) (-1011 "RCFIELD.spad" 1685568 1685579 1688286 1688291) (-1010 "RCAGG.spad" 1683480 1683491 1685558 1685563) (-1009 "RCAGG.spad" 1681319 1681332 1683399 1683404) (-1008 "RATRET.spad" 1680679 1680690 1681309 1681314) (-1007 "RATFACT.spad" 1680371 1680383 1680669 1680674) (-1006 "RANDSRC.spad" 1679690 1679699 1680361 1680366) (-1005 "RADUTIL.spad" 1679444 1679453 1679680 1679685) (-1004 "RADIX.spad" 1676345 1676359 1677911 1678004) (-1003 "RADFF.spad" 1674758 1674795 1674877 1675033) (-1002 "RADCAT.spad" 1674351 1674360 1674748 1674753) (-1001 "RADCAT.spad" 1673942 1673953 1674341 1674346) (-1000 "QUEUE.spad" 1673284 1673295 1673549 1673576) (-999 "QUAT.spad" 1671866 1671876 1672208 1672273) (-998 "QUATCT2.spad" 1671485 1671503 1671856 1671861) (-997 "QUATCAT.spad" 1669650 1669660 1671415 1671480) (-996 "QUATCAT.spad" 1667566 1667578 1669333 1669338) (-995 "QUAGG.spad" 1666392 1666402 1667534 1667561) (-994 "QQUTAST.spad" 1666161 1666169 1666382 1666387) (-993 "QFORM.spad" 1665624 1665638 1666151 1666156) (-992 "QFCAT.spad" 1664327 1664337 1665526 1665619) (-991 "QFCAT.spad" 1662621 1662633 1663822 1663827) (-990 "QFCAT2.spad" 1662312 1662328 1662611 1662616) (-989 "QEQUAT.spad" 1661869 1661877 1662302 1662307) (-988 "QCMPACK.spad" 1656616 1656635 1661859 1661864) (-987 "QALGSET.spad" 1652691 1652723 1656530 1656535) (-986 "QALGSET2.spad" 1650687 1650705 1652681 1652686) (-985 "PWFFINTB.spad" 1647997 1648018 1650677 1650682) (-984 "PUSHVAR.spad" 1647326 1647345 1647987 1647992) (-983 "PTRANFN.spad" 1643452 1643462 1647316 1647321) (-982 "PTPACK.spad" 1640540 1640550 1643442 1643447) (-981 "PTFUNC2.spad" 1640361 1640375 1640530 1640535) (-980 "PTCAT.spad" 1639610 1639620 1640329 1640356) (-979 "PSQFR.spad" 1638917 1638941 1639600 1639605) (-978 "PSEUDLIN.spad" 1637775 1637785 1638907 1638912) (-977 "PSETPK.spad" 1623208 1623224 1637653 1637658) (-976 "PSETCAT.spad" 1617128 1617151 1623188 1623203) (-975 "PSETCAT.spad" 1611022 1611047 1617084 1617089) (-974 "PSCURVE.spad" 1610005 1610013 1611012 1611017) (-973 "PSCAT.spad" 1608772 1608801 1609903 1610000) (-972 "PSCAT.spad" 1607629 1607660 1608762 1608767) (-971 "PRTITION.spad" 1606574 1606582 1607619 1607624) (-970 "PRTDAST.spad" 1606293 1606301 1606564 1606569) (-969 "PRS.spad" 1595855 1595872 1606249 1606254) (-968 "PRQAGG.spad" 1595286 1595296 1595823 1595850) (-967 "PROPLOG.spad" 1594581 1594589 1595276 1595281) (-966 "PROPFRML.spad" 1593389 1593400 1594571 1594576) (-965 "PROPERTY.spad" 1592875 1592883 1593379 1593384) (-964 "PRODUCT.spad" 1590555 1590567 1590841 1590896) (-963 "PR.spad" 1588941 1588953 1589646 1589773) (-962 "PRINT.spad" 1588693 1588701 1588931 1588936) (-961 "PRIMES.spad" 1586944 1586954 1588683 1588688) (-960 "PRIMELT.spad" 1584925 1584939 1586934 1586939) (-959 "PRIMCAT.spad" 1584548 1584556 1584915 1584920) (-958 "PRIMARR.spad" 1583553 1583563 1583731 1583758) (-957 "PRIMARR2.spad" 1582276 1582288 1583543 1583548) (-956 "PREASSOC.spad" 1581648 1581660 1582266 1582271) (-955 "PPCURVE.spad" 1580785 1580793 1581638 1581643) (-954 "PORTNUM.spad" 1580560 1580568 1580775 1580780) (-953 "POLYROOT.spad" 1579389 1579411 1580516 1580521) (-952 "POLY.spad" 1576722 1576732 1577239 1577366) (-951 "POLYLIFT.spad" 1575983 1576006 1576712 1576717) (-950 "POLYCATQ.spad" 1574085 1574107 1575973 1575978) (-949 "POLYCAT.spad" 1567491 1567512 1573953 1574080) (-948 "POLYCAT.spad" 1560235 1560258 1566699 1566704) (-947 "POLY2UP.spad" 1559683 1559697 1560225 1560230) (-946 "POLY2.spad" 1559278 1559290 1559673 1559678) (-945 "POLUTIL.spad" 1558219 1558248 1559234 1559239) (-944 "POLTOPOL.spad" 1556967 1556982 1558209 1558214) (-943 "POINT.spad" 1555805 1555815 1555892 1555919) (-942 "PNTHEORY.spad" 1552471 1552479 1555795 1555800) (-941 "PMTOOLS.spad" 1551228 1551242 1552461 1552466) (-940 "PMSYM.spad" 1550773 1550783 1551218 1551223) (-939 "PMQFCAT.spad" 1550360 1550374 1550763 1550768) (-938 "PMPRED.spad" 1549829 1549843 1550350 1550355) (-937 "PMPREDFS.spad" 1549273 1549295 1549819 1549824) (-936 "PMPLCAT.spad" 1548343 1548361 1549205 1549210) (-935 "PMLSAGG.spad" 1547924 1547938 1548333 1548338) (-934 "PMKERNEL.spad" 1547491 1547503 1547914 1547919) (-933 "PMINS.spad" 1547067 1547077 1547481 1547486) (-932 "PMFS.spad" 1546640 1546658 1547057 1547062) (-931 "PMDOWN.spad" 1545926 1545940 1546630 1546635) (-930 "PMASS.spad" 1544934 1544942 1545916 1545921) (-929 "PMASSFS.spad" 1543899 1543915 1544924 1544929) (-928 "PLOTTOOL.spad" 1543679 1543687 1543889 1543894) (-927 "PLOT.spad" 1538510 1538518 1543669 1543674) (-926 "PLOT3D.spad" 1534930 1534938 1538500 1538505) (-925 "PLOT1.spad" 1534071 1534081 1534920 1534925) (-924 "PLEQN.spad" 1521287 1521314 1534061 1534066) (-923 "PINTERP.spad" 1520903 1520922 1521277 1521282) (-922 "PINTERPA.spad" 1520685 1520701 1520893 1520898) (-921 "PI.spad" 1520292 1520300 1520659 1520680) (-920 "PID.spad" 1519248 1519256 1520218 1520287) (-919 "PICOERCE.spad" 1518905 1518915 1519238 1519243) (-918 "PGROEB.spad" 1517502 1517516 1518895 1518900) (-917 "PGE.spad" 1508755 1508763 1517492 1517497) (-916 "PGCD.spad" 1507637 1507654 1508745 1508750) (-915 "PFRPAC.spad" 1506780 1506790 1507627 1507632) (-914 "PFR.spad" 1503437 1503447 1506682 1506775) (-913 "PFOTOOLS.spad" 1502695 1502711 1503427 1503432) (-912 "PFOQ.spad" 1502065 1502083 1502685 1502690) (-911 "PFO.spad" 1501484 1501511 1502055 1502060) (-910 "PF.spad" 1501058 1501070 1501289 1501382) (-909 "PFECAT.spad" 1498724 1498732 1500984 1501053) (-908 "PFECAT.spad" 1496418 1496428 1498680 1498685) (-907 "PFBRU.spad" 1494288 1494300 1496408 1496413) (-906 "PFBR.spad" 1491826 1491849 1494278 1494283) (-905 "PERM.spad" 1487507 1487517 1491656 1491671) (-904 "PERMGRP.spad" 1482243 1482253 1487497 1487502) (-903 "PERMCAT.spad" 1480795 1480805 1482223 1482238) (-902 "PERMAN.spad" 1479327 1479341 1480785 1480790) (-901 "PENDTREE.spad" 1478666 1478676 1478956 1478961) (-900 "PDRING.spad" 1477157 1477167 1478646 1478661) (-899 "PDRING.spad" 1475656 1475668 1477147 1477152) (-898 "PDEPROB.spad" 1474671 1474679 1475646 1475651) (-897 "PDEPACK.spad" 1468673 1468681 1474661 1474666) (-896 "PDECOMP.spad" 1468135 1468152 1468663 1468668) (-895 "PDECAT.spad" 1466489 1466497 1468125 1468130) (-894 "PCOMP.spad" 1466340 1466353 1466479 1466484) (-893 "PBWLB.spad" 1464922 1464939 1466330 1466335) (-892 "PATTERN.spad" 1459353 1459363 1464912 1464917) (-891 "PATTERN2.spad" 1459089 1459101 1459343 1459348) (-890 "PATTERN1.spad" 1457391 1457407 1459079 1459084) (-889 "PATRES.spad" 1454938 1454950 1457381 1457386) (-888 "PATRES2.spad" 1454600 1454614 1454928 1454933) (-887 "PATMATCH.spad" 1452757 1452788 1454308 1454313) (-886 "PATMAB.spad" 1452182 1452192 1452747 1452752) (-885 "PATLRES.spad" 1451266 1451280 1452172 1452177) (-884 "PATAB.spad" 1451030 1451040 1451256 1451261) (-883 "PARTPERM.spad" 1448392 1448400 1451020 1451025) (-882 "PARSURF.spad" 1447820 1447848 1448382 1448387) (-881 "PARSU2.spad" 1447615 1447631 1447810 1447815) (-880 "script-parser.spad" 1447135 1447143 1447605 1447610) (-879 "PARSCURV.spad" 1446563 1446591 1447125 1447130) (-878 "PARSC2.spad" 1446352 1446368 1446553 1446558) (-877 "PARPCURV.spad" 1445810 1445838 1446342 1446347) (-876 "PARPC2.spad" 1445599 1445615 1445800 1445805) (-875 "PAN2EXPR.spad" 1445011 1445019 1445589 1445594) (-874 "PALETTE.spad" 1443981 1443989 1445001 1445006) (-873 "PAIR.spad" 1442964 1442977 1443569 1443574) (-872 "PADICRC.spad" 1440294 1440312 1441469 1441562) (-871 "PADICRAT.spad" 1438309 1438321 1438530 1438623) (-870 "PADIC.spad" 1438004 1438016 1438235 1438304) (-869 "PADICCT.spad" 1436545 1436557 1437930 1437999) (-868 "PADEPAC.spad" 1435224 1435243 1436535 1436540) (-867 "PADE.spad" 1433964 1433980 1435214 1435219) (-866 "OWP.spad" 1433204 1433234 1433822 1433889) (-865 "OVERSET.spad" 1432777 1432785 1433194 1433199) (-864 "OVAR.spad" 1432558 1432581 1432767 1432772) (-863 "OUT.spad" 1431642 1431650 1432548 1432553) (-862 "OUTFORM.spad" 1420938 1420946 1431632 1431637) (-861 "OUTBFILE.spad" 1420356 1420364 1420928 1420933) (-860 "OUTBCON.spad" 1419354 1419362 1420346 1420351) (-859 "OUTBCON.spad" 1418350 1418360 1419344 1419349) (-858 "OSI.spad" 1417825 1417833 1418340 1418345) (-857 "OSGROUP.spad" 1417743 1417751 1417815 1417820) (-856 "ORTHPOL.spad" 1416204 1416214 1417660 1417665) (-855 "OREUP.spad" 1415657 1415685 1415884 1415923) (-854 "ORESUP.spad" 1414956 1414980 1415337 1415376) (-853 "OREPCTO.spad" 1412775 1412787 1414876 1414881) (-852 "OREPCAT.spad" 1406832 1406842 1412731 1412770) (-851 "OREPCAT.spad" 1400779 1400791 1406680 1406685) (-850 "ORDSET.spad" 1399945 1399953 1400769 1400774) (-849 "ORDSET.spad" 1399109 1399119 1399935 1399940) (-848 "ORDRING.spad" 1398499 1398507 1399089 1399104) (-847 "ORDRING.spad" 1397897 1397907 1398489 1398494) (-846 "ORDMON.spad" 1397752 1397760 1397887 1397892) (-845 "ORDFUNS.spad" 1396878 1396894 1397742 1397747) (-844 "ORDFIN.spad" 1396698 1396706 1396868 1396873) (-843 "ORDCOMP.spad" 1395163 1395173 1396245 1396274) (-842 "ORDCOMP2.spad" 1394448 1394460 1395153 1395158) (-841 "OPTPROB.spad" 1393086 1393094 1394438 1394443) (-840 "OPTPACK.spad" 1385471 1385479 1393076 1393081) (-839 "OPTCAT.spad" 1383146 1383154 1385461 1385466) (-838 "OPSIG.spad" 1382798 1382806 1383136 1383141) (-837 "OPQUERY.spad" 1382347 1382355 1382788 1382793) (-836 "OP.spad" 1382089 1382099 1382169 1382236) (-835 "OPERCAT.spad" 1381553 1381563 1382079 1382084) (-834 "OPERCAT.spad" 1381015 1381027 1381543 1381548) (-833 "ONECOMP.spad" 1379760 1379770 1380562 1380591) (-832 "ONECOMP2.spad" 1379178 1379190 1379750 1379755) (-831 "OMSERVER.spad" 1378180 1378188 1379168 1379173) (-830 "OMSAGG.spad" 1377968 1377978 1378136 1378175) (-829 "OMPKG.spad" 1376580 1376588 1377958 1377963) (-828 "OM.spad" 1375545 1375553 1376570 1376575) (-827 "OMLO.spad" 1374970 1374982 1375431 1375470) (-826 "OMEXPR.spad" 1374804 1374814 1374960 1374965) (-825 "OMERR.spad" 1374347 1374355 1374794 1374799) (-824 "OMERRK.spad" 1373381 1373389 1374337 1374342) (-823 "OMENC.spad" 1372725 1372733 1373371 1373376) (-822 "OMDEV.spad" 1367014 1367022 1372715 1372720) (-821 "OMCONN.spad" 1366423 1366431 1367004 1367009) (-820 "OINTDOM.spad" 1366186 1366194 1366349 1366418) (-819 "OFMONOID.spad" 1362373 1362383 1366176 1366181) (-818 "ODVAR.spad" 1361634 1361644 1362363 1362368) (-817 "ODR.spad" 1361278 1361304 1361446 1361595) (-816 "ODPOL.spad" 1358660 1358670 1359000 1359127) (-815 "ODP.spad" 1348507 1348527 1348880 1349011) (-814 "ODETOOLS.spad" 1347090 1347109 1348497 1348502) (-813 "ODESYS.spad" 1344740 1344757 1347080 1347085) (-812 "ODERTRIC.spad" 1340681 1340698 1344697 1344702) (-811 "ODERED.spad" 1340068 1340092 1340671 1340676) (-810 "ODERAT.spad" 1337619 1337636 1340058 1340063) (-809 "ODEPRRIC.spad" 1334510 1334532 1337609 1337614) (-808 "ODEPROB.spad" 1333767 1333775 1334500 1334505) (-807 "ODEPRIM.spad" 1331041 1331063 1333757 1333762) (-806 "ODEPAL.spad" 1330417 1330441 1331031 1331036) (-805 "ODEPACK.spad" 1317019 1317027 1330407 1330412) (-804 "ODEINT.spad" 1316450 1316466 1317009 1317014) (-803 "ODEIFTBL.spad" 1313845 1313853 1316440 1316445) (-802 "ODEEF.spad" 1309212 1309228 1313835 1313840) (-801 "ODECONST.spad" 1308731 1308749 1309202 1309207) (-800 "ODECAT.spad" 1307327 1307335 1308721 1308726) (-799 "OCT.spad" 1305465 1305475 1306181 1306220) (-798 "OCTCT2.spad" 1305109 1305130 1305455 1305460) (-797 "OC.spad" 1302883 1302893 1305065 1305104) (-796 "OC.spad" 1300382 1300394 1302566 1302571) (-795 "OCAMON.spad" 1300230 1300238 1300372 1300377) (-794 "OASGP.spad" 1300045 1300053 1300220 1300225) (-793 "OAMONS.spad" 1299565 1299573 1300035 1300040) (-792 "OAMON.spad" 1299426 1299434 1299555 1299560) (-791 "OAGROUP.spad" 1299288 1299296 1299416 1299421) (-790 "NUMTUBE.spad" 1298875 1298891 1299278 1299283) (-789 "NUMQUAD.spad" 1286737 1286745 1298865 1298870) (-788 "NUMODE.spad" 1277873 1277881 1286727 1286732) (-787 "NUMINT.spad" 1275431 1275439 1277863 1277868) (-786 "NUMFMT.spad" 1274271 1274279 1275421 1275426) (-785 "NUMERIC.spad" 1266343 1266353 1274076 1274081) (-784 "NTSCAT.spad" 1264845 1264861 1266311 1266338) (-783 "NTPOLFN.spad" 1264390 1264400 1264762 1264767) (-782 "NSUP.spad" 1257436 1257446 1261976 1262129) (-781 "NSUP2.spad" 1256828 1256840 1257426 1257431) (-780 "NSMP.spad" 1253059 1253078 1253367 1253494) (-779 "NREP.spad" 1251431 1251445 1253049 1253054) (-778 "NPCOEF.spad" 1250677 1250697 1251421 1251426) (-777 "NORMRETR.spad" 1250275 1250314 1250667 1250672) (-776 "NORMPK.spad" 1248177 1248196 1250265 1250270) (-775 "NORMMA.spad" 1247865 1247891 1248167 1248172) (-774 "NONE.spad" 1247606 1247614 1247855 1247860) (-773 "NONE1.spad" 1247282 1247292 1247596 1247601) (-772 "NODE1.spad" 1246751 1246767 1247272 1247277) (-771 "NNI.spad" 1245638 1245646 1246725 1246746) (-770 "NLINSOL.spad" 1244260 1244270 1245628 1245633) (-769 "NIPROB.spad" 1242801 1242809 1244250 1244255) (-768 "NFINTBAS.spad" 1240261 1240278 1242791 1242796) (-767 "NETCLT.spad" 1240235 1240246 1240251 1240256) (-766 "NCODIV.spad" 1238433 1238449 1240225 1240230) (-765 "NCNTFRAC.spad" 1238075 1238089 1238423 1238428) (-764 "NCEP.spad" 1236235 1236249 1238065 1238070) (-763 "NASRING.spad" 1235831 1235839 1236225 1236230) (-762 "NASRING.spad" 1235425 1235435 1235821 1235826) (-761 "NARNG.spad" 1234769 1234777 1235415 1235420) (-760 "NARNG.spad" 1234111 1234121 1234759 1234764) (-759 "NAGSP.spad" 1233184 1233192 1234101 1234106) (-758 "NAGS.spad" 1222709 1222717 1233174 1233179) (-757 "NAGF07.spad" 1221102 1221110 1222699 1222704) (-756 "NAGF04.spad" 1215334 1215342 1221092 1221097) (-755 "NAGF02.spad" 1209143 1209151 1215324 1215329) (-754 "NAGF01.spad" 1204746 1204754 1209133 1209138) (-753 "NAGE04.spad" 1198206 1198214 1204736 1204741) (-752 "NAGE02.spad" 1188548 1188556 1198196 1198201) (-751 "NAGE01.spad" 1184432 1184440 1188538 1188543) (-750 "NAGD03.spad" 1182352 1182360 1184422 1184427) (-749 "NAGD02.spad" 1174883 1174891 1182342 1182347) (-748 "NAGD01.spad" 1168996 1169004 1174873 1174878) (-747 "NAGC06.spad" 1164783 1164791 1168986 1168991) (-746 "NAGC05.spad" 1163252 1163260 1164773 1164778) (-745 "NAGC02.spad" 1162507 1162515 1163242 1163247) (-744 "NAALG.spad" 1162042 1162052 1162475 1162502) (-743 "NAALG.spad" 1161597 1161609 1162032 1162037) (-742 "MULTSQFR.spad" 1158555 1158572 1161587 1161592) (-741 "MULTFACT.spad" 1157938 1157955 1158545 1158550) (-740 "MTSCAT.spad" 1155972 1155993 1157836 1157933) (-739 "MTHING.spad" 1155629 1155639 1155962 1155967) (-738 "MSYSCMD.spad" 1155063 1155071 1155619 1155624) (-737 "MSET.spad" 1153005 1153015 1154769 1154808) (-736 "MSETAGG.spad" 1152850 1152860 1152973 1153000) (-735 "MRING.spad" 1149821 1149833 1152558 1152625) (-734 "MRF2.spad" 1149389 1149403 1149811 1149816) (-733 "MRATFAC.spad" 1148935 1148952 1149379 1149384) (-732 "MPRFF.spad" 1146965 1146984 1148925 1148930) (-731 "MPOLY.spad" 1144436 1144451 1144795 1144922) (-730 "MPCPF.spad" 1143700 1143719 1144426 1144431) (-729 "MPC3.spad" 1143515 1143555 1143690 1143695) (-728 "MPC2.spad" 1143157 1143190 1143505 1143510) (-727 "MONOTOOL.spad" 1141492 1141509 1143147 1143152) (-726 "MONOID.spad" 1140811 1140819 1141482 1141487) (-725 "MONOID.spad" 1140128 1140138 1140801 1140806) (-724 "MONOGEN.spad" 1138874 1138887 1139988 1140123) (-723 "MONOGEN.spad" 1137642 1137657 1138758 1138763) (-722 "MONADWU.spad" 1135656 1135664 1137632 1137637) (-721 "MONADWU.spad" 1133668 1133678 1135646 1135651) (-720 "MONAD.spad" 1132812 1132820 1133658 1133663) (-719 "MONAD.spad" 1131954 1131964 1132802 1132807) (-718 "MOEBIUS.spad" 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(-70 "ASP30.spad" 79256 79269 80354 80359) (-69 "ASP29.spad" 78722 78735 79246 79251) (-68 "ASP28.spad" 69995 70008 78712 78717) (-67 "ASP27.spad" 68892 68905 69985 69990) (-66 "ASP24.spad" 67979 67992 68882 68887) (-65 "ASP20.spad" 67443 67456 67969 67974) (-64 "ASP1.spad" 66824 66837 67433 67438) (-63 "ASP19.spad" 61510 61523 66814 66819) (-62 "ASP12.spad" 60924 60937 61500 61505) (-61 "ASP10.spad" 60195 60208 60914 60919) (-60 "ARRAY2.spad" 59555 59564 59802 59829) (-59 "ARRAY1.spad" 58390 58399 58738 58765) (-58 "ARRAY12.spad" 57059 57070 58380 58385) (-57 "ARR2CAT.spad" 52721 52742 57027 57054) (-56 "ARR2CAT.spad" 48403 48426 52711 52716) (-55 "ARITY.spad" 47775 47782 48393 48398) (-54 "APPRULE.spad" 47019 47041 47765 47770) (-53 "APPLYORE.spad" 46634 46647 47009 47014) (-52 "ANY.spad" 45491 45498 46624 46629) (-51 "ANY1.spad" 44562 44571 45481 45486) (-50 "ANTISYM.spad" 43001 43017 44542 44557) (-49 "ANON.spad" 42694 42701 42991 42996) (-48 "AN.spad" 40995 41002 42510 42603) (-47 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T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566)))))) (((|#1|) . T) (($) . T)) ((((-566)) . T)) ((((-566)) . T)) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) ((((-566)) . T)) ((((-566)) . T)) ((((-409 (-566))) . T) (($) . T)) @@ -230,13 +230,13 @@ ((((-862)) . T)) ((((-862)) . T)) (((|#1| |#1|) . T)) -(((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566)))) ((|#1| |#1|) . T) (($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) -((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1| |#1|) . 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T) (($) -2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -247,10 +247,10 @@ ((((-169 (-225))) |has| |#1| (-1022)) (((-169 (-381))) |has| |#1| (-1022)) (((-538)) |has| |#1| (-614 (-538))) (((-1171 |#1|)) . T) (((-892 (-566))) |has| |#1| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381))))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . 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T)) (((|#1| (-971)) . T)) ((((-566)) . T) ((|#2|) . T)) @@ -349,7 +349,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1150)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) (|has| (-1250 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1250 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -361,27 +361,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-566)) |has| |#2| (-639 (-566)))) -((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-818 (-1175))) . T) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . T)) +((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-818 (-1175))) . T) (($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . 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T)) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-862)) . T)) ((((-862)) . T)) (|has| (-1249 |#2| |#3| |#4|) (-147)) @@ -392,16 +392,16 @@ ((((-862)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((|#1|) . T)) ((((-566) |#1|) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) (((|#1|) . 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T)) ((((-862)) . T)) ((((-862)) . T)) @@ -811,34 +811,34 @@ (|has| |#1| (-1099)) (((|#2|) . T)) ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566))))) -(((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2809 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2809 (|has| |#3| (-172)) (|has| |#3| (-365)))) ((((-862)) . T)) (((|#1|) . 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T)) (|has| (-409 |#2|) (-147)) (|has| (-409 |#2|) (-145)) @@ -851,15 +851,15 @@ (|has| |#1| (-558)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-862)) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) -((((-390) (-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-390) (-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#2| (-1150)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) @@ -877,7 +877,7 @@ ((((-390) (-1157)) . T)) (|has| |#1| (-558)) ((((-566) |#1|) . T)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) (((|#2|) . T)) @@ -893,7 +893,7 @@ ((((-644 |#1|)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-850)) (|has| |#1| (-1099))) (((|#2|) |has| |#2| (-310 |#2|))) (((#0=(-566) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -903,14 +903,14 @@ (((#0=(-566) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) . T)) (|has| |#2| (-370)) -(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-850)) (|has| |#1| (-1099))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) |has| |#1| (-172))) (((|#1| |#2|) . T)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1| |#2|) . T)) ((((-862)) . T)) @@ -918,8 +918,8 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((($) . T) (((-409 (-566))) -2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-862)) . T)) ((((-1173 |#1| |#2| |#3|) $) -12 (|has| (-1173 |#1| |#2| |#3|) (-287 (-1173 |#1| |#2| |#3|) (-1173 |#1| |#2| |#3|))) (|has| |#1| (-365))) (($ $) . T)) ((($ $) . T)) @@ -931,14 +931,14 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-566)) . T) (($) . T)) -((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((($) . T) (((-566)) . T) ((|#2|) . T)) ((((-566)) . T) (($) . T) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566))))) ((((-409 (-566))) . T) (((-566)) . T)) ((((-566) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-112)) . T)) @@ -947,31 +947,31 @@ ((((-862)) . T)) ((((-1180)) . T)) (|has| |#1| (-820)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) ((|#1|) . T)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#2|) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) . 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T)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-558))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-1264 |#1|) (-1264 |#1|)) . T)) ((((-566) (-144)) . T)) ((($) . T)) -(-2805 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2809 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2809 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-1180)) . T) (((-862)) . T)) ((((-1180)) . T)) ((((-862)) . T)) @@ -979,20 +979,20 @@ (((|#1| (-971)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((($) . T) (((-566)) . T) (((-870 |#1|)) . T) (((-409 (-566))) . T)) (((|#1|) . T)) (|has| |#2| (-793)) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#2| (-848)) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) -(-2805 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) +(-2809 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-172)) ((|#4|) . T) (((-566)) . T)) (((|#2|) |has| |#2| (-172))) @@ -1004,7 +1004,7 @@ (((|#1|) . T)) ((((-409 (-566))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-409 (-566))) . T)) -((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) (|has| |#1| (-828)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) (|has| |#1| (-1099)) @@ -1015,13 +1015,13 @@ (((|#4|) |has| |#4| (-1099))) (((|#3|) |has| |#3| (-1099))) (|has| |#3| (-370)) -((($) |has| |#1| (-558)) ((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +((($) |has| |#1| (-558)) ((|#1|) . T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) ((((-862)) . T)) ((((-862)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558)))) +(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-365)) @@ -1029,19 +1029,19 @@ (((|#1|) |has| |#1| (-172))) ((((-409 (-566))) . T) (((-566)) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) -((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) +((($ $) -2809 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) ((($) . T) (((-566)) . T)) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) +((($) -2809 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) ((((-144)) . T)) ((((-144)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#) ((|#2|) . T) (((-566)) . T)) (((|#1| |#2| |#3|) . T)) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (((|#1|) |has| |#1| (-172))) (|has| $ (-147)) (|has| $ (-147)) @@ -1051,15 +1051,15 @@ ((((-862)) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-475)) (|has| |#1| (-558)) (|has| |#1| (-1049)) (|has| |#1| (-1111))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-475)) (|has| |#1| (-558)) (|has| |#1| (-1049)) (|has| |#1| (-1111))) ((($ $) |has| |#1| (-287 $ $)) ((|#1| $) |has| |#1| (-287 |#1| |#1|))) (((|#1| (-409 (-566))) . T)) (((|#1|) . T)) ((((-409 (-566))) . T) (((-566)) . T) (($) . T)) ((((-1175)) . T)) (|has| |#1| (-558)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-558)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) @@ -1070,7 +1070,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-848)) -(((|#2| (-240 (-3020 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-240 (-3018 |#1|) (-771)) (-864 |#1|)) . T)) (|has| |#3| (-848)) (((|#1| (-533 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1085,20 +1085,20 @@ (|has| |#1| (-145)) ((((-409 (-566))) |has| |#2| (-365)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2805 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2809 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2809 (|has| |#1| (-351)) (|has| |#1| (-370))) ((((-1141 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1049))) -(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) -(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) -(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) +(((|#2|) . T) (((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) +(-2809 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2809 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-699)) . T)) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (|has| |#1| (-558)) (((|#1|) . T)) (((|#1|) . T)) @@ -1122,11 +1122,11 @@ (((|#1| (-409 (-566))) . T)) (((|#3|) . T) (((-612 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#1|) . 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T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-409 |#2|)) . T)) ((((-409 (-566))) |has| #0=(-409 |#2|) (-1038 (-409 (-566)))) (((-566)) |has| #0# (-1038 (-566))) ((#0#) . T)) @@ -1479,11 +1479,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1521,7 +1521,7 @@ ((((-999 |#1|)) . T) ((|#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-409 (-566))) . T) (((-409 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1171 |#1|)) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) @@ -1530,8 +1530,8 @@ (((|#1|) . T) (((-566)) . T) (($) . T)) (((|#2|) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-566) |#2|) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) . T)) @@ -1544,7 +1544,7 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) #0#) |has| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (-310 (-2 (|:| -2004 |#1|) (|:| -3867 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1099)) (|has| |#1| (-38 (-409 (-566)))) @@ -1556,14 +1556,14 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) -((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) |has| |#1| (-172)) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) |has| |#1| (-172)) (($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1157) (-52)) . T)) (((|#1|) . T)) -((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T) (($) -2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2|) |has| |#2| (-172))) -((($) -2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((-566)) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) +((($) -2809 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((-566)) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) ((((-566) |#3|) . T)) ((((-566) (-144)) . T)) ((((-144)) . T)) @@ -1589,19 +1589,19 @@ (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1| |#2|) . T)) ((((-566) (-144)) . T)) -(((#0=(-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) #0#) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) -((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((#0=(-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) #0#) |has| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (-310 (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +((($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (|has| |#1| (-850)) (((|#2| (-771) (-1081)) . T)) (((|#1| |#2|) . T)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-558))) (|has| |#1| (-791)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2805 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) -(-2805 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) +(-2809 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) +(-2809 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1157) |#1|) . T)) @@ -1615,24 +1615,24 @@ (((|#3|) . T)) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-566)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-566)) . T) (($) . T)) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-566)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-566)) . T) (($) . T)) ((((-862)) . T)) -(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-850)) (|has| |#1| (-1099))) (((|#1|) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) (((-566)) . T) (($) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099))) (((-958 |#1|)) . T)) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099))) (((-958 |#1|)) . T)) (|has| |#1| (-848)) (|has| |#1| (-848)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-958 |#1|)) . T)) -(((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2809 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2809 (|has| |#3| (-172)) (|has| |#3| (-365)))) (|has| |#2| (-365)) (((|#1|) |has| |#1| (-172))) -(((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049))) (($) |has| |#4| (-172))) -(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049))) (($) |has| |#3| (-172))) +(((|#4|) -2809 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049))) (($) |has| |#4| (-172))) +(((|#3|) -2809 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049))) (($) |has| |#3| (-172))) (((|#2|) |has| |#2| (-1049))) ((((-1157) |#1|) . T)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) @@ -1641,8 +1641,8 @@ ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) ((((-390) (-1157)) . T)) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -((((-862)) -2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-613 (-862))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) (((-1264 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2050 (-1157)) (|:| -2849 #0#))) . T)) +((((-862)) -2809 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-613 (-862))) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-370)) (|has| |#2| (-726)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049)) (|has| |#2| (-1099))) (((-1264 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2004 (-1157)) (|:| -3867 #0#))) . T)) (((|#1|) . T)) ((((-862)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) @@ -1651,7 +1651,7 @@ ((((-566)) . T)) (|has| |#2| (-147)) (|has| |#1| (-475)) -(-2805 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2809 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (|has| |#1| (-365)) ((((-862)) . T)) (|has| |#1| (-38 (-409 (-566)))) @@ -1662,8 +1662,8 @@ (|has| |#1| (-848)) ((((-862)) . T)) (((|#2|) . T)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558)))) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2|) . T) (((-566)) . T) (((-819 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1672,7 +1672,7 @@ ((((-862)) . T)) ((((-862)) . T)) (|has| |#1| (-1099)) -(((|#2| (-484 (-3020 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-484 (-3018 |#1|) (-771)) (-864 |#1|)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#)) (((|#1| (-533 (-1175)) (-1175)) . T)) (((|#1|) . T)) @@ -1693,17 +1693,17 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) +((((-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-1175) (-52)) . T)) ((($ $) . T)) (((|#1| (-566)) . T)) ((((-910 |#1|)) . T)) -(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +(((|#1|) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2809 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) (|has| |#1| (-850)) (|has| |#1| (-850)) @@ -1721,13 +1721,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) -(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)))) -((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -(-2805 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-909))) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((|#3|) -2809 (|has| |#3| (-172)) (|has| |#3| (-365)))) +((($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(-2809 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-909))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) ((((-566) |#2|) . T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)))) (|has| |#1| (-351)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) (((|#2|) . T) (((-566)) . T)) @@ -1736,7 +1736,7 @@ (|has| |#1| (-820)) (|has| |#1| (-820)) (((|#1|) . T)) -(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-848)) (|has| |#1| (-848)) (|has| |#1| (-848)) @@ -1745,14 +1745,14 @@ ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-1175)) |has| |#1| (-900 (-1175))) (((-1081)) . T)) (((|#1|) . 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T)) @@ -1894,35 +1894,35 @@ (|has| |#2| (-909)) (|has| |#1| (-365)) (((|#2|) |has| |#2| (-1099))) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-538)) . T) (((-409 (-1171 (-566)))) . T) (((-225)) . T) (((-381)) . T)) ((((-381)) . T) (((-225)) . T) (((-862)) . T)) (|has| |#1| (-909)) (|has| |#1| (-909)) (|has| |#1| (-909)) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-909))) ((($) . T)) -(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((($) . T) ((|#2|) . T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)))) ((((-1173 |#1| |#2| |#3|)) -12 (|has| (-1173 |#1| |#2| |#3|) (-310 (-1173 |#1| |#2| |#3|))) (|has| |#1| (-365)))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) (((|#1|) . T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) ((((-862)) . T)) ((((-862)) . T)) ((($ $) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((($ $) . T)) ((((-566) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-566)) . T)) ((((-112)) . T)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-38 (-409 (-566)))) (((|#1| (-566)) . T)) ((($) . T)) @@ -1944,7 +1944,7 @@ (((|#1| (-1228 |#1| |#2| |#3|)) . T)) (((|#1| (-771)) . T)) (((|#1|) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-862)) . T)) (|has| |#1| (-1099)) ((((-1157) |#1|) . T)) @@ -1965,18 +1965,18 @@ (((|#1|) . T)) ((((-566)) . T)) ((((-862)) . T)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-351))) ((((-862)) . T)) (|has| |#1| (-147)) (((|#3|) . T)) -(-2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2809 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-862)) . T)) ((((-1249 |#2| |#3| |#4|)) . T) (((-1250 |#1| |#2| |#3| |#4|)) . T)) ((((-862)) . 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T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)))) ((((-1249 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-820)) @@ -2014,8 +2014,8 @@ (|has| |#1| (-848)) (|has| |#1| (-848)) (((|#1| (-566) (-1081)) . T)) -(-2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +(-2809 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#1| (-409 (-566)) (-1081)) . T)) (((|#1| (-771) (-1081)) . T)) (|has| |#1| (-850)) @@ -2029,41 +2029,41 @@ ((((-910 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-1099)) ((((-409 (-566))) |has| |#2| (-365)) (($) . T) (((-566)) . T)) -((((-566)) -2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +((((-566)) -2809 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((|#1|) . 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T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 (-52)))) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) @@ -2181,17 +2181,17 @@ ((((-699)) . T) (((-409 (-566))) . T) (((-566)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -((($) . T) (((-566)) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-566)) . T) (((-409 (-566))) -2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-566) |#1|) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) |has| (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)) (-310 (-2 (|:| -2050 |#1|) (|:| -2849 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) |has| (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)) (-310 (-2 (|:| -2004 |#1|) (|:| -3867 |#2|)))) ((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2253,12 +2253,12 @@ ((((-538)) |has| |#1| (-614 (-538))) (((-892 (-566))) |has| |#1| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381)))) (((-381)) . #0=(|has| |#1| (-1022))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-365))) ((((-862)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((($ $) . T) (((-612 $) $) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) ((($) . 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T)) @@ -2464,10 +2464,10 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) @@ -2477,10 +2477,10 @@ (((|#1|) . T) (($) . T) (((-409 (-566))) . T)) (((|#1|) . T) (($) . T) (((-409 (-566))) . T)) (((|#2|) |has| |#2| (-365))) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#2|) . T)) ((((-409 (-566))) . T) (((-699)) . T) (($) . T)) -((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((#0=(-780 |#1| (-864 |#2|)) #0#) |has| (-780 |#1| (-864 |#2|)) (-310 (-780 |#1| (-864 |#2|))))) ((((-566)) . T) (($) . T)) @@ -2499,13 +2499,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) (|has| |#1| (-558)) (((|#2|) . T)) ((((-566)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#1|) . T)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-583 |#1|)) . T)) ((($) . T)) @@ -2525,7 +2525,7 @@ (((|#1|) . T)) (((|#3|) . T) (((-566)) . T)) ((((-1249 |#2| |#3| |#4|)) . T) (((-566)) . T) (((-1250 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-409 (-566))) . T)) -((((-48)) -12 (|has| |#1| (-558)) (|has| |#1| (-1038 (-566)))) (((-566)) -2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1038 (-566))) (|has| |#1| (-1049))) ((|#1|) . T) (((-612 $)) . T) (($) |has| |#1| (-558)) (((-409 (-566))) -2805 (|has| |#1| (-558)) (|has| |#1| (-1038 (-409 (-566))))) (((-409 (-952 |#1|))) |has| |#1| (-558)) (((-952 |#1|)) |has| |#1| (-1049)) (((-1175)) . T)) +((((-48)) -12 (|has| |#1| (-558)) (|has| |#1| (-1038 (-566)))) (((-566)) -2809 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1038 (-566))) (|has| |#1| (-1049))) ((|#1|) . T) (((-612 $)) . T) (($) |has| |#1| (-558)) (((-409 (-566))) -2809 (|has| |#1| (-558)) (|has| |#1| (-1038 (-409 (-566))))) (((-409 (-952 |#1|))) |has| |#1| (-558)) (((-952 |#1|)) |has| |#1| (-1049)) (((-1175)) . 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T)) (((|#1| $) |has| |#1| (-287 |#1| |#1|))) ((((-1250 |#1| |#2| |#3| |#4|)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-558)) (($) |has| |#1| (-558))) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) (|has| |#1| (-365)) -((($) |has| |#1| (-848)) (((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-848)))) +((($) |has| |#1| (-848)) (((-566)) -2809 (|has| |#1| (-21)) (|has| |#1| (-848)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) @@ -2566,17 +2566,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (((|#2| |#3|) . T)) -(-2805 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2809 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((|#1| (-533 |#2|)) . T)) (((|#1| (-771)) . T)) (((|#1| (-533 (-1087 (-1175)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-909)) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-862)) . T)) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) -(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) ((($ $) . T) ((#0=(-1249 |#2| |#3| |#4|) #0#) . T) ((#1=(-409 (-566)) #1#) |has| #0# (-38 (-409 (-566))))) ((((-910 |#1|)) . T)) (-12 (|has| |#1| (-365)) (|has| |#2| (-820))) @@ -2584,14 +2584,14 @@ ((((-862)) . T)) ((($) . T)) ((($) . T)) -(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-365)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1249 |#2| |#3| |#4|)) . T) (((-409 (-566))) |has| #0# (-38 (-409 (-566))))) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(-2805 (-12 (|has| |#1| (-308)) (|has| |#1| (-909))) (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2809 (-12 (|has| |#1| (-308)) (|has| |#1| (-909))) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) ((((-566)) |has| |#1| (-639 (-566))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-862)) . T)) @@ -2636,28 +2636,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#2|) . T)) -(((|#2|) -2805 (|has| |#2| (-6 (-4416 "*"))) (|has| |#2| (-172)))) -(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(((|#2|) -2809 (|has| |#2| (-6 (-4416 "*"))) (|has| |#2| (-172)))) +(-2809 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#2| (-909)) (|has| |#1| (-909)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-862)) . T)) ((((-862)) . T)) ((((-538)) . T) (((-566)) . T) (((-892 (-566))) . T) (((-381)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-862)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) (((|#1| (-409 (-566))) . T)) (((|#1|) . T)) -(-2805 (|has| |#1| (-291)) (|has| |#1| (-365))) +(-2809 (|has| |#1| (-291)) (|has| |#1| (-365))) ((((-144)) . T)) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) (|has| |#1| (-848)) @@ -2673,7 +2673,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-187)) . T) (((-862)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -2686,7 +2686,7 @@ ((((-862)) . T)) ((((-1157)) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) (|has| |#1| (-850)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) @@ -2698,16 +2698,16 @@ (((|#2|) . T)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) . T) (((-612 $)) . T)) -(-2805 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2805 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2809 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2809 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-1175) (-52)) . T)) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (|has| |#1| (-909)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) (|has| |#1| (-909)) @@ -2724,12 +2724,12 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#1| (-820)) (((#0=(-910 |#1|) #0#) . T) (($ $) . T) ((#1=(-409 (-566)) #1#) . T)) ((((-409 |#2|)) . T)) (|has| |#1| (-848)) -((((-1200 |#1|)) . T) (((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-1200 |#1|)) . T) (((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) . T) ((#1=(-566) #1#) . T) (($ $) . T)) ((((-910 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) (((|#2|) |has| |#2| (-1049)) (((-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049)))) @@ -2745,28 +2745,28 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) -((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2050 (-1175)) (|:| -2849 #0#))) . T)) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) +((((-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2004 (-1175)) (|:| -3867 #0#))) . T)) (|has| |#1| (-351)) ((((-566)) . T)) ((((-862)) . T)) (((|#1|) . T)) (((#0=(-1250 |#1| |#2| |#3| |#4|) $) |has| #0# (-287 #0# #0#))) (|has| |#1| (-365)) -(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +(((|#1|) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2809 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((-566)) -2809 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((#0=(-1081) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) (((#0=(-409 (-566)) #0#) . T) ((#1=(-699) #1#) . T) (($ $) . T)) ((((-317 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-365))) ((((-862)) . T)) (|has| |#1| (-1099)) (((|#1|) . T)) -(((|#1|) -2805 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) -(((|#1|) -2805 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2809 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2809 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) (((|#2|) . T)) ((((-409 (-566))) . T) (((-699)) . T) (($) . T)) ((((-581)) . T)) @@ -2791,7 +2791,7 @@ (((|#1|) . T)) ((((-566)) . T)) (((|#2|) . T) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((|#1|) . T) (($) . T) (((-566)) . T)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((|#2|) . T) (((-566)) |has| |#2| (-639 (-566)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2835,7 +2835,7 @@ (|has| |#2| (-1022)) ((($) . T)) (|has| |#1| (-909)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2844,10 +2844,10 @@ (|has| |#1| (-365)) ((((-910 |#1|)) . T)) ((($) . T) (((-566)) . T) ((|#1|) . T) (((-409 (-566))) . T)) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -((($) |has| |#1| (-848)) (((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-848)))) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) |has| |#1| (-848)) (((-566)) -2809 (|has| |#1| (-21)) (|has| |#1| (-848)))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) -(-2805 (|has| |#1| (-370)) (|has| |#1| (-850))) +(-2809 (|has| |#1| (-370)) (|has| |#1| (-850))) (((|#1|) . T)) ((((-771)) . T)) ((((-862)) . T)) @@ -2858,17 +2858,17 @@ ((((-566)) . T) (($) . T)) ((((-566)) . T) (($) . T)) ((((-771) |#1|) . T)) -(((|#2| (-240 (-3020 |#1|) (-771))) . T)) +(((|#2| (-240 (-3018 |#1|) (-771))) . T)) (((|#1| (-533 |#3|)) . T)) ((((-409 (-566))) . T)) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-1157)) . T) (((-862)) . T)) -(((#0=(-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) #0#) |has| (-2 (|:| -2050 (-1175)) (|:| -2849 (-52))) (-310 (-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))))) +(((#0=(-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) #0#) |has| (-2 (|:| -2004 (-1175)) (|:| -3867 (-52))) (-310 (-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))))) ((((-1157)) . T)) (|has| |#1| (-909)) (|has| |#2| (-365)) (((|#1|) . T) (($) . T) (((-566)) . T)) -(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-862)) . T)) (((|#1|) . T)) @@ -2885,11 +2885,11 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (-12 (|has| |#1| (-547)) (|has| |#1| (-828))) ((((-862)) . T)) -((((-1175)) -2805 (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-900 (-1175)))))) +((((-1175)) -2809 (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-900 (-1175)))))) (|has| |#1| (-365)) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-409 (-566)) |#1|))) (|has| |#1| (-900 (-1175))))) (|has| |#1| (-365)) @@ -2901,7 +2901,7 @@ (((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#1| (-365))) ((((-566)) . T) (($) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2931,11 +2931,11 @@ (((|#2|) |has| |#1| (-365))) ((((-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-381)))) (((-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-566))))) (|has| |#1| (-365)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (((|#1|) . T)) ((($) . T) (((-566)) . T) ((|#2|) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (((|#3|) . T)) ((((-1157)) . T) (((-508)) . T) (((-225)) . T) (((-566)) . T)) @@ -2943,23 +2943,23 @@ (|has| |#1| (-558)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) -(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((|#2|) . T)) (((|#2|) . T)) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-409 (-566)))) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) ((((-1157) |#1|) . T)) (|has| |#1| (-147)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) (|has| |#1| (-147)) ((((-583 |#1|)) . T)) @@ -2973,7 +2973,7 @@ ((((-409 (-566))) |has| |#2| (-1038 (-566))) (((-566)) |has| |#2| (-1038 (-566))) (((-1175)) |has| |#2| (-1038 (-1175))) ((|#2|) . T)) (((#0=(-409 |#2|) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2805 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-145)) (|has| |#1| (-351))) (|has| |#1| (-147)) ((((-862)) . T)) ((($) . T)) @@ -2998,7 +2998,7 @@ ((((-862)) . T)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3020,7 +3020,7 @@ ((((-566)) . T)) ((((-862)) . T)) ((((-566)) . T)) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -3032,9 +3032,9 @@ (((|#1|) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) (|has| |#1| (-1150)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) ((((-910 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) @@ -3051,25 +3051,25 @@ (((|#1|) |has| |#1| (-310 |#1|))) ((((-566) |#1|) . T)) ((((-1175) |#1|) . T)) -(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T)) -(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049)))) +(((|#1|) -2809 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049)))) ((((-566)) . T) (((-409 (-566))) . T)) (((|#1|) . T)) (|has| |#1| (-558)) ((($) . T) (((-566)) . T) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-365))) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-381)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-558)) (|has| |#1| (-1099)) ((((-780 |#1| (-864 |#2|))) |has| (-780 |#1| (-864 |#2|)) (-310 (-780 |#1| (-864 |#2|))))) -(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2809 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3081,13 +3081,13 @@ (|has| |#2| (-365)) ((((-583 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 (-52)))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-566)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-862)) . T)) ((((-862)) . T)) -(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2809 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . T)) ((((-1119)) . T) (((-862)) . T)) ((((-538)) . T) (((-862)) . T)) @@ -3098,12 +3098,12 @@ ((((-566)) . T)) (((|#3|) . T)) ((((-862)) . T)) -(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) -((((-566)) . T) (((-409 (-566))) -2805 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566))))) ((|#2|) . T) (($) -2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-864 |#1|)) . T)) -((((-1124 |#1| |#2|)) . T) ((|#2|) . T) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) -((((-1171 |#1|)) . T) (((-566)) . T) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((-1081)) . T) ((|#1|) . 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T) (($ $) -2805 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +(((#0=(-409 (-566)) #0#) |has| |#2| (-38 (-409 (-566)))) ((|#2| |#2|) . T) (($ $) -2809 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) @@ -3129,21 +3129,21 @@ (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) -((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) -((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1| |#1|) . 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T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (|has| |#2| (-909)) (|has| |#1| (-909)) -((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-862)) . T)) (((|#1|) . T)) -((((-2 (|:| -2050 (-1157)) (|:| -2849 |#1|))) . T)) +((((-2 (|:| -2004 (-1157)) (|:| -3867 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3162,10 +3162,10 @@ (((#0=(-409 (-566)) #0#) . T)) ((((-409 (-566))) . T)) (((|#1|) |has| |#1| (-172))) -(-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((|#1|) . T)) (((|#1|) . T)) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((|#1|) . T)) ((((-409 (-566))) . T) (((-566)) . T) (($) . T)) ((((-538)) . T)) @@ -3184,14 +3184,14 @@ ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) ((((-1175)) |has| |#1| (-900 (-1175)))) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) -((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) -(((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566)))) ((|#1| |#1|) . 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T)) (|has| |#2| (-820)) (|has| |#2| (-820)) -((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) . T)) +((((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-409 (-566))) -2809 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) ((((-566)) |has| |#1| (-886 (-566))) (((-381)) |has| |#1| (-886 (-381)))) @@ -3228,7 +3228,7 @@ (((|#1|) . 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T)) -(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) -(-2805 (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-12 (|has| |#1| (-850)) (|has| |#2| (-850)))) +(-2809 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2809 (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-12 (|has| |#1| (-850)) (|has| |#2| (-850)))) ((((-870 |#1|)) . T)) (((|#1|) . T)) (|has| |#1| (-370)) @@ -3274,7 +3274,7 @@ (((|#1|) . T)) ((((-862)) . T)) (|has| |#2| (-909)) -((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) +((((-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))) . T)) ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566))))) ((((-862)) . T)) ((((-862)) . T)) @@ -3301,7 +3301,7 @@ ((((-1180)) . T)) ((((-644 |#1|)) . T)) ((($) . T) (((-566)) . T) (((-1250 |#1| |#2| |#3| |#4|)) . T) (((-409 (-566))) . T)) -((((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (($) -2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-558))) +((((-566)) -2809 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (($) -2809 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-558))) ((((-1180)) . T)) ((((-1180)) . T)) ((((-566)) . T) (((-409 (-566))) . T)) @@ -3317,12 +3317,12 @@ ((((-409 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1099)) -(((|#2| (-484 (-3020 |#1|) (-771))) . T)) +(((|#2| (-484 (-3018 |#1|) (-771))) . T)) ((((-566) |#1|) . T)) ((((-1157)) . T) (((-862)) . T)) (((|#2| |#2|) . T)) (((|#1| (-533 (-1175))) . 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T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1|) . T)) (((|#2| |#2|) . T) ((#0=(-409 (-566)) #0#) . T) (($ $) . T)) ((((-566)) . T)) @@ -3608,17 +3608,17 @@ ((($) . T) (((-566)) . T) (((-116 |#1|)) . T) (((-409 (-566))) . T)) ((((-862)) . T)) ((((-1256 |#1| |#2| |#3|)) . T)) -((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2809 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) ((($) . T) (((-566)) . T)) -((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1103)) . T)) ((((-862)) . T)) -((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((($) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) ((($) . T)) -((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1256 |#1| |#2| |#3|)) |has| |#1| (-365))) (|has| |#1| (-365)) ((((-1256 |#1| |#2| |#3|)) . T) (((-1228 |#1| |#2| |#3|)) . T)) @@ -3630,7 +3630,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-699)) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-1180)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1180)) . T)) @@ -3647,13 +3647,13 @@ ((((-1180)) . T)) ((((-1180)) . T)) ((((-1180)) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1180)) . T)) ((((-1180)) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -(-2805 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-172)) (|has| |#1| (-558))) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) (((|#1| (-771)) . T)) @@ -3668,16 +3668,16 @@ ((((-892 (-381))) . T) (((-892 (-566))) . T) (((-1175)) . T) (((-538)) . T)) (((|#1|) . T)) ((((-862)) . T)) -(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -(-2805 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793)))) +(-2809 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793)))) ((((-566)) . T)) ((((-566)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2809 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((((-1175)) -12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) -(-2805 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) +(-2809 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-365)) @@ -3708,7 +3708,7 @@ (((|#1| |#2|) . T)) ((((-566)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-566)) . T)) -(-2805 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2809 (|has| |#1| (-351)) (|has| |#1| (-370))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-409 (-566))) . T) (($) . T) (((-566)) . T)) @@ -3720,7 +3720,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((($) . T) (((-409 (-566))) . T)) (|has| |#1| (-909)) (|has| |#1| (-909)) @@ -3731,14 +3731,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-566)) . T)) ((((-1180)) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-848))) (((|#2|) . T)) -(-2805 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2809 (|has| |#1| (-21)) (|has| |#1| (-848))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-862)) -2805 (-12 (|has| |#1| (-613 (-862))) (|has| |#2| (-613 (-862)))) (-12 (|has| |#1| (-1099)) (|has| |#2| (-1099))))) +((((-862)) -2809 (-12 (|has| |#1| (-613 (-862))) (|has| |#2| (-613 (-862)))) (-12 (|has| |#1| (-1099)) (|has| |#2| (-1099))))) ((((-409 |#2|) |#3|) . T)) ((((-409 (-566))) . T) (($) . T)) (|has| |#1| (-38 (-409 (-566)))) @@ -3752,19 +3752,19 @@ (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((#0=(-566) #0#) . T)) ((($) . T) (((-409 (-566))) . T)) -(-2805 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2805 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2809 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2809 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-862)) . T) (((-1180)) . T)) (|has| |#4| (-793)) -(-2805 (|has| |#4| (-793)) (|has| |#4| (-848))) +(-2809 (|has| |#4| (-793)) (|has| |#4| (-848))) (|has| |#4| (-848)) (|has| |#3| (-793)) ((((-1180)) . T)) -(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2809 (|has| |#3| (-793)) (|has| |#3| (-848))) (|has| |#3| (-848)) ((((-566)) . T)) (((|#2|) . T)) -((((-1175)) -2805 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) +((((-1175)) -2809 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-409 (-566)) |#1|))) (|has| |#1| (-900 (-1175))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-771) |#1|))) (|has| |#1| (-900 (-1175))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3779,11 +3779,11 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1139 |#1| |#2|)) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) -((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) +((((-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1022)) -(((|#2|) . T) (((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) ((((-862)) . T)) ((((-538)) |has| |#2| (-614 (-538))) (((-892 (-566))) |has| |#2| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#2| (-614 (-892 (-381)))) (((-381)) . #0=(|has| |#2| (-1022))) (((-225)) . #0#)) ((((-295 |#3|)) . T)) @@ -3800,15 +3800,15 @@ ((((-1173 |#1| |#2| |#3|)) . T)) ((((-1173 |#1| |#2| |#3|)) . T) (((-1166 |#1| |#2| |#3|)) . T)) ((((-862)) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-566) |#1|) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-365)) -(((|#3|) . T) ((|#2|) . T) (($) -2805 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) ((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049)))) -(((|#2|) . T) (($) -2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) +(((|#3|) . T) ((|#2|) . T) (($) -2809 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) ((|#4|) -2809 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049)))) +(((|#2|) . T) (($) -2809 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((|#3|) -2809 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) @@ -3823,7 +3823,7 @@ ((((-187)) . T) (((-862)) . T)) ((((-862)) . T)) (((|#1|) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-129)) . T) (((-862)) . T)) ((((-566) |#1|) . T)) ((((-129)) . T)) @@ -3832,13 +3832,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) -(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) +(-2809 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-533 |#2|)) . T)) -((((-2 (|:| -2050 (-1175)) (|:| -2849 (-52)))) . T)) +((((-2 (|:| -2004 (-1175)) (|:| -3867 (-52)))) . T)) ((((-566) (-129)) . T)) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) @@ -3853,8 +3853,8 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) -(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2809 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2809 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((($) . T)) (((|#2| (-533 (-864 |#1|))) . T)) ((((-1180)) . T)) @@ -3869,13 +3869,13 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-1180)) . T)) -((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2809 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1|) . T)) (((|#2| (-771)) . T)) (((|#1| |#2|) . T)) ((((-1157) |#1|) . T)) ((((-409 |#2|)) . T)) -((((-2 (|:| -2050 |#1|) (|:| -2849 |#2|))) . T)) +((((-2 (|:| -2004 |#1|) (|:| -3867 |#2|))) . T)) (|has| |#1| (-558)) (|has| |#1| (-558)) ((($) . T) ((|#2|) . T)) @@ -3886,14 +3886,14 @@ ((((-566)) . T) (($) . T)) (((|#2| $) |has| |#2| (-287 |#2| |#2|))) (((|#1| (-644 |#1|)) |has| |#1| (-848))) -(-2805 (|has| |#1| (-233)) (|has| |#1| (-351))) -(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-233)) (|has| |#1| (-351))) +(-2809 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1260 |#1|)) . T) (((-566)) . T) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-1038 (-409 (-566))))) (|has| |#1| (-1099)) (((|#1|) . T)) -((((-1260 |#1|)) . T) (((-566)) . T) (($) -2805 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-1081)) . T) ((|#2|) . T) (((-409 (-566))) -2805 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566)))))) +((((-1260 |#1|)) . T) (((-566)) . T) (($) -2809 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-1081)) . T) ((|#2|) . T) (((-409 (-566))) -2809 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566)))))) ((((-409 (-566))) . T) (($) . T)) -((((-999 |#1|)) . T) ((|#1|) . T) (((-566)) -2805 (|has| (-999 |#1|) (-1038 (-566))) (|has| |#1| (-1038 (-566)))) (((-409 (-566))) -2805 (|has| (-999 |#1|) (-1038 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566)))))) +((((-999 |#1|)) . T) ((|#1|) . T) (((-566)) -2809 (|has| (-999 |#1|) (-1038 (-566))) (|has| |#1| (-1038 (-566)))) (((-409 (-566))) -2809 (|has| (-999 |#1|) (-1038 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566)))))) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) @@ -3909,10 +3909,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1139 |#1| |#2|) #0#) |has| (-1139 |#1| |#2|) (-310 (-1139 |#1| |#2|)))) (((|#1|) . 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116514) ((-1101 . -235) 116498) ((-64 . -398) T) ((-64 . -397) T) ((-110 . -102) T) ((-484 . -640) 116440) ((-40 . -379) 116417) ((-96 . -102) T) ((-653 . -852) 116401) ((-1134 . -1082) T) ((-1061 . -21) T) ((-1061 . -25) T) ((-1054 . -1051) 116385) ((-815 . -231) 116354) ((-952 . -25) T) ((-952 . -21) T) ((-1054 . -640) 116296) ((-621 . -1057) T) ((-1119 . -370) T) ((-1027 . -310) 116234) ((-670 . -646) 116193) ((-483 . -25) T) ((-483 . -21) T) ((-387 . -1051) 116177) ((-889 . -613) 116159) ((-885 . -613) 116141) ((-525 . -516) 116074) ((-252 . -850) 116025) ((-251 . -850) 115976) ((-387 . -640) 115946) ((-871 . -639) 115923) ((-478 . -310) 115861) ((-465 . -310) 115799) ((-353 . -291) T) ((-1155 . -1252) 115783) ((-1141 . -613) 115745) ((-1141 . -614) 115706) ((-1139 . -102) T) ((-999 . -1056) 115602) ((-40 . -900) 115554) ((-1155 . -604) 115531) ((-1292 . -648) 115518) ((-866 . -492) 115495) ((-1062 . -151) 115441) ((-872 . -1218) T) ((-999 . -111) 115323) ((-341 . -717) 115307) 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. -1056) 94796) ((-347 . -717) 94748) ((-341 . -111) 94727) ((-174 . -1056) 94659) ((-217 . -646) 94609) ((-174 . -111) 94520) ((-108 . -717) 94470) ((-275 . -1099) T) ((-274 . -1099) T) ((-273 . -1099) T) ((-272 . -1099) T) ((-271 . -1099) T) ((-270 . -1099) T) ((-269 . -1099) T) ((-212 . -1099) T) ((-211 . -1099) T) ((-169 . -1202) 94448) ((-169 . -1199) 94426) ((-209 . -1099) T) ((-208 . -1099) T) ((-116 . -1049) T) ((-207 . -1099) T) ((-206 . -1099) T) ((-203 . -1099) T) ((-202 . -1099) T) ((-201 . -1099) T) ((-200 . -1099) T) ((-199 . -1099) T) ((-198 . -1099) T) ((-197 . -1099) T) ((-196 . -1099) T) ((-195 . -1099) T) ((-194 . -1099) T) ((-193 . -1099) T) ((-240 . -102) 94216) ((-169 . -35) 94194) ((-169 . -95) 94172) ((-654 . -1038) 94068) ((-484 . -1057) 93998) ((-1112 . -1099) 93788) ((-1141 . -34) T) ((-670 . -491) 93772) ((-73 . -1214) T) ((-105 . -613) 93754) ((-1288 . -613) 93736) ((-383 . -613) 93718) ((-341 . -616) 93670) ((-174 . -616) 93587) ((-1213 . -492) 93568) 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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 e3dfad8b..a003788e 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3453990493) +(30 . 3454219020) (4417 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -478,662 +478,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |arity| |rightLcm| |lookup| |squareTop| - |intermediateResultsIF| |option?| |wordInStrongGenerators| |c06fuf| - |getOperands| |functionIsOscillatory| |cCos| |f01mcf| |bracket| - |LazardQuotient2| |incrementKthElement| |coth2trigh| |mpsode| |addmod| - |OMreceive| |categoryFrame| |Ci| |generate| |symmetricTensors| - |parametersOf| |lieAdmissible?| |critT| |retractable?| |parameters| - |extendedEuclidean| |createNormalPoly| |perfectSqrt| |leadingSupport| - |imagJ| |clipParametric| |writable?| |leftRankPolynomial| |realZeros| - |companionBlocks| |makeSin| |outputMeasure| |quasiRegular| - |monicRightDivide| |lighting| |incrementBy| |generalizedEigenvectors| - |e01bef| |rowEch| |f04mbf| |mapdiv| |atrapezoidal| |distdfact| - |normalForm| |primextintfrac| |showScalarValues| |expand| |linGenPos| - |f04arf| |midpoint| |expr| |rational?| |bezoutMatrix| |firstDenom| - |completeSmith| |collectQuasiMonic| |isAnd| |shiftRight| |filterWhile| - |highCommonTerms| |hostByteOrder| |mathieu24| |zCoord| |s21bbf| - |stack| |removeZeroes| |OMputString| |sturmVariationsOf| |binding| - |green| |filterUntil| |normalizedAssociate| |complete| |iiacot| - |critMonD1| |clipBoolean| |iiacsch| |indiceSubResultantEuclidean| - |controlPanel| |makeFloatFunction| |showRegion| |select| - |inverseIntegralMatrixAtInfinity| |monicDecomposeIfCan| - |complementaryBasis| |trivialIdeal?| |completeEchelonBasis| RF2UTS - |style| |leadingExponent| |singularAtInfinity?| - |removeRedundantFactors| |normalDeriv| |body| - |createMultiplicationMatrix| |e02daf| |variable| |stFunc1| - |semiResultantEuclideannaif| |lifting1| |ScanRoman| |legendreP| - |shiftLeft| |clearTheIFTable| |squareMatrix| |symbol| |primlimitedint| - |unrankImproperPartitions1| |polygon| |iterators| |showTheIFTable| - |mapCoef| |bipolarCylindrical| |edf2ef| |d02ejf| |cAcoth| - |systemCommand| |sizeMultiplication| |s17dgf| |expression| |f02adf| - |redmat| |interval| |OMputEndError| |s13aaf| |changeNameToObjf| - |denominator| |nodes| |firstSubsetGray| |romberg| |integer| |sqfree| - |extractProperty| |laurentRep| UP2UTS |getMultiplicationTable| |sum| - |box| |ffactor| |eisensteinIrreducible?| |lfinfieldint| |OMgetEndBVar| - |infinite?| ** |whitePoint| |remove!| |pointColor| |getGraph| - |monomial?| |expandTrigProducts| |degreePartition| - |factorSquareFreeByRecursion| |reducedQPowers| |createGenericMatrix| - |makeRecord| |OMgetSymbol| |typeLists| |c05adf| |e02aef| |cyclicGroup| - |linearlyDependentOverZ?| |reopen!| |eulerPhi| |invertibleSet| - |makingStats?| |port| |freeOf?| |cycleLength| |OMunhandledSymbol| - |evaluateInverse| |infiniteProduct| |printCode| |parabolic| - |transcendent?| |f2st| |hasPredicate?| |e01sef| |monicModulo| - |critMTonD1| |selectOptimizationRoutines| |expintegrate| |initial| - |genericRightDiscriminant| |lowerCase?| |mix| |getMatch| - |lazyIrreducibleFactors| |lp| |t| |denominators| |rowEchelon| |c05nbf| - |d02bhf| |countRealRoots| |error| |elseBranch| |outputArgs| - |direction| |OMgetEndAtp| |nextPrime| - |functionIsContinuousAtEndPoints| |s14baf| |d03edf| |chiSquare1| - |f02bbf| |bindings| |assert| |getConstant| |splitSquarefree| - |BasicMethod| |extendedIntegrate| |clearTheFTable| |UnVectorise| - |light| |s17aef| |label| |stopTable!| |rootNormalize| |lepol| - |explicitlyEmpty?| |patternMatch| |d01amf| |d03eef| |float?| |htrigs| - |normalizedDivide| |newSubProgram| |groebner| |positive?| |readByte!| - |purelyTranscendental?| |ratDsolve| |cycleRagits| |rule| |sdf2lst| - |aQuadratic| |f01rdf| |definingInequation| |deepCopy| |cn| |delta| - |orthonormalBasis| |leastPower| |stosePrepareSubResAlgo| |writeBytes!| - |sh| |exteriorDifferential| |complexElementary| |aspFilename| |diff| - |singleFactorBound| |subPolSet?| |infieldIntegrate| - |extendedSubResultantGcd| |logGamma| |wholeRadix| |basisOfNucleus| - |tubePoints| |encodingDirectory| |bombieriNorm| |bivariate?| - |listRepresentation| |lift| |sort| |initiallyReduce| |sort!| - |returnTypeOf| |goodnessOfFit| |numberOfChildren| |size?| |basis| - |curryRight| |internalDecompose| |semiResultantEuclidean2| |palgint| - |reduce| |genericLeftTraceForm| |rootPower| |any?| - |getMultiplicationMatrix| |sumSquares| |bits| |movedPoints| |qqq| - |simpsono| |hostPlatform| |round| |constructor| - |primPartElseUnitCanonical!| |rightUnit| |makeUnit| |integerIfCan| - |square?| |module| |lazyPseudoDivide| |endOfFile?| |writeLine!| - |mindegTerm| |morphism| |drawToScale| |swapColumns!| |patternVariable| - |coerceListOfPairs| |multisect| |basisOfCentroid| |option| |nullary| - |squareFreePrim| |hasHi| |OMbindTCP| |forLoop| |void| |c06eaf| - |random| |testModulus| |cot2trig| |column| |mapSolve| |central?| - |sPol| |removeRedundantFactorsInContents| |limitedIntegrate| - |invertible?| |OMgetAttr| |lambda| |even?| |zeroVector| |sequences| - |coercePreimagesImages| |lazyResidueClass| |pr2dmp| |Vectorise| - |setvalue!| |cyclic?| |fixPredicate| |subQuasiComponent?| |powers| - |cExp| |belong?| |multiplyExponents| |createLowComplexityTable| - |exprToUPS| |minordet| |df2ef| |hclf| |Gamma| |raisePolynomial| - |numberOfFactors| |maxRowIndex| |say| |legendre| |genericRightNorm| - |intensity| |normInvertible?| |curve?| |rightTrim| |minus!| |ptFunc| - |s13adf| |diagonalMatrix| |delay| |LyndonWordsList1| |f02awf| - |squareFreeLexTriangular| |listLoops| |limitedint| |headReduce| - |leftTrim| |biRank| |numberOfComputedEntries| |coleman| - |primitiveElement| |depth| |quadraticForm| |defineProperty| - |changeVar| |leftOne| |rightDiscriminant| |orbit| |fintegrate| - |byteBuffer| |musserTrials| |overlap| |readUInt16!| |exprex| |iicsch| - |result| |s17ajf| |pascalTriangle| |palgextint0| |setProperty| - |eigenvector| |fi2df| |pmintegrate| |f04faf| |insertionSort!| - |monicCompleteDecompose| |stronglyReduced?| |minPoints| |pdct| - |lazyPremWithDefault| |iisqrt3| |logical?| |setProperties!| |rightOne| - |nextPrimitiveNormalPoly| |mainVariables| |OMgetObject| |close| - |setStatus!| |ranges| |reset| |meshFun2Var| |lowerCase!| - |rectangularMatrix| |medialSet| |rootKerSimp| |evaluate| - |extensionDegree| |characteristicSet| |addPoint| |safeCeiling| |recur| - |d01gaf| |integralAtInfinity?| |hasSolution?| |kind| - |powerAssociative?| |prinshINFO| |makeTerm| |cot2tan| |display| - |inGroundField?| |f02aff| |subMatrix| |write| |infinityNorm| - |factorFraction| |repeatUntilLoop| |slex| |constantLeft| |op| |c02aff| - |characteristicSerie| |f07adf| |viewPosDefault| |variable?| - |setMaxPoints| |save| |rootProduct| |modularGcdPrimitive| |tanNa| - |sec2cos| |internalIntegrate0| |f04asf| |bat| |double?| |low| |front| - |c06frf| |rootRadius| |iflist2Result| |numerators| |llprop| - |precision| |redPo| |normal?| |partition| |pattern| - |internalSubPolSet?| |extendIfCan| |moebiusMu| |logpart| - |genericLeftDiscriminant| |OMread| |laguerre| |endSubProgram| - |basisOfLeftAnnihilator| |commutator| |prime?| |laurentIfCan| - |lagrange| |leftRecip| |pushNewContour| |selectAndPolynomials| - |selectIntegrationRoutines| |mantissa| |exponential| |empty| |input| - |approxNthRoot| |normFactors| |satisfy?| |checkRur| - |setLegalFortranSourceExtensions| |aLinear| |rarrow| - |bivariatePolynomials| |leadingIdeal| |modifyPointData| |library| - |e04ucf| |totalLex| |lazyVariations| |supersub| |hexDigit| - |nextNormalPrimitivePoly| |perfectNthRoot| |f07fef| |union| |localAbs| - |d01apf| |message| |fixedPointExquo| |setlast!| |extractTop!| - |zeroDimPrime?| |selectNonFiniteRoutines| |tube| |varList| - |getProperties| |deref| |curry| |univariate?| |getOperator| |rombergo| - |setleaves!| |f2df| |lyndon| |sts2stst| |minimize| |froot| - |principalAncestors| |fractionFreeGauss!| |ParCondList| |pToDmp| - |identitySquareMatrix| |cAcsch| |startTableGcd!| |extractPoint| - |level| |testDim| |heap| |computeCycleEntry| |seed| |imagI| |mr| - |sumOfDivisors| |expintfldpoly| |qPot| |rowEchLocal| |factorials| - |frst| |d01asf| |LyndonWordsList| |quasiMonicPolynomials| |subNodeOf?| - |stripCommentsAndBlanks| |leftTrace| |maxrank| |components| |part?| - |retract| |lazyGintegrate| F2FG |stoseIntegralLastSubResultant| - |UP2ifCan| |cotIfCan| |cons| |divergence| |c06gcf| |point| |mapDown!| - |lflimitedint| |iibinom| |alternating| |fillPascalTriangle| - |binaryTree| |matrix| |trim| |invmod| |d01ajf| |mvar| |iisin| - |dAndcExp| |radicalRoots| |expandPower| |coerceP| |closedCurve?| - |makeVariable| |quartic| |determinant| |imports| - |stoseInternalLastSubResultant| |radicalOfLeftTraceForm| - |setMinPoints3D| |any| |toScale| |series| |changeWeightLevel| |fTable| - |OMencodingBinary| |addiag| |external?| |d01fcf| |ref| - |subResultantGcd| |setFormula!| |prevPrime| |notelem| - |LyndonCoordinates| |Lazard2| |clearTheSymbolTable| |hconcat| - |subResultantChain| |Is| |setfirst!| |exponents| |linearAssociatedExp| - |increasePrecision| |usingTable?| |fortranDouble| |explicitlyFinite?| - |categories| |setPoly| |iCompose| |colorDef| |has?| |functorData| - |lifting| |possiblyInfinite?| |lfextendedint| |s14aaf| |setrest!| - |e02bef| |setelt!| |pseudoQuotient| |qfactor| |bitCoef| |moduleSum| - |min| |acosIfCan| |multiEuclidean| |OMreadStr| |fortranDoubleComplex| - |s14abf| |unravel| |lazyPseudoQuotient| |ratPoly| |contractSolve| - |plus| |s18dcf| |cycleEntry| |harmonic| |divideIfCan| |completeHensel| - |purelyAlgebraic?| |ef2edf| |integers| |leftDiscriminant| - |insertMatch| |minColIndex| |externalList| |unitCanonical| - |OMmakeConn| |composite| |quote| |yellow| |s19acf| |weakBiRank| - |stoseInvertibleSet| |coefChoose| |maxint| |diagonal| |sncndn| |back| - |ipow| |ceiling| |var1Steps| |mainVariable| |consnewpol| |nthRoot| - |lquo| |linearAssociatedOrder| |showTheFTable| |asechIfCan| |reduced?| - GF2FG |noncommutativeJordanAlgebra?| |fortranLiteralLine| |signAround| - |stirling1| |henselFact| |dark| |times| |polyPart| - |showTheRoutinesTable| |eigenvectors| |changeMeasure| - |numberOfComposites| |permutations| |OMputAttr| |parent| - |fortranLogical| |pToHdmp| |semiIndiceSubResultantEuclidean| - |rightAlternative?| |dimension| |myDegree| |isPower| |taylorRep| - |outputAsScript| |linears| |rename!| |qinterval| |thetaCoord| - |applyRules| |matrixGcd| |read!| |setPrologue!| |limit| |curveColor| - |halfExtendedResultant2| |toseLastSubResultant| |magnitude| - |nextSubsetGray| |patternMatchTimes| |iterationVar| |readInt8!| - |asinIfCan| |rename| |messagePrint| |sortConstraints| |airyBi| - |monicDivide| |algebraicDecompose| |leftMinimalPolynomial| - |relationsIdeal| |node| |monom| |e02adf| |monic?| |component| - |identityMatrix| |plotPolar| |key| |atom?| |setTopPredicate| - |mainCoefficients| |lintgcd| |rightRemainder| |callForm?| - |sumOfKthPowerDivisors| |enterInCache| |cyclicEqual?| - |numberOfComponents| |bubbleSort!| |bfEntry| |measure2Result| |hex| - |phiCoord| |parabolicCylindrical| |polyRDE| |explogs2trigs| |dequeue!| - |filename| |selectFiniteRoutines| |thenBranch| |sin?| |critBonD| - |pdf2ef| |f02aef| |common| |bit?| |shufflein| - |dimensionOfIrreducibleRepresentation| |setOrder| |outputSpacing| - |f02abf| |cAcosh| |drawStyle| |deriv| |rquo| |oddintegers| |points| - |prepareDecompose| |separate| |zeroMatrix| |parse| |setFieldInfo| - |eval| |normalizeIfCan| |npcoef| |summation| - |internalSubQuasiComponent?| |coord| |Hausdorff| |inputBinaryFile| - |leftQuotient| |increment| |powerSum| |dioSolve| |upperCase!| |degree| - |groebgen| |splitDenominator| |iicosh| |rootBound| |rdregime| EQ - |nextIrreduciblePoly| |mainKernel| |algintegrate| |elementary| - |contract| |plenaryPower| |d01alf| |conjug| |addBadValue| - |knownInfBasis| |nthRootIfCan| |elColumn2!| |cycleSplit!| |intChoose| - |showAll?| |brillhartTrials| |exactQuotient!| |innerSolve1| |nextItem| - |nlde| |karatsubaOnce| |conditionsForIdempotents| |unexpand| |isList| - |contours| |indices| |tan2trig| |divisors| |viewDeltaYDefault| - |rootOfIrreduciblePoly| |cCosh| |zag| |fixedPoints| |escape| - |addMatchRestricted| |relativeApprox| |twoFactor| |RittWuCompare| - |dimensions| |numberOfVariables| |countRealRootsMultiple| |c06ebf| - |subresultantSequence| |mapExpon| |vconcat| |axesColorDefault| - |integralBasis| |operators| |scaleRoots| |var2StepsDefault| - |lastSubResultant| |s17adf| |complexNumericIfCan| |charClass| - |minGbasis| |cyclotomicDecomposition| |trapezoidalo| - |doublyTransitive?| |explicitEntries?| |iicsc| |equation| - |curveColorPalette| |zeroDimPrimary?| |OMconnectTCP| |squareFreePart| - |viewWriteAvailable| |zero| |factorsOfDegree| |member?| |varselect| - |hessian| |f01maf| |ridHack1| |nullary?| |elliptic?| |basisOfCenter| - |rightFactorCandidate| |nonSingularModel| |makeViewport2D| |elRow2!| - |e01sbf| |functionIsFracPolynomial?| |lcm| |stopTableInvSet!| - |setRealSteps| |fortranInteger| |pointColorPalette| - |complexEigenvalues| |And| |alphanumeric| |regularRepresentation| - |setMinPoints| |totalDegree| |index| |floor| |reducedSystem| |rk4f| - |monomRDEsys| |iidprod| |semiLastSubResultantEuclidean| |delete| |Or| - |resetAttributeButtons| |bernoulliB| |equiv| |selectODEIVPRoutines| - |gcdPolynomial| |append| |pointSizeDefault| |argument| |OMgetBind| - |iiacosh| |numerator| |Not| |c06gbf| |leftDivide| |linearMatrix| - |compactFraction| |branchIfCan| |readInt32!| |gcd| |setsubMatrix!| - |setAdaptive3D| |gbasis| |scale| |OMputEndObject| |continuedFraction| - |stiffnessAndStabilityFactor| |resultantEuclideannaif| |infix| |pair| - |OMputVariable| |false| |f01rcf| |fractRadix| |divisorCascade| - |routines| |value| |processTemplate| |permanent| |computeInt| - |partitions| |sincos| |irreducibleFactors| |repSq| |meshPar1Var| - |iiacoth| |cAtanh| |exprHasLogarithmicWeights| |times!| |expint| - |bumptab1| |UpTriBddDenomInv| |sparsityIF| |rational| |nodeOf?| - |accuracyIF| |f02aaf| |specialTrigs| |mainDefiningPolynomial| |prem| - |cyclicCopy| |tableForDiscreteLogarithm| |associates?| |outputAsTex| - |diagonals| |regime| |maxdeg| |flexible?| |internalAugment| - |getIdentifier| |nextSublist| |doubleFloatFormat| |generic?| - |partialQuotients| |boundOfCauchy| |simplifyPower| |btwFact| |sn| - |charpol| |extend| |f04axf| |univariateSolve| |entry?| |cycleTail| - |iisech| |mapUnivariate| |hermite| |invmultisect| - |createIrreduciblePoly| |graphImage| |polygamma| |substring?| - |PDESolve| |linearlyDependent?| |hexDigit?| |LyndonBasis| - |nextsubResultant2| |cardinality| |overset?| |plus!| |addPoint2| - |idealiserMatrix| |sechIfCan| |shellSort| |hMonic| - |rangePascalTriangle| |tValues| |implies| |nilFactor| - |stoseInvertible?reg| |drawComplexVectorField| |tower| |leftMult| - |suffix?| |monomials| |alternatingGroup| |tan2cot| |probablyZeroDim?| - |baseRDE| |univariatePolynomials| |overlabel| |initiallyReduced?| - |trueEqual| |ScanFloatIgnoreSpaces| |ord| |wholeRagits| |expt| - |createNormalPrimitivePoly| |inverse| |divisor| |setImagSteps| - |discreteLog| |createNormalElement| |findBinding| |cup| |connectTo| - |sinhcosh| |prefix?| |OMUnknownSymbol?| |jacobiIdentity?| - |ListOfTerms| |nary?| |cosSinInfo| |associative?| - |currentCategoryFrame| |log10| |pile| |collectUpper| |OMputAtp| - |moduloP| |LowTriBddDenomInv| |e04mbf| |bitTruth| |lazyIntegrate| - |push| |parametric?| |bitand| |symmetricPower| |powern| - |nonLinearPart| |lastSubResultantEuclidean| - |leftRegularRepresentation| |binomial| |fortranReal| |inR?| - |mapUnivariateIfCan| |largest| |complexNumeric| |bitior| - |positiveRemainder| F |untab| |paren| |primitivePart!| |rotatey| - |closedCurve| |indicialEquations| |child| |nextsousResultant2| |clip| - |symbolTable| |viewDefaults| |f02fjf| |listBranches| |rightPower| - |quotientByP| |latex| |tubePointsDefault| |kernels| |shade| - |ellipticCylindrical| |traverse| |primes| |idealSimplify| |setnext!| - |prologue| |ideal| |list?| |wreath| |operator| - |pushFortranOutputStack| |infix?| |conjugates| |complexNormalize| - |inHallBasis?| |OMclose| |null| |frobenius| |linearDependenceOverZ| - |rotate| |rationalApproximation| |popFortranOutputStack| |mask| - |readLineIfCan!| |imagk| |iiacos| |brillhartIrreducible?| - |complexForm| |xn| |zeroDimensional?| |not| |algSplitSimple| - |univariate| |curryLeft| |outputAsFortran| |vspace| |denomRicDE| - |mapExponents| |createPrimitivePoly| |condition| |OMgetEndObject| - |and| |nextPartition| |resetVariableOrder| |search| |quadratic| - |lexGroebner| |scalarMatrix| |rspace| |terms| |exponent| |prod| |ran| - |quickSort| |constant| |or| |startTableInvSet!| |subst| |head| - |drawCurves| |minimumDegree| |airyAi| |modulus| |odd?| |xor| - |operation| |symFunc| |factor| |associatorDependence| |perspective| - |OMputApp| |makeSketch| |cyclotomic| |selectfirst| - |genericLeftMinimalPolynomial| |tablePow| |case| |elRow1!| |sqrt| - |OMgetAtp| |wholePart| |invertibleElseSplit?| |mainSquareFreePart| - |s19abf| |curve| |algint| |s20acf| |Zero| |maximumExponent| |real| - |plot| |setTex!| |range| |linearPart| |alphabetic| |clearTable!| - |deleteProperty!| |imag| |twist| |csc2sin| |evenInfiniteProduct| - |createPrimitiveElement| |extension| |OMputEndBVar| |cycle| |lllip| - |directProduct| |mulmod| |getlo| |hitherPlane| |parents| |listexp| - |swap!| Y |SFunction| |unprotectedRemoveRedundantFactors| |ScanArabic| - |subset?| |backOldPos| |leftZero| |physicalLength| |objects| |besselK| - |cLog| |mathieu11| |headReduced?| |kroneckerDelta| |showAllElements| - |oddlambert| |brace| |rightMinimalPolynomial| |groebnerIdeal| - |findConstructor| |fractionPart| |expandLog| |transcendenceDegree| - |hyperelliptic| |coordinates| |subResultantGcdEuclidean| |destruct| - |bigEndian| |rotate!| |dfRange| |graphCurves| |constantKernel| - |mathieu23| |lookupFunction| |showFortranOutputStack| |comment| - |componentUpperBound| |select!| |bumprow| |e01bhf| |singularitiesOf| - |optpair| |areEquivalent?| |OMencodingXML| |extractIfCan| |trunc| - |mapUp!| |iiexp| |cAcsc| |vector| |copy!| |generalPosition| - |mainPrimitivePart| |goto| |scanOneDimSubspaces| |clipSurface| - |branchPointAtInfinity?| |pol| |c05pbf| |differentiate| |maxIndex| - |factorsOfCyclicGroupSize| |evenlambert| |element?| |setref| - |leftCharacteristicPolynomial| |monomial| |host| |ddFact| |shiftRoots| - |showSummary| |compile| |hspace| |palgRDE0| |localIntegralBasis| - |integralMatrixAtInfinity| |deepestInitial| |s13acf| |multivariate| - |generalizedInverse| |f02axf| |isOr| |zeroOf| |antiCommutative?| |obj| - |genericLeftNorm| |shallowExpand| |primintfldpoly| |augment| - |variables| |putColorInfo| |headAst| |computePowers| |att2Result| - |represents| |youngGroup| |minRowIndex| |cache| |showAttributes| - |schema| |userOrdered?| |approxSqrt| |numberOfFractionalTerms| - |addMatch| |complexZeros| |dmpToHdmp| |pushup| |nor| |mergeFactors| - |constantOpIfCan| |binomThmExpt| |leftNorm| |toseInvertibleSet| - |s21bcf| |s20adf| |pquo| |e04fdf| |crest| |inc| |OMgetType| |name| - |d02kef| |OMencodingSGML| |f01qdf| |adjoint| |unit?| |mainExpression| - |adaptive3D?| |isImplies| |e02zaf| |updatF| |fortranLinkerArgs| - |tanh2trigh| |normDeriv2| |getZechTable| |multiplyCoefficients| - |whatInfinity| |viewDeltaXDefault| |isPlus| |weights| |cscIfCan| - |setleft!| |remove| |resultant| |fibonacci| |conditionP| - |indicialEquation| |nonQsign| |moebius| |rischNormalize| |rroot| - |factors| |sub| |palgextint| |resetBadValues| |scalarTypeOf| |leaf?| - |chebyshevU| |integerBound| |showTheSymbolTable| |d02bbf| |last| |rk4| - |bottom!| |setMaxPoints3D| |entries| |ReduceOrder| |sinIfCan| - |rewriteIdealWithQuasiMonicGenerators| |outlineRender| - |removeRedundantFactorsInPols| |assoc| |palglimint0| |newReduc| - |LazardQuotient| |numberOfIrreduciblePoly| |padicallyExpand| - |flagFactor| |startPolynomial| |seriesToOutputForm| |identification| - |laguerreL| |genericRightMinimalPolynomial| - |semiSubResultantGcdEuclidean2| |OMconnOutDevice| |rootDirectory| - |rdHack1| |bitLength| |c06fpf| |whileLoop| |max| |explimitedint| - |factorial| |minIndex| |jacobi| |leftFactorIfCan| - |numberOfImproperPartitions| |lexico| |OMserve| |closeComponent| - |norm| |complexIntegrate| |d02gbf| |useEisensteinCriterion| |randomR| - |nthCoef| |setPosition| |hasoln| |in?| |polar| |cyclic| - |sylvesterSequence| |decompose| |df2st| BY |SturmHabicht| |rightMult| - |nullity| |d02gaf| |sizeLess?| |neglist| |cAsinh| |makeYoungTableau| - |generalInfiniteProduct| |fortranCharacter| |updatD| |zeroDim?| - |inverseColeman| |palgLODE0| |reflect| |isExpt| |minimalPolynomial| - |s17def| |solveLinearPolynomialEquationByRecursion| |acothIfCan| - |subTriSet?| |primitivePart| |iomode| |convergents| |corrPoly| - |optAttributes| |prime| |merge!| |imaginary| |f04mcf| |anticoord| - |taylorQuoByVar| |solveInField| |arg1| |stoseInvertible?| - |integralRepresents| |cPower| |OMputFloat| |elliptic| - |groebnerFactorize| |realSolve| |newLine| |complexExpand| |arg2| - |rootOf| |leftRank| |complex?| |mirror| |genericRightTraceForm| - |contains?| |OMgetApp| |pleskenSplit| |bandedJacobian| - |realEigenvectors| |const| |removeRoughlyRedundantFactorsInPols| - |digit?| |pureLex| |removeSuperfluousQuasiComponents| |graphStates| - |subCase?| NOT |polarCoordinates| |totalfract| |allRootsOf| - |conditions| |seriesSolve| |lyndon?| |cSin| |prinpolINFO| |leftFactor| - OR |generalSqFr| |perfectNthPower?| |s15adf| |numFunEvals3D| |match| - |rightNorm| |stoseSquareFreePart| |decreasePrecision| |matrixConcat3D| - |acoshIfCan| |eyeDistance| |asimpson| AND |outputGeneral| - |stopMusserTrials| |s17dhf| |createPrimitiveNormalPoly| - |diophantineSystem| |leastAffineMultiple| |mindeg| |dimensionsOf| - |taylorIfCan| |resultantReduit| |sizePascalTriangle| - |createRandomElement| |pow| |OMgetFloat| |makeGraphImage| |acsc| - |trailingCoefficient| |insertRoot!| |univariatePolynomialsGcds| - |iifact| |identity| |nthExpon| |bandedHessian| |deleteRoutine!| |sinh| - |hdmpToDmp| |ode2| |linkToFortran| |euclideanGroebner| |normalized?| - |entry| |getProperty| |OMParseError?| |OMwrite| |cosh| - |semicolonSeparate| |polyred| |bipolar| |removeCoshSq| |putGraph| - |ocf2ocdf| |iiperm| |reciprocalPolynomial| |viewSizeDefault| - |safetyMargin| |debug| |tanh| |quotedOperators| |divideExponents| - |OMgetVariable| |blue| |figureUnits| |pomopo!| - |absolutelyIrreducible?| |readable?| |unparse| |lfextlimint| D |coth| - |d01akf| |var1StepsDefault| |setLength!| |distFact| |setAdaptive| - |ratpart| |solveLinear| |is?| |getMeasure| |jacobian| |sech| - |monicLeftDivide| |setRow!| |antiAssociative?| |null?| |omError| - |eulerE| |roughEqualIdeals?| |changeThreshhold| |csch| |red| |sign| - |assign| |primeFrobenius| |c06gsf| |insert!| |sequence| |OMgetBVar| - |f02ajf| |asinh| |padicFraction| |argscript| |compdegd| |polCase| - |abelianGroup| |mkIntegral| * |rootSimp| |char| |negative?| - |removeSinSq| |revert| |acosh| |printTypes| |truncate| - |normalizeAtInfinity| |lastSubResultantElseSplit| |scopes| |bag| - |properties| |recip| |subscriptedVariables| |exptMod| |atanh| - |structuralConstants| |plusInfinity| |leftScalarTimes!| - |exprHasWeightCosWXorSinWX| |chiSquare| |readUInt32!| |comparison| - |translate| |distribute| |OMputError| |mapMatrixIfCan| |acoth| - |minusInfinity| |randnum| |meshPar2Var| |listOfLists| |swapRows!| - |rem| = |particularSolution| |innerint| |toseSquareFreePart| |asech| - |blankSeparate| |redpps| |topFortranOutputStack| |polyRicDE| |pair?| - |quo| |calcRanges| |innerEigenvectors| |cAcos| |setEpilogue!| - |traceMatrix| |roughBasicSet| |lineColorDefault| - |stiffnessAndStabilityOfODEIF| |cyclicEntries| - |selectSumOfSquaresRoutines| |complexLimit| < - |basisOfCommutingElements| |primaryDecomp| |pushdterm| - |purelyAlgebraicLeadingMonomial?| |multiple| |print| |radPoly| - |stirling2| |e01saf| |tubePlot| |div| > |interpretString| |applyQuote| - |float| |beauzamyBound| |OMputBVar| |resolve| |tab| - |fortranCarriageReturn| |stop| |reduceBasisAtInfinity| |directSum| - |leadingIndex| |exquo| |f02xef| <= |permutationRepresentation| - |gderiv| |jordanAlgebra?| |e02bcf| |type| |getBadValues| |f02wef| - |partialFraction| |f04qaf| ~= >= |triangularSystems| |changeName| - |inf| |basisOfLeftNucloid| |zero?| |showArrayValues| |arbitrary| - |fullDisplay| |fglmIfCan| |#| |heapSort| |f04atf| |ruleset| - |viewPhiDefault| |deepExpand| |virtualDegree| |moreAlgebraic?| ~ - |expIfCan| |setProperties| |quadraticNorm| |f01ref| |interpret| - |cycleElt| |antiCommutator| |lllp| |generalizedEigenvector| |getCurve| - |unary?| + |principalIdeal| |content| - |zeroSetSplitIntoTriangularSystems| |every?| |point?| |cos2sec| - |unitVector| |pseudoDivide| |signature| |leftGcd| - |selectsecond| - |setStatus| |pointColorDefault| |suchThat| |bivariateSLPEBR| |create| - |space| |qelt| |useSingleFactorBound| |/\\| / - |semiResultantEuclidean1| |gcdprim| |midpoints| |retractIfCan| - |unaryFunction| |string?| |s18aef| |sorted?| |transcendentalDecompose| - |arguments| |qsetelt| |\\/| |readIfCan!| |transform| |s18acf| - |besselI| GE |integralDerivationMatrix| |factorSFBRlcUnit| |push!| - |tryFunctionalDecomposition| |HermiteIntegrate| |xRange| |qroot| - |eof?| |numer| |leadingCoefficientRicDE| GT |e04jaf| - |listYoungTableaus| |crushedSet| |factor1| |normalise| |yRange| - |elem?| |cosh2sech| |generators| |denom| |e02bdf| LE |integer?| - |solve1| |sech2cosh| |zRange| |basicSet| |integral?| |typeList| - |removeSinhSq| LT |critM| |atoms| |anfactor| |topPredicate| - |printInfo!| |map!| |nsqfree| |pastel| |pi| |rightTrace| |f04maf| - |exists?| |rightExactQuotient| |fortranLiteral| |d03faf| |rk4qc| - |qsetelt!| |shift| |collect| |infinity| |removeCosSq| |palgLODE| - |d01anf| |leadingBasisTerm| |opeval| |redPol| |prolateSpheroidal| - |iiasech| |connect| |totolex| |printHeader| |interactiveEnv| |leftLcm| - |numericalIntegration| |cCot| |intersect| |ode1| |iiacsc| - |rightRegularRepresentation| |makeCos| |map| |OMgetEndAttr| - |outputForm| UTS2UP |relerror| |viewThetaDefault| |outputFloating| - |kernel| |lowerCase| |OMlistSymbols| |Beta| |setVariableOrder| - |viewpoint| |property| |separateFactors| |f02akf| - |possiblyNewVariety?| |gradient| |chvar| |draw| |s17aff| - |factorSquareFree| |center| |makeSeries| |over| |palgRDE| |cSech| - |subHeight| |irreducibleRepresentation| |acsch| |cond| - |numberOfCycles| |bezoutDiscriminant| |e02dcf| |OMopenString| - |BumInSepFFE| |finiteBound| |cAtan| |s17dcf| |internalZeroSetSplit| - |makeResult| |prefixRagits| |symmetric?| |infieldint| |ParCond| - |units| |useNagFunctions| |OMputInteger| |viewZoomDefault| |constant?| - |lieAlgebra?| |stoseLastSubResultant| |convert| |createThreeSpace| - |coerceImages| |makeSUP| |tanQ| |e04naf| |nthr| |minPoints3D| - |makeObject| |dflist| |e01bgf| |clikeUniv| |currentSubProgram| - |weierstrass| |unrankImproperPartitions0| |roughBase?| |unmakeSUP| - |secIfCan| |semiDiscriminantEuclidean| |coef| |just| |f04adf| - |charthRoot| |order| |checkForZero| |computeCycleLength| |algebraicOf| - |leftPower| |nativeModuleExtension| |e01daf| |rubiksGroup| - |hypergeometric0F1| |internalLastSubResultant| |imagi| |bright| - |irreducibleFactor| |rationalFunction| |dn| |e02gaf| |numberOfHues| - |alphanumeric?| |measure| |rootsOf| |complement| |code| |nil?| - |readBytes!| |mainMonomial| |iiGamma| |fortranCompilerName| |status| - |arrayStack| |attributeData| |binaryFunction| |algebraic?| - |setClipValue| LODO2FUN |failed| |adaptive?| |minrank| |scan| |copies| - |B1solve| |setright!| |datalist| |reorder| |graphState| |squareFree| - |modularFactor| |OMlistCDs| |fortran| |tanh2coth| |members| - |buildSyntax| |bat1| |OMputObject| |rightRankPolynomial| |errorInfo| - |function| |OMconnInDevice| |combineFeatureCompatibility| |graphs| - |multiEuclideanTree| |inconsistent?| |totalDifferential| |cfirst| |lo| - |hermiteH| |sylvesterMatrix| |var2Steps| |baseRDEsys| |e04gcf| - |f01bsf| |universe| |listOfMonoms| |asecIfCan| |localReal?| |refine| - |differentialVariables| |kmax| |difference| |OMreadFile| |meatAxe| - |genericRightTrace| |mesh?| |discriminant| |roughUnitIdeal?| - |predicates| |karatsubaDivide| |fixedDivisor| |elements| |spherical| - |qualifier| |dom| |leaves| |horizConcat| |createZechTable| - |inputOutputBinaryFile| |sqfrFactor| |rur| |concat!| |iroot| |diag| - |makeMulti| |radix| |initials| |s17acf| |headRemainder| |conical| - |abs| |psolve| |initializeGroupForWordProblem| |addPointLast| - |getExplanations| |stFuncN| |mappingAst| |decimal| - |standardBasisOfCyclicSubmodule| |schwerpunkt| |shrinkable| - |basisOfLeftNucleus| |fractRagits| |ldf2vmf| |makeCrit| |lazyPrem| - |lhs| |skewSFunction| |roman| |makeViewport3D| |cTanh| - |solveLinearPolynomialEquation| |inverseIntegralMatrix| - |factorGroebnerBasis| |quasiMonic?| |slash| |antisymmetric?| |coerceS| - |rhs| |normal| |ODESolve| |extractClosed| |triangSolve| |nthExponent| - |roughSubIdeal?| |mkcomm| |numberOfNormalPoly| - |semiResultantReduitEuclidean| |s17ahf| |commaSeparate| |title| - |compose| |iidsum| |simpleBounds?| |variationOfParameters| - |tensorProduct| |rightUnits| |divideIfCan!| |child?| - |primPartElseUnitCanonical| |resetNew| |LiePoly| |pack!| - |indiceSubResultant| |e01sff| |subResultantsChain| |tubeRadiusDefault| - |isOpen?| |composites| |minPoly| |safeFloor| |c06gqf| |doubleComplex?| - |OMputEndApp| |normal01| |generalLambert| |coth2tanh| |true| |janko2| - |xCoord| |deepestTail| |argumentList!| |e| |script| |cartesian| - |mkAnswer| |selectPolynomials| |reducedContinuedFraction| |unknown| - |mainContent| |compBound| |s19adf| |systemSizeIF| |reverse!| - |paraboloidal| |reduction| |unitsColorDefault| |fortranTypeOf| - |noKaratsuba| |key?| |duplicates| |yCoord| |enterPointData| |df2fi| - |PollardSmallFactor| |associator| |position!| |sayLength| - |commutative?| |signatureAst| |linearAssociatedLog| |isNot| |nothing| - |tex| |palginfieldint| |firstUncouplingMatrix| |SturmHabichtSequence| - |iExquo| |vark| |setprevious!| |normalDenom| |open?| |showClipRegion| - |readInt16!| |gcdPrimitive| |reify| |tubeRadius| |replaceKthElement| - |power!| |isConnected?| |finite?| |sinh2csch| |triangular?| - |coefficients| |iteratedInitials| |power| |ramifiedAtInfinity?| - |invertIfCan| |empty?| |isMult| |optional?| |d01gbf| |poisson| |one?| - |limitPlus| |reverseLex| |outputList| |euclideanSize| |d02cjf| |queue| - |bumptab| |pushdown| |rootPoly| |radicalEigenvectors| |permutation| - |diagonal?| |hasTopPredicate?| |OMgetInteger| |critpOrder| - |radicalEigenvector| |rk4a| |swap| |saturate| |monomialIntPoly| - |SturmHabichtCoefficients| |birth| |printInfo| |currentEnv| - |expenseOfEvaluation| |rightExtendedGcd| |solveid| |generalTwoFactor| - |uniform| |width| |credPol| |setLabelValue| |f02bjf| - |generalizedContinuumHypothesisAssumed| |more?| - |exprHasAlgebraicWeight| |wordsForStrongGenerators| |factorList| - |cyclePartition| |iitanh| |reverse| |zerosOf| - |degreeSubResultantEuclidean| |completeHermite| |constantRight| - |normalize| |collectUnder| |trigs| |cyclotomicFactorization| |ldf2lst| - |reduceByQuasiMonic| |localUnquote| |subscript| |call| |OMputSymbol| - |linearPolynomials| |interReduce| |se2rfi| |OMcloseConn| |move| - |quasiAlgebraicSet| |bringDown| |OMsend| |getDatabase| |pointPlot| - |algebraicSort| |adaptive| |getStream| |aCubic| |GospersMethod| |open| - |radicalEigenvalues| |constDsolve| |rightDivide| |matrixDimensions| - |coHeight| |taylor| |Nul| |Si| |euler| |c02agf| |sumOfSquares| - |modularGcd| |tRange| |dictionary| |exprToXXP| |laurent| |e02akf| - |s21baf| |coshIfCan| |expextendedint| |f01qcf| |f04jgf| - |numberOfOperations| |leftAlternative?| |puiseux| |partialNumerators| - |dihedral| |kovacic| |singRicDE| |cylindrical| |optional| - |permutationGroup| |rischDE| |leftUnits| |debug3D| - |removeRoughlyRedundantFactorsInContents| - |tryFunctionalDecomposition?| |iprint| |edf2fi| |incr| |wrregime| - |operations| |block| |s18adf| |less?| |Frobenius| |inv| - |constantToUnaryFunction| |nullSpace| |RemainderList| |ricDsolve| |hi| - |dmp2rfi| |find| |realEigenvalues| |rootSplit| |product| |ground?| - |aromberg| |splitNodeOf!| |drawComplex| |csch2sinh| |nand| - |definingPolynomial| |setAttributeButtonStep| |high| |ground| |f02agf| - |octon| |numericalOptimization| |toseInvertible?| |reindex| - |copyInto!| |stopTableGcd!| |prinb| |c06ekf| |leadingMonomial| |iisec| - |leviCivitaSymbol| |currentScope| |nil| |OMUnknownCD?| |acscIfCan| - |returns| |parseString| |recoverAfterFail| |screenResolution| |init| - |leadingCoefficient| |intPatternMatch| |separateDegrees| |optimize| - |newTypeLists| |physicalLength!| |cothIfCan| |symbolTableOf| - |quasiRegular?| |primitiveMonomials| |getGoodPrime| |e01bff| - |diagonalProduct| |wronskianMatrix| |iicot| |extractBottom!| |cAsech| - |realElementary| |quotient| |reductum| SEGMENT |makeprod| |ode| - |subspace| |countable?| |approximate| |stoseInvertibleSetsqfreg| - |commutativeEquality| |hcrf| |representationType| |cSinh| |rules| - |isAbsolutelyIrreducible?| |ratDenom| - |generalizedContinuumHypothesisAssumed?| |complex| |loopPoints| - |basisOfRightAnnihilator| |principal?| |rightScalarTimes!| |vedf2vef| - |pseudoRemainder| |setchildren!| |factorByRecursion| |split!| |log| - |e02baf| |rCoord| |primeFactor| |lambert| |packageCall| |innerSolve| - |interpolate| |getVariableOrder| |factorOfDegree| |OMputEndAttr| - |denomLODE| |certainlySubVariety?| |lowerPolynomial| |cyclicParents| - |ignore?| |edf2df| |setEmpty!| |flatten| |reseed| |lexTriangular| - |outputBinaryFile| |makeop| |eigenMatrix| |rangeIsFinite| |write!| - |complexEigenvectors| |primitive?| |OMencodingUnknown| |cubic| |lprop| - |multiple?| |uniform01| |fixedPoint| |c06ecf| - |constantCoefficientRicDE| |Aleph| |balancedFactorisation| - |completeEval| |sturmSequence| |definingEquations| |set| - |stronglyReduce| |simplifyExp| |OMReadError?| |viewWriteDefault| - |gcdcofact| |e04ycf| |mathieu22| |mainMonomials| |bfKeys| - |reducedForm| |palgintegrate| |palgint0| |getRef| |e02ajf| |concat| - |iiasin| |nextColeman| |tab1| |OMgetString| |linear?| |byte| |cCsc| - |rightTraceMatrix| |logIfCan| |extendedint| |OMputEndBind| - |rationalPower| |bothWays| |linearDependence| |e02ddf| |dualSignature| - |multiset| |e02bbf| |equality| |unvectorise| |simpson| |nthFactor| - |fill!| |strongGenerators| |printingInfo?| |lfintegrate| - |resultantEuclidean| |iiasec| |coefficient| |associatedEquations| - |fullPartialFraction| |separant| |simplifyLog| |unitNormal| |int| - |minset| |doubleResultant| |inspect| |computeBasis| |acschIfCan| - |besselJ| |category| |presub| |OMgetEndError| |torsion?| |f01brf| - |outerProduct| |radicalSimplify| |Ei| |d01aqf| |monomialIntegrate| - |chainSubResultants| |coerce| |domain| |karatsuba| |e04dgf| - |startTable!| |setCondition!| |expenseOfEvaluationIF| |bounds| - |vectorise| |droot| |rewriteSetWithReduction| |construct| |package| - |mightHaveRoots| |polynomialZeros| |minimumExponent| |mapGen| |source| - 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|multinomial| |mapmult| |replace| |scripts| |update| |fmecg| - |presuper| |zoom| |toroidal| |removeZero| |sec| |badNum| |postfix| - |readLine!| |choosemon| |distance| |imagK| |tanSum| |root| |integral| - |csc| |autoCoerce| |modifyPoint| |list| |digit| |gethi| - |solveLinearPolynomialEquationByFractions| |commonDenominator| - |tableau| |epilogue| |setErrorBound| |getOrder| |asin| |splitLinear| - |car| |prindINFO| |OMgetEndApp| |rst| |s17akf| |lazyPseudoRemainder| - |reducedDiscriminant| |quoted?| |characteristic| |acos| |OMgetEndBind| - |cdr| |iiabs| |supRittWu?| |OMopenFile| |acotIfCan| |chebyshevT| - |iisqrt2| |smith| |exponentialOrder| |gramschmidt| |atan| - |setDifference| |cschIfCan| |powmod| |surface| |subtractIfCan| - |position| |preprocess| |pointLists| |besselY| |rationalPoints| - |e01baf| |acot| |rotatez| |setIntersection| |selectOrPolynomials| - |quatern| |genus| |declare| |aQuartic| |rightRecip| |overbar| - |rotatex| |internalInfRittWu?| |asec| |eigenvalues| |setUnion| - |splitConstant| |tanIfCan| |isTerm| |match?| |partialDenominators| - 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|createMultiplicationTable| |shallowCopy| |removeSquaresIfCan| - |cosIfCan| |super| |mat| |cap| |iitan| |subresultantVector| |linear| - |useEisensteinCriterion?| |genericLeftTrace| |exprToGenUPS| |isTimes| - |integralBasisAtInfinity| |fortranComplex| |nextLatticePermutation| - |singular?| |lyndonIfCan| |initTable!| |expressIdealMember| |check| - |segment| |jordanAdmissible?| |modTree| |tanintegrate| |exQuo| - |polynomial| |radicalSolve| |sin2csc| |lazyPquo| |getPickedPoints| - |euclideanNormalForm| |lists| |degreeSubResultant| - |univariatePolynomial| |weighted| |dim| |tracePowMod| |asinhIfCan| - |remainder| |test| |numberOfMonomials| |numFunEvals| |iiatanh| - |firstNumer| |repeating?| |homogeneous?| |pointData| |superscript| - |loadNativeModule| |rewriteIdealWithRemainder| |LiePolyIfCan| - |isEquiv| |semiSubResultantGcdEuclidean1| - |halfExtendedSubResultantGcd1| |upperCase?| |s01eaf| - |compiledFunction| |HenselLift| |rischDEsys| |id| - |antisymmetricTensors| |littleEndian| |findCycle| |f07aef| |geometric| - |factorSquareFreePolynomial| |enumerate| |eq| |inrootof| - |numericIfCan| |cAsec| |dihedralGroup| |formula| |hue| |flexibleArray| - |maxPoints3D| |table| |upDateBranches| |iter| |exportedOperators| - |binary| |prefix| |makeEq| |writeUInt8!| |numberOfPrimitivePoly| - |shuffle| |decomposeFunc| |inRadical?| |new| |mkPrim| |e02dff| - |rightZero| |subNode?| |constantIfCan| |fracPart| |rowEchelonLocal| - |insert| |setScreenResolution| |symbolIfCan| |root?| |OMsetEncoding| - |iicoth| |getCode| |setColumn!| |checkPrecision| |uncouplingMatrices| - |insertBottom!| |mainForm| |quoByVar| |clearCache| |randomLC| |nrows| - |s18def| |totalGroebner| |options| |nextNormalPoly| |validExponential| - |superHeight| |palglimint| |OMsupportsSymbol?| |unknownEndian| - |create3Space| |output| |ncols| |keys| - |selectMultiDimensionalRoutines| |approximants| |rationalPoint?| - |returnType!| |e02def| |monomRDE| |directory| |multMonom| |log2| - |leftExactQuotient| |perfectSquare?| |oddInfiniteProduct| |socf2socdf| - |f01qef| |trace2PowMod| |predicate| |fprindINFO| |symmetricRemainder| - |One| |removeIrreducibleRedundantFactors| - |semiDegreeSubResultantEuclidean| |string| |exp| |balancedBinaryTree| - |tanAn| |outputFixed| |exactQuotient| |leftRemainder| |lfunc| - |rewriteIdealWithHeadRemainder| |removeRoughlyRedundantFactorsInPol| - |monicRightFactorIfCan| |exp1| |mdeg| |leastMonomial| |axes| - |errorKind| |doubleDisc| |dequeue| |readUInt8!| |domainTemplate| - |ramified?| |createLowComplexityNormalBasis| |second| - |derivationCoordinates| |restorePrecision| |OMputEndAtp| |coordinate| - |rewriteSetByReducingWithParticularGenerators| - |halfExtendedResultant1| |viewport2D| |primextendedint| |stFunc2| - |numberOfDivisors| |third| |characteristicPolynomial| |numeric| |eq?| - |capacity| |decrease| |cAsin| |graeffe| |lex| |getButtonValue| - |branchPoint?| |left| |listConjugateBases| |radical| |s15aef| - |binaryTournament| |sup| |exponential1| |iipow| |iiasinh| - |primlimintfrac| |trigs2explogs| |solveLinearlyOverQ| |pole?| |elt| - |right| |nil| |infinite| |arbitraryExponent| |approximate| |complex| - |shallowMutable| |canonical| |noetherian| |central| - |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| - |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| - |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| - |finiteAggregate| |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |copyInto!| |dominantTerm| |sumOfSquares| |prod| + |map| |imagj| |ellipticCylindrical| |tableau| |makeCos| + |beauzamyBound| |kernel| |lllip| |createPrimitivePoly| + |removeRoughlyRedundantFactorsInPol| |chiSquare| |ldf2lst| + |divideExponents| |monic?| |draw| |iitan| |prevPrime| |enumerate| + |f01rdf| |center| |eigenvectors| |shufflein| + |resultantReduitEuclidean| |pseudoQuotient| |presub| |simpsono| + |mpsode| |rootOfIrreduciblePoly| |e02daf| |e02bdf| |rdHack1| + |countRealRoots| |viewPhiDefault| |resetBadValues| |elliptic?| + |mathieu11| |binaryFunction| |measure| |basisOfRightAnnihilator| + |increment| |c02aff| |formula| |assign| |OMreadFile| |newTypeLists| + |expr| |nlde| |convert| |qroot| |e01bgf| |optpair| |setImagSteps| + |makeObject| |stopMusserTrials| |swapColumns!| |optAttributes| + |besselY| |asechIfCan| |cyclic| |OMsupportsSymbol?| + |ramifiedAtInfinity?| |sqfrFactor| |build| |coef| |dmpToP| |seed| + |predicate| |minRowIndex| |Vectorise| |symmetricGroup| + |leftTraceMatrix| |numberOfOperations| |fractionFreeGauss!| + |stronglyReduce| |skewSFunction| |e04ucf| |reverse| |laurentRep| + |d01ajf| |nrows| |sechIfCan| |body| |ran| |modularGcd| |variable| + |call| |viewport2D| |traverse| |scale| |component| |ncols| |symbol| + |indicialEquationAtInfinity| |realZeros| |status| |OMgetEndObject| + |iterators| |monicRightFactorIfCan| |overlap| |OMgetVariable| + |reduceByQuasiMonic| |OMgetEndAttr| |expression| |alphabetic| |pair?| + |definingInequation| |subresultantVector| |partialQuotients| + |scalarTypeOf| |integer| |exists?| |csch2sinh| |cCosh| |stFunc1| + |janko2| |distance| |exponential| |OMgetEndError| ** |qinterval| + |s01eaf| |rootsOf| |algebraic?| |changeName| |insertTop!| |factorList| + |dimensionOfIrreducibleRepresentation| |characteristicSerie| + |dualSignature| |e04gcf| |rationalPoints| |mergeDifference| + |normalizeAtInfinity| |cAtan| |child| |colorDef| |discreteLog| |port| + |isImplies| |semiResultantEuclidean2| |eof?| |numeric| |countable?| + |selectOptimizationRoutines| |invertIfCan| |rightUnit| |OMconnectTCP| + |lo| |iiacos| |OMputEndAttr| |parameters| |radical| |primextendedint| + |separate| |graphCurves| |torsionIfCan| |shellSort| |vertConcat| + |s15adf| |t| |fprindINFO| |GospersMethod| |insertBottom!| |reduced?| + |error| |constant?| UP2UTS |intensity| |removeSuperfluousCases| + |signatureAst| |middle| |htrigs| |FormatArabic| |schema| |assert| + |removeRedundantFactorsInContents| |squareFreePolynomial| + |companionBlocks| |numberOfNormalPoly| |s17aef| |label| |reify| + |simplifyExp| |mappingAst| |closeComponent| |normal| + |removeSuperfluousQuasiComponents| |calcRanges| |mvar| |knownInfBasis| + |repSq| |readUInt16!| |numerator| |empty| |UP2ifCan| + |univariatePolynomials| |nand| |multiset| |jacobian| |rubiksGroup| + |boundOfCauchy| |bipolar| |cyclePartition| |constantToUnaryFunction| + |e02agf| |e02zaf| |pade| |clearTable!| |chebyshevT| |sort| |xCoord| + |nextsousResultant2| |imagK| |redmat| |wholePart| |makeUnit| + |compiledFunction| |isExpt| |imagJ| |over| |rationalIfCan| |has?| + |internalIntegrate| |iiatanh| |totolex| |linearAssociatedLog| + |leadingExponent| |palgint| |unknown| |purelyAlgebraic?| |polyRDE| + |lastSubResultantElseSplit| |createNormalPoly| |expintegrate| + |bombieriNorm| |asinIfCan| |hMonic| |f01bsf| |brillhartIrreducible?| + |point?| |minimumExponent| GF2FG |lieAlgebra?| |inf| + |fullPartialFraction| |errorInfo| |constructor| + |factorsOfCyclicGroupSize| |innerEigenvectors| |squareFreePart| + |univariate?| |random| |padicallyExpand| |leadingCoefficientRicDE| + |constantKernel| |zeroMatrix| |fibonacci| |lastSubResultant| + |numFunEvals3D| |transpose| |denomLODE| |radicalEigenvalues| |option| + |llprop| |OMReadError?| |noLinearFactor?| |stoseInvertibleSetsqfreg| + FG2F |makeTerm| |basisOfCommutingElements| |algebraicCoefficients?| + |gensym| |symmetricRemainder| |bitTruth| |userOrdered?| |mainForm| + |norm| |tubeRadius| |graphStates| |iisin| |c06fuf| |normalizedDivide| + |stopTable!| |OMgetInteger| |limitedIntegrate| |stFunc2| + |approxNthRoot| |outputList| |overlabel| |cotIfCan| |makeSin| + |changeWeightLevel| |hypergeometric0F1| |meshPar1Var| |previous| + |close!| |exprex| |decimal| |clip| |rightGcd| |nullSpace| |rightTrim| + |deleteProperty!| |updatF| |semiResultantReduitEuclidean| + |nthRootIfCan| |iiacot| |iitanh| |simplifyPower| |currentEnv| |c06gbf| + |interval| |invertibleElseSplit?| |leftTrim| |e02bbf| + |definingPolynomial| |weight| |iisqrt2| |palgRDE| |deepestTail| + |halfExtendedSubResultantGcd2| |tanSum| |firstNumer| |rename| + |HenselLift| |integerIfCan| |minimalPolynomial| |monicLeftDivide| + |c05adf| |box| |scopes| |genericRightDiscriminant| |removeCoshSq| + |s17adf| |printHeader| |universe| |rangePascalTriangle| |ef2edf| + |singularAtInfinity?| |explogs2trigs| |digamma| |basisOfLeftNucloid| + |setFieldInfo| |separant| |bivariate?| |genericLeftTraceForm| |cAcos| + |getOperator| |cos2sec| |flagFactor| |close| + |noncommutativeJordanAlgebra?| |functorData| |stoseLastSubResultant| + |OMconnInDevice| |conditionP| |mapGen| |isNot| |viewWriteAvailable| + |constDsolve| |certainlySubVariety?| |lift| |uniform| |e04jaf| + |perfectSqrt| |complexIntegrate| |imagE| |cot2tan| |kind| |rightNorm| + |redPo| |viewport3D| |complexForm| |evenlambert| |display| |reduce| + |approxSqrt| |laurent| |commutativeEquality| |setOfMinN| + |replaceKthElement| |subCase?| |primaryDecomp| |op| |divide| + |removeIrreducibleRedundantFactors| |infLex?| |critpOrder| + |viewWriteDefault| |puiseux| |normFactors| |mathieu23| |divergence| + |initiallyReduced?| |delta| |fTable| |squareTop| |rootNormalize| + |newSubProgram| |lazyIntegrate| |numberOfDivisors| |zerosOf| + |quoByVar| |gcdcofactprim| |mainSquareFreePart| |outputMeasure| + |getOperands| |setRow!| |elColumn2!| |leftUnit| |pattern| |iicsch| + |inv| |invertible?| |viewDefaults| |OMputEndError| |RemainderList| + |equality| |dAndcExp| |iiacoth| |internalLastSubResultant| |cSech| + |ground?| |btwFact| |linSolve| |leftDivide| |interactiveEnv| + |repeating?| |mantissa| |setAttributeButtonStep| |fortranLinkerArgs| + |s17ahf| |s17def| |input| |e02aef| |ground| |argumentList!| + |lowerCase?| |standardBasisOfCyclicSubmodule| |messagePrint| + |listRepresentation| |twist| |square?| |color| |smith| |library| + |dequeue!| |bag| |leadingMonomial| |normalizeIfCan| |root| + |combineFeatureCompatibility| |indicialEquation| |setButtonValue| + |rischDEsys| |union| |lowerPolynomial| |removeRedundantFactors| + |startPolynomial| |message| |init| |laplace| |leadingCoefficient| + |createThreeSpace| |putGraph| |complexNumericIfCan| |simplifyLog| + |rootPower| |palginfieldint| |element?| |xn| |delete!| + |fortranLiteralLine| |primitiveMonomials| |lifting| |d01bbf| + |polarCoordinates| |inGroundField?| |lambda| |factorsOfDegree| + |tValues| |rombergo| |semiDegreeSubResultantEuclidean| |normal?| + |listYoungTableaus| |reductum| |d02gbf| |zero?| |trueEqual| |bytes| + |listOfMonoms| |setEpilogue!| |groebner| |rightDivide| |push| + |lookupFunction| |gcdcofact| |mr| |satisfy?| |rules| |power!| |c06gcf| + |functionIsOscillatory| |stoseSquareFreePart| |cAtanh| + |extendedResultant| |radicalEigenvector| |numberOfFractionalTerms| + |maxColIndex| |hcrf| |zCoord| |integralCoordinates| |s19abf| + |pushdterm| |split| |lepol| |commaSeparate| |mainCharacterization| + |randomLC| |characteristicPolynomial| |maxRowIndex| |f02fjf| |s13aaf| + |ricDsolve| |top| |irreducibleRepresentation| |cons| + |intermediateResultsIF| |comp| |OMencodingBinary| |exponentialOrder| + |imagi| |cyclicGroup| |s17ajf| |OMgetAttr| + |degreeSubResultantEuclidean| |charClass| |sortConstraints| + |identification| |flatten| |radicalRoots| |unvectorise| + |antiAssociative?| |cycleSplit!| |subHeight| |cartesian| |schwerpunkt| + |pushucoef| |homogeneous?| |leftLcm| |tanh2trigh| |quasiRegular| + |ksec| |pToDmp| |selectFiniteRoutines| |linearMatrix| |charpol| + |continue| |mix| |unitNormal| |totalfract| |module| |high| + |solveLinearPolynomialEquationByRecursion| |setref| |groebner?| + |csubst| |ocf2ocdf| |npcoef| |nonQsign| |initiallyReduce| + |traceMatrix| |csc2sin| |normalDeriv| |cyclicParents| + |seriesToOutputForm| |f02aff| |recip| |coerceImages| |integral| |list| + |graphs| |iFTable| |antisymmetricTensors| |setleaves!| + |balancedBinaryTree| |partition| |useEisensteinCriterion| |signAround| + |isConnected?| |showArrayValues| |withPredicates| |car| |any?| |cCos| + |zeroDimensional?| |positive?| |rk4a| |mapDown!| |crushedSet| + |intcompBasis| |possiblyInfinite?| |ScanFloatIgnoreSpaces| |cdr| + |asecIfCan| |purelyAlgebraicLeadingMonomial?| + |exprHasLogarithmicWeights| |matrixDimensions| |parametric?| + |representationType| |e04ycf| |checkRur| |setDifference| |dmp2rfi| + |supDimElseRittWu?| |member?| |addiag| |createMultiplicationTable| + |compose| |mapBivariate| |changeNameToObjf| |addMatch| + |showFortranOutputStack| |s21bbf| |setIntersection| |curve| + |decreasePrecision| |normDeriv2| |explicitlyEmpty?| |gramschmidt| + |linearlyDependentOverZ?| |eq?| |setUnion| |s18def| |listBranches| + |numericalIntegration| |pointData| |alternative?| |outerProduct| + |simpson| |integrate| |rational?| |null?| |sort!| |pascalTriangle| + |even?| |completeHermite| |apply| |airyBi| |leftDiscriminant| + |precision| |monicRightDivide| |lazyPseudoDivide| + |identitySquareMatrix| |irreducibleFactor| |shrinkable| |solve| + |multiEuclideanTree| |moebius| |pseudoDivide| |setRealSteps| + |expandPower| |ignore?| |intChoose| |leftOne| |minGbasis| |getMatch| + |compactFraction| |minset| |size| |explimitedint| |f02agf| |elements| + |leftCharacteristicPolynomial| |complexSolve| |flexible?| |iiperm| + |summation| |subMatrix| |laplacian| |ptree| |roughBasicSet| + |evenInfiniteProduct| |acothIfCan| |tanAn| |c06gqf| |modifyPoint| + |makeSUP| |ord| |allRootsOf| |createMultiplicationMatrix| |readByte!| + |rootSimp| |arbitrary| |lflimitedint| |randomR| |finite?| |first| + |cSec| |myDegree| |s20acf| |iidsum| |f2df| |key| |splitConstant| + |find| |lfextendedint| |pop!| |number?| |rest| |sin?| + |realEigenvalues| |topPredicate| |algSplitSimple| |times!| + |integralDerivationMatrix| |point| |setLegalFortranSourceExtensions| + |algint| |cSinh| |isQuotient| |substitute| |denominator| |extendedint| + |numberOfCycles| |rewriteIdealWithRemainder| |omError| |coHeight| + |filename| |consnewpol| |removeDuplicates| |cCot| |superscript| + |totalDifferential| |critB| |OMencodingSGML| |cschIfCan| |shallowCopy| + |Aleph| |erf| |cAsech| |cAcosh| |cyclotomicDecomposition| + |monicDivide| |goodnessOfFit| |laguerreL| |solveLinearlyOverQ| + |bezoutMatrix| |cAcsch| |headAst| |parse| |series| |prefixRagits| + |root?| |eval| |doubleResultant| |returnTypeOf| + |shanksDiscLogAlgorithm| |trapezoidalo| |extendIfCan| |edf2df| + |patternMatch| |restorePrecision| |testModulus| |makeGraphImage| + |iisinh| |rischNormalize| |nextPrimitiveNormalPoly| |saturate| + |lyndon?| EQ |rightDiscriminant| |dilog| |cyclicSubmodule| + |selectODEIVPRoutines| |height| |infinityNorm| |inconsistent?| |df2fi| + |d02raf| |powern| |elementary| |ODESolve| |doubleComplex?| |sin| |abs| + |laurentIfCan| |seriesSolve| |wholeRagits| |any| |alternating| + |someBasis| |cardinality| |checkForZero| |distFact| |internalAugment| + |min| |cos| |setLabelValue| |removeZero| |iibinom| |sinh2csch| + |rootSplit| |bezoutDiscriminant| |toseSquareFreePart| + |fortranCharacter| |characteristic| |tanIfCan| |tan| |untab| + |normalized?| |critBonD| |maximumExponent| |isPower| + |discriminantEuclidean| |contractSolve| |negative?| |cot| |shuffle| + |getBadValues| |OMlistCDs| |whatInfinity| + |genericRightMinimalPolynomial| |printInfo!| |LiePolyIfCan| |getCurve| + |monicDecomposeIfCan| |factorSFBRlcUnit| |sec| |usingTable?| + |transcendent?| |bezoutResultant| |strongGenerators| |f01qdf| + |rightQuotient| |numberOfChildren| |zeroDimPrime?| |packageCall| + |arg1| |nthRoot| |csc| |realElementary| |symmetric?| |pleskenSplit| + |safeCeiling| |doublyTransitive?| |moebiusMu| |OMputEndBind| |zero| + |pointPlot| |scanOneDimSubspaces| |balancedFactorisation| |asin| + |coordinates| |drawStyle| |setprevious!| |maxrank| |pole?| + |showScalarValues| |cfirst| |perfectSquare?| |linearDependenceOverZ| + |outlineRender| |clearFortranOutputStack| |computePowers| |acos| |lcm| + |OMsetEncoding| |edf2fi| |leftMult| |nonLinearPart| + |PollardSmallFactor| |cSin| |And| |constantOperator| |df2ef| |low| + |index| |OMputEndAtp| |atan| |trailingCoefficient| |cot2trig| + |modTree| |cyclotomic| |solveid| |monomialIntPoly| |delete| + |setPredicates| |mainVariables| |Or| |BasicMethod| |permanent| |pile| + |append| |orbit| |acot| |gcdPolynomial| |lagrange| |edf2ef| |weighted| + |fillPascalTriangle| |declare| |cCoth| |symmetricDifference| |inR?| + |Not| |computeCycleLength| |extractClosed| |pushdown| |getIdentifier| + |f02bjf| |asec| |psolve| |gcd| |leadingBasisTerm| + |extendedSubResultantGcd| |pdf2ef| |overset?| |plot| |contract| + |OMgetEndBind| |showIntensityFunctions| |tail| |getProperty| |pair| + |OMputEndApp| |acsc| |paren| |false| |vconcat| |toseLastSubResultant| + |e02dcf| |value| |blankSeparate| |product| |quadratic?| |setAdaptive| + |normalizedAssociate| |isTerm| |sinh| |badNum| |decomposeFunc| + |printingInfo?| |tanh2coth| |isEquiv| |controlPanel| |incr| |unary?| + |updatD| |degreePartition| |removeSinSq| |f2st| |fortranDouble| + |bandedJacobian| |viewDeltaXDefault| |size?| |nsqfree| + |complementaryBasis| |s18dcf| |bfEntry| |push!| |infieldint| |f02wef| + |recur| |polygon?| |depth| |explicitEntries?| |taylorRep| |hi| + |innerSolve| |selectNonFiniteRoutines| |gradient| |double| |lquo| + |quotient| |deriv| |normalDenom| |components| |adjoint| |hermiteH| + |algebraicSort| |clipSurface| |removeRedundantFactorsInPols| + |att2Result| |insertRoot!| |subResultantGcdEuclidean| |wrregime| + |monomials| |prinpolINFO| |rationalPower| |oddInfiniteProduct| + |rotate| |vectorise| |completeEval| |iicoth| |internal?| + |tanintegrate| |selectfirst| |plus!| |failed?| |hclf| |updateStatus!| + |front| |coordinate| |leftRecip| |column| |tracePowMod| |d02ejf| + |binaryTree| |OMgetObject| |computeInt| |extendedIntegrate| |rootPoly| + |fintegrate| |generalizedContinuumHypothesisAssumed| + |initializeGroupForWordProblem| |logGamma| |opeval| |clipParametric| + |associator| |semiSubResultantGcdEuclidean2| |plenaryPower| + |triangSolve| |li| |collectUpper| |nextSublist| |primitivePart!| + |pointSizeDefault| |members| |magnitude| |aromberg| |redpps| + |zeroSetSplit| |iiabs| |algebraicOf| |resize| |normal01| |inRadical?| + |OMParseError?| |lfintegrate| |axesColorDefault| |log10| |mesh| + |setTex!| |zeroDim?| |ratpart| |arity| |partialDenominators| + |declare!| |postfix| |hasPredicate?| |realEigenvectors| |isPlus| + |makeFloatFunction| |semiSubResultantGcdEuclidean1| |bitand| + |principalIdeal| |conjugate| |droot| |revert| |partialFraction| + |ParCond| |d01gaf| |enqueue!| |basis| |pastel| |bitior| + |trivialIdeal?| |cycleEntry| |factorSquareFreeByRecursion| F + |linearAssociatedOrder| |explicitlyFinite?| |rquo| |alternatingGroup| + |part?| |sylvesterMatrix| |outputAsScript| |branchPointAtInfinity?| + |tube| |chvar| |tryFunctionalDecomposition| |bigEndian| + |pushNewContour| |block| |open?| |iicsc| |unit?| + |rationalApproximation| |interpolate| |measure2Result| |represents| + |rotatey| |makeprod| |genericLeftMinimalPolynomial| |cAcoth| + |bothWays| |s21bdf| |socf2socdf| |adaptive| |palglimint0| + |sturmSequence| |getCode| |more?| |redPol| |asinhIfCan| |null| + |position!| |leftFactor| |rightCharacteristicPolynomial| |Gamma| + |c06frf| |rewriteSetByReducingWithParticularGenerators| |mkPrim| + |mapSolve| |nextSubsetGray| |wholeRadix| |not| |writable?| |dim| + |addPoint2| |nthExponent| |clearTheFTable| |OMputAtp| |test| + |byteBuffer| |segment| |argument| |e01sef| |weights| |buildSyntax| + |and| |sn| |search| |topFortranOutputStack| |trim| |leftPower| + |partitions| |radicalEigenvectors| |doubleFloatFormat| + |useNagFunctions| |addPointLast| |resultantEuclidean| |integralBasis| + |or| |range| |printStats!| |solveLinear| |d01alf| |resultantnaif| + |generalLambert| |OMwrite| |oddintegers| |alphabetic?| + |integralAtInfinity?| |xor| |splitNodeOf!| |showRegion| |supRittWu?| + |inverseColeman| |reducedQPowers| |children| |univcase| |readLine!| + |const| |tan2cot| |case| |rightTrace| |halfExtendedSubResultantGcd1| + |eq| |harmonic| |real?| |hex| |printTypes| |setPoly| + |numberOfImproperPartitions| |lazyGintegrate| |showClipRegion| |Zero| + |iter| |curryRight| |linears| |content| |completeEchelonBasis| + |s17aff| |prefix| |showTheFTable| |f04qaf| |selectAndPolynomials| + |zeroSquareMatrix| |tablePow| |curveColorPalette| |linearDependence| + |getProperties| |pol| |newReduc| |HermiteIntegrate| + |exprHasAlgebraicWeight| |rotate!| |sizeMultiplication| |s18adf| + |var2Steps| |mainExpression| |getStream| |getVariableOrder| + |rewriteSetWithReduction| |bitLength| |youngGroup| Y |closedCurve| + |ode| |prolateSpheroidal| |remainder| |round| |SturmHabichtMultiple| + |f01qef| |readLineIfCan!| |rootRadius| |legendre| |definingEquations| + |setColumn!| |e02dff| |basisOfNucleus| |patternMatchTimes| |sayLength| + |generalSqFr| |raisePolynomial| |minPol| |permutation| |central?| + |halfExtendedResultant1| |monicModulo| |output| |iiasec| |operators| + |checkPrecision| |leftRankPolynomial| |idealiserMatrix| |extract!| + |roughSubIdeal?| |swap| |moduloP| |musserTrials| |OMputInteger| + |OMgetBind| |cscIfCan| |bat1| |invmod| |polyRicDE| |UnVectorise| + |sincos| |groebSolve| |symmetricPower| |generic?| |getExplanations| + |points| |hasSolution?| |removeRoughlyRedundantFactorsInPols| + |drawComplex| |LagrangeInterpolation| |exp| |OMopenFile| |conjug| + |createGenericMatrix| |coth2tanh| |cCsch| |choosemon| |readInt16!| + |compound?| |linearPart| |inverseIntegralMatrixAtInfinity| |is?| + |nativeModuleExtension| |phiCoord| |pdf2df| |lexico| + |semicolonSeparate| F2FG |probablyZeroDim?| |upperCase?| |f04maf| + |second| |palgLODE0| |zeroSetSplitIntoTriangularSystems| + |factorSquareFree| |showSummary| |truncate| |iCompose| + |selectIntegrationRoutines| |printStatement| |elRow1!| + |zeroDimPrimary?| |third| |rename!| |divideIfCan| RF2UTS + |mightHaveRoots| |obj| |iiacsch| |indicialEquations| + |triangularSystems| |s17dgf| |less?| |e02ddf| |internalDecompose| + |factorOfDegree| |deref| |LazardQuotient| |iiasech| |dfRange| + |wordsForStrongGenerators| |cache| |showAttributes| + |numberOfMonomials| |logpart| |adaptive3D?| |baseRDEsys| |c05pbf| + |imagk| |sturmVariationsOf| |aQuartic| |rightZero| |subspace| + |tubePoints| |iterationVar| |perfectNthPower?| |linGenPos| + |primPartElseUnitCanonical!| |printInfo| |trace2PowMod| |aCubic| + |iflist2Result| |sncndn| |uncouplingMatrices| |critMTonD1| |setleft!| + |scaleRoots| |commutative?| |factorset| |name| |mkcomm| + |setScreenResolution3D| |s18aff| |sorted?| |subst| |sPol| + |prepareDecompose| |OMputObject| |coefficient| |binarySearchTree| + |irreducibleFactors| |diagonal?| |antiCommutative?| |operation| + |iiacosh| |viewZoomDefault| |lSpaceBasis| |powerAssociative?| + |incrementBy| |sup| |e01daf| |acotIfCan| |LowTriBddDenomInv| |lprop| + |remove| |generic| |stFuncN| |pureLex| |gcdPrimitive| |pdct| |expand| + |light| |getMeasure| |parabolicCylindrical| |dequeue| |OMserve| + |polyred| |baseRDE| |stoseIntegralLastSubResultant| |polygamma| + |filterWhile| |completeHensel| |addBadValue| |OMgetSymbol| |coleman| + |last| |rightRank| |OMgetAtp| |filterUntil| |fortranTypeOf| |reflect| + |every?| |makeSeries| |assoc| |associates?| |e01bff| |OMsupportsCD?| + |f02adf| |Frobenius| |realRoots| |select| |style| |leadingSupport| + |polynomialZeros| |tubeRadiusDefault| |genericLeftDiscriminant| + |constantIfCan| |readInt8!| |numFunEvals| |objects| |randnum| + |maxIndex| |curry| |numberOfIrreduciblePoly| |rightRecip| + |squareFreePrim| |OMUnknownCD?| |encodingDirectory| |base| |connect| + |fortranLogical| |binding| |argscript| |iidprod| + |unprotectedRemoveRedundantFactors| |associatedEquations| + |rightRankPolynomial| |systemCommand| |typeList| |iicosh| |cExp| + |parents| |numerators| |genericLeftNorm| |maxPoints3D| |radix| BY + |resultant| |var2StepsDefault| |OMgetString| |factorGroebnerBasis| + |secIfCan| |e04mbf| |sum| |back| |freeOf?| |deleteRoutine!| + |prinshINFO| |orbits| |pquo| |inverseLaplace| |OMputVariable| + |hasTopPredicate?| |transcendentalDecompose| + |functionIsFracPolynomial?| |replace| |makeRecord| |exponential1| + |unparse| |d02gaf| |complexRoots| |multiple?| |lieAdmissible?| + |karatsubaDivide| |exteriorDifferential| |expextendedint| + |lazyPremWithDefault| |rst| |f07fef| |complete| |readUInt8!| |solid| + |f02xef| |B1solve| |terms| |PDESolve| |wreath| |fortranDoubleComplex| + |typeLists| |initial| |primitiveElement| |Is| |taylorIfCan| + |RittWuCompare| |nextLatticePermutation| |lp| |noKaratsuba| |f01ref| + |OMcloseConn| |isOpen?| |OMread| |hostByteOrder| |leftRank| + |squareMatrix| |factorAndSplit| |cAcsc| |cross| |bottom!| NOT + |outputAsTex| |findConstructor| |ScanArabic| |applyRules| |cycles| + |meshPar2Var| |d03edf| |split!| |chainSubResultants| OR |compdegd| + |acscIfCan| |diagonalProduct| |fortranLiteral| |d01asf| |pToHdmp| + |rootBound| |e02def| |tanNa| AND |overbar| |fracPart| |upDateBranches| + |wordInGenerators| |odd?| |belong?| |removeSinhSq| + |semiDiscriminantEuclidean| |rule| |jacobiIdentity?| |ipow| |cn| + |hasHi| |cycleLength| |rischDE| |stoseInvertible?| |e04fdf| + |sizeLess?| |shiftRight| |limitPlus| |readIfCan!| |fixedDivisor| + |semiLastSubResultantEuclidean| |sin2csc| |medialSet| |linear?| + |primintegrate| |f01rcf| |setValue!| |shallowExpand| + |stopTableInvSet!| |initials| |exponent| |complexElementary| |iipow| + |qelt| |localAbs| |quasiMonic?| |whitePoint| |uniform01| |duplicates?| + |hdmpToDmp| |setright!| |f01qcf| |debug| |qsetelt| |iisqrt3| + |lfextlimint| |conjugates| |callForm?| |domainTemplate| + |resultantReduit| |fmecg| |singular?| |dimensions| D |key?| |xRange| + |s17akf| |move| |Beta| |quadraticForm| |critT| |laguerre| |complex?| + |primlimitedint| |leader| |linearlyDependent?| |yRange| |cycleElt| + |c06fqf| |setMaxPoints3D| |returns| |composites| + |permutationRepresentation| |void| |matrixGcd| |infRittWu?| |zRange| + |stoseInvertible?sqfreg| |s14abf| |chiSquare1| |karatsuba| |diagonals| + |subset?| |setfirst!| |leftUnits| |d03faf| |map!| |listOfLists| + |copy!| |just| |sec2cos| * |exportedOperators| |rotatex| |char| + |mathieu24| |integralRepresents| |LyndonWordsList| |qsetelt!| |critM| + |e02baf| |rdregime| |reverseLex| |polCase| |wronskianMatrix| + |OMunhandledSymbol| |unitNormalize| |symFunc| |say| |plusInfinity| + |semiIndiceSubResultantEuclidean| |neglist| |monomRDE| |ListOfTerms| + |transform| |sizePascalTriangle| |fractionPart| |rootKerSimp| + |lazyPquo| |cCsc| |minusInfinity| |highCommonTerms| |bsolve| |An| + |rem| = |ceiling| |rowEchelonLocal| |symbol?| |oneDimensionalArray| + |lyndonIfCan| |crest| |d01apf| |multiplyExponents| |remove!| |quo| + |resetAttributeButtons| |primintfldpoly| |result| |endSubProgram| + |aspFilename| |unrankImproperPartitions1| |iiasinh| |slash| + |quasiAlgebraicSet| |sumOfKthPowerDivisors| |fixedPoint| < + |backOldPos| |OMbindTCP| |read!| |reorder| |print| |hexDigit?| |acsch| + |fractRadix| |complexNormalize| |ramified?| |setVariableOrder| + |parseString| |div| |s17acf| > |float| |rk4qc| |numberOfVariables| + |reset| |resolve| |logical?| |top!| |d01akf| |entries| |exquo| <= + |defineProperty| |binary| |presuper| |cPower| |mirror| |type| |unit| + |f02bbf| |lazyPseudoRemainder| |e04dgf| |minPoly| ~= |evaluateInverse| + >= |ode2| |quasiMonicPolynomials| |sample| |write| |duplicates| + |unravel| |nextIrreduciblePoly| |internalIntegrate0| |#| |exponents| + |regime| |save| |s17dcf| |associatorDependence| |evaluate| |swapRows!| + |f04adf| |antiCommutator| |nary?| ~ |signature| |abelianGroup| + |retractable?| |setOrder| |debug3D| |firstUncouplingMatrix| + |rightAlternative?| |generalPosition| |cAsinh| |euclideanSize| + |internalInfRittWu?| + |createRandomElement| |gderiv| |implies| + |getPickedPoints| |atoms| |lastSubResultantEuclidean| |OMputBind| + |rCoord| |makeFR| |node| |var1Steps| - |iicot| |solveRetract| |diff| + |initTable!| |rightTraceMatrix| |SturmHabichtCoefficients| |multMonom| + |fixedPointExquo| |pointColor| |/\\| |s18acf| / + |basisOfLeftAnnihilator| |expandLog| |countRealRootsMultiple| + |polygon| |symmetricSquare| |OMgetType| |divisorCascade| |firstDenom| + |enterInCache| |\\/| |leftZero| |c06ecf| |setScreenResolution| GE + |collect| |graphState| |generate| |primlimintfrac| |f02aef| + |createLowComplexityTable| |bringDown| |viewpoint| |forLoop| |augment| + |recoverAfterFail| GT |genericRightTraceForm| |setPrologue!| + |setProperties!| |varList| |OMopenString| |inHallBasis?| + |antisymmetric?| |ReduceOrder| |createLowComplexityNormalBasis| + |makeEq| |bernoulliB| LE |cAcot| |e02ahf| |LyndonBasis| + |OMconnOutDevice| |useSingleFactorBound?| |reducedDiscriminant| + |startTable!| |safeFloor| |headRemainder| |infiniteProduct| LT + |OMputFloat| |subNodeOf?| |before?| |level| |leftExtendedGcd| |yCoord| + |bindings| |var1StepsDefault| |f04asf| |directory| |changeVar| + |outputSpacing| |linkToFortran| + |removeRoughlyRedundantFactorsInContents| |extensionDegree| + |internalSubPolSet?| |leftRegularRepresentation| |particularSolution| + |mainKernel| |lazyPseudoQuotient| |d02cjf| |shift| |maxdeg| + |internalZeroSetSplit| |zoom| |nilFactor| |perspective| |birth| + |maxrow| |charthRoot| |lllp| |cosSinInfo| |mkIntegral| + |extendedEuclidean| |pow| |euclideanNormalForm| |SturmHabichtSequence| + |anfactor| |closed?| |recolor| |primeFactor| |solid?| |eigenvalues| + |linearAssociatedExp| |positiveSolve| |singleFactorBound| + |expressIdealMember| |bit?| |matrix| |dimension| |mainPrimitivePart| + |makeYoungTableau| |getGraph| |cond| |mainVariable| |jordanAlgebra?| + |commutator| |c06ebf| |showTheIFTable| |property| |d02kef| + |BumInSepFFE| |option?| |setlast!| |separateFactors| |besselI| + |extractBottom!| |physicalLength| |limit| |squareFree| |logIfCan| + |extractIndex| |log2| |completeSmith| |cyclicEqual?| |putColorInfo| + |equation| |screenResolution| |transcendenceDegree| |contains?| + |removeCosSq| |trigs2explogs| |rootDirectory| |exprToUPS| |OMclose| + |sinIfCan| |constantCoefficientRicDE| |symbolIfCan| |writeUInt8!| + |elliptic| |ScanFloatIgnoreSpacesIfCan| |units| |innerint| + |numberOfFactors| |coerceS| |OMsend| |setCondition!| |printCode| + |derivationCoordinates| |categories| |c06eaf| |symmetricProduct| + |stripCommentsAndBlanks| |arguments| |rightOne| |expenseOfEvaluation| + |edf2efi| |routines| |bat| |conical| |f02abf| + |tryFunctionalDecomposition?| |characteristicSet| |binomial| + |nextsubResultant2| |setLength!| |getConstant| |associative?| + |primPartElseUnitCanonical| |makeResult| |equiv| |iExquo| |OMputApp| + |dec| |plus| |factorPolynomial| |enterPointData| |algintegrate| + |quoted?| |queue| |s19acf| |toroidal| |OMgetFloat| + |degreeSubResultant| |stoseInvertible?reg| |finiteBound| |bright| + |maxPoints| |ratPoly| |order| |rightFactorIfCan| + |semiResultantEuclidean1| |euclideanGroebner| |mathieu12| |subPolSet?| + |check| |code| |generalizedEigenvector| |integralLastSubResultant| + |monomial?| |rangeIsFinite| |fortran| |increasePrecision| |prime?| + |mapCoef| |modularFactor| |constantOpIfCan| |goto| |failed| + |generalInfiniteProduct| |f02akf| |deepestInitial| + |numberOfPrimitivePoly| |e02bcf| |curveColor| |subresultantSequence| + |palgint0| |times| |extractTop!| |lambert| |numberOfComponents| + |squareFreeLexTriangular| |parabolic| |hyperelliptic| |function| + |palgLODE| |OMgetApp| |getButtonValue| |frobenius| |leftExactQuotient| + |expenseOfEvaluationIF| |c06gsf| |addPoint| |merge| |systemSizeIF| + |getDatabase| |wordInStrongGenerators| + |rewriteIdealWithQuasiMonicGenerators| |f02aaf| |imports| + |setMinPoints| |drawComplexVectorField| |leftTrace| |mapUnivariate| + |reduceLODE| |minordet| |double?| |resetNew| |addmod| |mapdiv| + |makeSketch| |vark| |dom| |f04faf| |monom| |processTemplate| + |splitSquarefree| |currentCategoryFrame| |e01baf| |mulmod| |notelem| + |jordanAdmissible?| |iprint| |iiatan| |bumptab| |weakBiRank| + |OMputBVar| |stopTableGcd!| |bipolarCylindrical| + |univariatePolynomial| |readUInt32!| |basisOfMiddleNucleus| |epilogue| + |pmComplexintegrate| |gcdprim| |inrootof| |physicalLength!| + |infieldIntegrate| |d01anf| |common| |changeMeasure| |deepExpand| + |elseBranch| |green| |write!| |basisOfCenter| |headReduced?| + |mapExpon| |halfExtendedResultant2| |integer?| |powerSum| |qfactor| + |expandTrigProducts| |s13acf| |patternVariable| |hostPlatform| |title| + |binomThmExpt| |principal?| |clikeUniv| |possiblyNewVariety?| + |listLoops| |totalDegree| |meatAxe| |primeFrobenius| |karatsubaOnce| + |getRef| |f07fdf| |areEquivalent?| |specialTrigs| |bubbleSort!| + |character?| |script| |rur| |tree| |prime| |imagI| |branchPoint?| + |unknownEndian| |sylvesterSequence| |bounds| |iilog| |LiePoly| + |s17dhf| |true| |leftAlternative?| |ParCondList| |e| |f04arf| + |symbolTable| |totalLex| |setvalue!| |rotatez| |atrapezoidal| + |univariatePolynomialsGcds| |quickSort| |tRange| |insertionSort!| + |localUnquote| |OMputEndObject| |identityMatrix| |insert!| |tex| + |LyndonCoordinates| |stoseInternalLastSubResultant| |exp1| + |nextPartition| |pushFortranOutputStack| |reverse!| |primes| |roman| + |outputForm| |midpoints| |getlo| |OMreceive| |useEisensteinCriterion?| + |deepCopy| |nothing| |popFortranOutputStack| |hermite| |setErrorBound| + |nthFlag| |torsion?| |stoseInvertibleSet| |prinb| |tab| |setClipValue| + |semiResultantEuclideannaif| |comparison| |chineseRemainder| + |outputAsFortran| |outputArgs| |blue| |leaf?| |kroneckerDelta| + |generalizedInverse| |generator| |numericIfCan| |complement| |zag| + |c06fpf| |s19aaf| |dioSolve| |virtualDegree| |f07adf| + |complexEigenvectors| |genericRightTrace| |cothIfCan| + |conditionsForIdempotents| |sumOfDivisors| |solve1| |bitCoef| + |currentSubProgram| |createNormalElement| |limitedint| + |rightFactorCandidate| |coerceListOfPairs| |partialNumerators| + |merge!| |numberOfComposites| |lazy?| |rightScalarTimes!| |empty?| + |pack!| |createPrimitiveNormalPoly| |floor| |tanhIfCan| + |startTableInvSet!| |leftNorm| |OMencodingXML| |decompose| + |FormatRoman| |width| |mainDefiningPolynomial| |idealiser| |concat!| + |dictionary| |mdeg| |e02ajf| |lazyVariations| |create3Space| + |getMultiplicationTable| |sequence| |radicalOfLeftTraceForm| |iifact| + |orthonormalBasis| |resetVariableOrder| |listConjugateBases| + |idealSimplify| |cyclic?| |plotPolar| |selectOrPolynomials| + |distdfact| |cRationalPower| |genericLeftTrace| |fixedPoints| |open| + |paraboloidal| |continuedFraction| |subscript| UTS2UP |primitive?| + |categoryFrame| |c06ekf| |lifting1| LODO2FUN |midpoint| |expPot| + |makeViewport3D| |f01brf| |unaryFunction| |fortranCarriageReturn| + |hitherPlane| |groebnerFactorize| |nil?| |monicCompleteDecompose| + |figureUnits| |direction| |chebyshevU| |coefChoose| |cAsec| |Lazard2| + |hdmpToP| |unexpand| |distribute| |upperCase!| |getOrder| + |viewPosDefault| |f02axf| |reopen!| |showAllElements| |imaginary| + |expintfldpoly| |operations| |invmultisect| |moduleSum| |weierstrass| + |isMult| |optional| |headReduce| |nonSingularModel| |symbolTableOf| + |dihedral| |problemPoints| |squareFreeFactors| |vector| |df2st| + |moreAlgebraic?| |findBinding| |substring?| |indiceSubResultant| + |mesh?| |multisect| |head| |setStatus!| |rightLcm| |differentiate| + |vedf2vef| |nthFractionalTerm| |simplify| |prem| |iroot| + |lazyEvaluate| |leastMonomial| |removeZeroes| |tower| |permutations| + |supersub| |extractIfCan| |ffactor| |suffix?| |OMgetBVar| + |reducedSystem| |diophantineSystem| |exprToXXP| |leastPower| + |sech2cosh| |setnext!| |selectMultiDimensionalRoutines| |relerror| + |quatern| |identity| |setMinPoints3D| |escape| |quadratic| |iiasin| + |OMputSymbol| |fixPredicate| |atom?| |nil| |prefix?| |maxint| + |badValues| |normalForm| |exprToGenUPS| |adaptive?| + |toseInvertibleSet| |stiffnessAndStabilityFactor| |nextPrimitivePoly| + |integerBound| |optimize| |string?| |iisec| |reduceBasisAtInfinity| + |ScanRoman| |selectPDERoutines| |normalElement| |s15aef| |cTanh| + |OMgetEndAtp| |radicalSimplify| |OMencodingUnknown| |Ci| |listexp| + |readBytes!| |realSolve| |goodPoint| SEGMENT |splitLinear| + |stronglyReduced?| |complexNumeric| |unrankImproperPartitions0| + |variable?| |approximate| |isOr| |dihedralGroup| |clearTheSymbolTable| + |qPot| |isList| |createIrreduciblePoly| |pomopo!| |degree| |cup| + |complex| |errorKind| |eulerPhi| |oddlambert| |kovacic| |f04mcf| + |sinhIfCan| |basisOfRightNucleus| |reduction| |kernels| |expIfCan| + |optional?| |biRank| |log| |discriminant| |quasiRegular?| |isOp| + |drawCurves| |normInvertible?| |removeDuplicates!| |acosIfCan| + |operator| |SturmHabicht| |generateIrredPoly| |infix?| |datalist| + |e01sff| |basisOfCentroid| |makeViewport2D| |ranges| |axes| |credPol| + |OMputError| |hexDigit| |pseudoRemainder| |eisensteinIrreducible?| + |mask| |cyclicCopy| |leastAffineMultiple| |diag| |basisOfRightNucloid| + |OMputString| |positiveRemainder| |lookup| |linearPolynomials| + |univariate| |trunc| |Ei| |genus| |e02akf| |rk4f| |padecf| + |stosePrepareSubResAlgo| |condition| |quasiComponent| |OMputAttr| + |approximants| |prologue| |setTopPredicate| |multinomial| |toScale| + |f02ajf| |set| |leaves| |addMatchRestricted| |lexGroebner| |constant| + |leftGcd| |basicSet| |integralMatrix| |subQuasiComponent?| + |viewThetaDefault| |zeroOf| |primextintfrac| |nthExpon| |minrank| + |isTimes| |insertMatch| |s21bcf| |solveLinearPolynomialEquation| + |nextPrime| |factor| |showTheSymbolTable| |concat| |s18aef| + |leviCivitaSymbol| |directSum| |newLine| |legendreP| |factorial| + |groebgen| |nextColeman| |resultantEuclideannaif| |sqrt| + |setMaxPoints| |diagonal| |swap!| |hconcat| |rowEchLocal| + |mainMonomial| |clearDenominator| |binaryTournament| + |absolutelyIrreducible?| |roughBase?| |real| |d01gbf| |cubic| |hue| + |symmetricTensors| |singRicDE| |contours| |curve?| |clipWithRanges| + |minPoints| |prindINFO| |imag| |connectTo| |fortranReal| |doubleDisc| + |rightMinimalPolynomial| |invertibleSet| |anticoord| |minimumDegree| + |upperCase| |setProperties| |graphImage| |directProduct| |rightMult| + |prepareSubResAlgo| |numberOfComputedEntries| |rightExtendedGcd| + |elRow2!| |getGoodPrime| |writeBytes!| |autoReduced?| |category| + |unitsColorDefault| |multiEuclidean| |nextNormalPrimitivePoly| + |lfinfieldint| |tableForDiscreteLogarithm| |roughUnitIdeal?| + |subNode?| |meshFun2Var| |relativeApprox| |coerce| |mapUp!| |domain| + |iicos| |ideal| |brace| |outputFloating| |subResultantsChain| + |largest| |index?| |nullary| |s21baf| |scan| |construct| |package| + |mapMatrixIfCan| |interReduce| |setchildren!| |destruct| |source| + |mainCoefficients| |padicFraction| |makeMulti| |mindeg| + |complexExpand| |scalarMatrix| |comment| |integral?| |rationalPoint?| + |subSet| |d01aqf| |SFunction| |integralBasisAtInfinity| |monomRDEsys| + |show| |trapezoidal| |parent| |functionIsContinuousAtEndPoints| + |powers| |d02bbf| |selectsecond| |bandedHessian| |currentScope| + |factorials| |shiftLeft| |s20adf| |inverseIntegralMatrix| + |splitDenominator| |rootProduct| |minColIndex| |cylindrical| + |flexibleArray| |mapmult| |taylorQuoByVar| |trace| |tab1| |infix| + |monomial| |unmakeSUP| |poisson| |isobaric?| |leadingIndex| |compile| + |makingStats?| |po| |airyAi| |leadingTerm| |readable?| |multivariate| + |target| |sinhcosh| |minIndex| |e01sbf| |subResultantChain| |exQuo| + |lowerCase!| |next| |mkAnswer| |changeBase| |OMgetEndApp| |variables| + |nullity| |increase| |minus!| |entry| |predicates| |parametersOf| + |rspace| |sh| |byte| |genericRightNorm| |extend| |quadraticNorm| + |perfectNthRoot| |lintgcd| |simpleBounds?| |groebnerIdeal| + |dimensionsOf| |stack| |copies| |coshIfCan| |subscriptedVariables| + |OMreadStr| |se2rfi| |OMgetEndBVar| |expint| |fortranComplex| + |twoFactor| |node?| |inc| |iiexp| |list?| |lowerCase| |derivative| + |ravel| |littleEndian| |stoseInvertibleSetreg| |clearTheIFTable| + |writeInt8!| |stirling1| |int| |submod| |factorByRecursion| + |monomialIntegrate| |reshape| |setStatus| |radPoly| + |getMultiplicationMatrix| |rightExactQuotient| |rootOf| |factor1| + |s14baf| |returnType!| |taylor| |rk4| |externalList| |localReal?| + |external?| |frst| |thetaCoord| |setelt| |complexZeros| + |modularGcdPrimitive| |yCoordinates| |varselect| |f01mcf| + |solveInField| |modulus| |mathieu22| |constantRight| + |componentUpperBound| |one?| |jacobi| |getZechTable| |matrixConcat3D| + |permutationGroup| |atanIfCan| |copy| |capacity| |rightPower| + |totalGroebner| |OMUnknownSymbol?| |ptFunc| |nthFactor| |KrullNumber| + |rectangularMatrix| |radicalSolve| |palgextint0| |zeroVector| + |extractSplittingLeaf| |mainVariable?| |variationOfParameters| + |update| |spherical| |coerceP| |f04axf| |basisOfLeftNucleus| + |lazyIrreducibleFactors| |infinite?| |max| |bumptab1| |endOfFile?| + |lighting| |host| |showAll?| |autoCoerce| |selectPolynomials| |tanQ| + |branchIfCan| |OMlistSymbols| |collectQuasiMonic| + |createPrimitiveElement| |fortranInteger| |outputFixed| + |rationalFunction| |colorFunction| |parts| |digit| + |internalSubQuasiComponent?| |rightRemainder| |algDsolve| |octon| + |repeating| |genericPosition| |purelyTranscendental?| |exptMod| + |reciprocalPolynomial| |nthCoef| |unitCanonical| |findCycle| + |lineColorDefault| |powmod| |subTriSet?| |normalise| |fullDisplay| + |screenResolution3D| |triangulate| |position| |pointColorDefault| + |stirling2| |sumSquares| |lyndon| |eulerE| |henselFact| |s14aaf| + |aLinear| |nodes| |bernoulli| |hessian| |d01fcf| |Nul| + |startTableGcd!| |dmpToHdmp| |select!| |normalize| |intersect| + |match?| |leftFactorIfCan| |bracket| |refine| |curryLeft| |ddFact| + |mainMonomials| |quotientByP| |isAbsolutelyIrreducible?| + |algebraicDecompose| |s13adf| |fill!| |acoshIfCan| + |removeSquaresIfCan| |setEmpty!| |arg2| |hash| |decrease| + |nextNormalPoly| |ip4Address| |inspect| |tensorProduct| + |argumentListOf| |multiplyCoefficients| |d01amf| |exactQuotient| + |count| |setProperty| |digit?| |denominators| |sequences| |rroot| + |UpTriBddDenomInv| |generalizedEigenvectors| |writeLine!| + |brillhartTrials| |ratDsolve| |conditions| |reducedContinuedFraction| + |readInt32!| |coord| |factorFraction| |isAnd| |pointColorPalette| + |extension| |dn| |iiGamma| |match| |univariateSolve| |e04naf| + |fractRagits| |triangular?| |getSyntaxFormsFromFile| |closedCurve?| + |qualifier| |indices| |primitivePart| |oblateSpheroidal| |setPosition| + |gethi| |expt| |OMmakeConn| |associatedSystem| |numericalOptimization| + |surface| |region| |structuralConstants| |coerceL| |viewSizeDefault| + |clipPointsDefault| |bivariateSLPEBR| |stiffnessAndStabilityOfODEIF| + |f07aef| |Si| |roughEqualIdeals?| |elem?| |fglmIfCan| |rarrow| + |firstSubsetGray| |diagonalMatrix| |bits| |e01saf| |extractPoint| + |sts2stst| |keys| |cosh| |dark| |collectUnder| |setrest!| + |leftMinimalPolynomial| |sparsityIF| |differentialVariables| |ref| + |shiftRoots| |vspace| |tanh| |bfKeys| |ratDenom| |latex| |ode1| + |rightUnits| |f01maf| |LazardQuotient2| |cosIfCan| |reseed| |coth| + |pushup| |OMgetError| |bumprow| |computeBasis| |doubleRank| + |startStats!| |mindegTerm| |d03eef| |leftRemainder| |sech| |cAsin| + |validExponential| |rowEchelon| |factors| |create| |horizConcat| + |eyeDistance| |indiceSubResultantEuclidean| |cycleRagits| |csch| + |eigenvector| |coercePreimagesImages| |nthr| |repeatUntilLoop| + |length| |composite| |makeVariable| |complexEigenvalues| |e02gaf| + |fortranCompilerName| |asinh| |entry?| |ldf2vmf| |Hausdorff| + |createNormalPrimitivePoly| |scripts| |palgRDE0| |e01bef| |digits| + |exactQuotient!| |tan2trig| |acosh| |mainContent| |setsubMatrix!| + |hasoln| |coefficients| |properties| |outputBinaryFile| |OMputEndBVar| + |cyclicEntries| |subtractIfCan| |iomode| |atanh| |leftScalarTimes!| + |safetyMargin| |algebraicVariables| |irreducible?| |tubePlot| |delay| + |removeConstantTerm| |toseInvertible?| |changeThreshhold| |translate| + |acoth| |atanhIfCan| |solveLinearPolynomialEquationByFractions| + |bivariatePolynomials| |romberg| |divideIfCan!| |geometric| + |incrementKthElement| |minimize| |testDim| |asech| |polyPart| + |heapSort| |trigs| |iiacsc| |movedPoints| |rational| |retract| + |subResultantGcd| |lexTriangular| |denomRicDE| |cosh2sech| |e02bef| + |tubePointsDefault| |relationsIdeal| |Lazard| |kmax| |intPatternMatch| + |hspace| |euler| |multiple| |nor| + |generalizedContinuumHypothesisAssumed?| |setProperty!| |sub| + |loadNativeModule| |space| |ridHack1| |besselK| |mat| |lfunc| + |applyQuote| |reducedForm| |c05nbf| |e01bhf| |acschIfCan| |id| + |morphism| |critMonD1| |stop| |asimpson| |sdf2lst| |float?| |graeffe| + |inputBinaryFile| |superHeight| |slex| |quote| |alphanumeric| + |mainValue| |arrayStack| |numberOfHues| |fi2df| |minPoints3D| + |lazyResidueClass| |iteratedInitials| |table| |makeop| + |createZechTable| |rowEch| |innerSolve1| |divisors| |ruleset| + |compBound| |makeCrit| |in?| |inverse| |new| |localIntegralBasis| + |selectSumOfSquaresRoutines| |quartic| |convergents| |red| |interpret| + |cycleTail| |pushuconst| |setAdaptive3D| |cTan| |insert| |s17agf| + |LyndonWordsList1| |reindex| |dot| |preprocess| |setClosed| + |exprHasWeightCosWXorSinWX| |leadingIdeal| |quotedOperators| |sqfree| + |integers| |child?| |setFormula!| |cycle| |heap| |froot| |suchThat| + |clearCache| |appendPoint| |cyclotomicFactorization| + |commonDenominator| |rightRegularRepresentation| |options| + |thenBranch| |mapExponents| |nodeOf?| |factorSquareFreePolynomial| + |interpretString| |super| |rewriteIdealWithHeadRemainder| + |retractIfCan| |generators| |setelt!| |shade| |e02adf| |s17dlf| |rank| + |coth2trigh| |qqq| |c02agf| |aQuadratic| |lhs| |showTheRoutinesTable| + |finiteBasis| |f04atf| |palgextint| |nullary?| |clipBoolean| + |separateDegrees| |numer| |cap| |attributeData| |mapUnivariateIfCan| + |rhs| |singularitiesOf| |mergeFactors| |d02bhf| |One| |besselJ| + |string| |yellow| |cLog| |denom| |difference| |alphanumeric?| + |viewDeltaYDefault| |generalTwoFactor| |palgintegrate| |dflist| + |loopPoints| |constantLeft| |unitVector| |useSingleFactorBound| + |outputGeneral| |drawToScale| |df2mf| |pointLists| |lex| |palglimint| + |leftQuotient| |divisor| |whileLoop| |integralMatrixAtInfinity| + |regularRepresentation| |pi| |scripted?| |nextItem| |sign| |linear| + |pmintegrate| |polar| |pr2dmp| |power| |inputOutputBinaryFile| + |eigenMatrix| |f04mbf| |infinity| |computeCycleEntry| |corrPoly| + |iisech| |gbasis| |writeByte!| |row| |left| |accuracyIF| + |complexLimit| |determinant| |principalAncestors| |f04jgf| + |polynomial| |s19adf| |lazyPrem| |modifyPointData| |elt| + |extractProperty| |right| |f02awf| |lists| |nil| |infinite| + |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| + |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| + |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| + |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| + |shallowlyMutable| |commutative|)
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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-616 #0=(-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-616 (-566)) -2805 (|has| |#2| (-1049)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-616 |#2|) -2805 (|has| |#2| (-1099)) (|has| |#2| (-172))) ((-613 (-862)) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-613 (-862))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-613 (-1264 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1049)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1049))) ((-287 #1=(-566) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1049)) ((-413 |#2|) |has| |#2| (-1099)) ((-491 |#2|) . T) ((-604 #1# |#2|) . T) ((-516 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-646 (-566)) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 $) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-648 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-648 $) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-640 |#2|) -2805 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-639 (-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049))) ((-639 |#2|) |has| |#2| (-1049)) ((-717 |#2|) -2805 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-726) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-791) |has| |#2| (-848)) ((-792) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-793) |has| |#2| (-793)) ((-794) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-795) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-848) |has| |#2| (-848)) ((-850) -2805 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-900 (-1175)) -12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049))) ((-1038 #0#) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-1038 (-566)) -12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) ((-1038 |#2|) |has| |#2| (-1099)) ((-1051 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1056 |#2|) -2805 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1056 $) |has| |#2| (-172)) ((-1049) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2805 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1214) . T) ((-1271 |#2|) |has| |#2| (-365))) -((-3264 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1580 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3152 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3264 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1580 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3152 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1214) (-1214)) (T -239)) -((-3152 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *7 (-1214)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1580 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *2 (-1214)) (-5 *1 (-239 *5 *6 *2)))) (-3264 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1214)) (-4 *5 (-1214)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 -3264 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1580 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3152 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) -((-3009 (((-112) $ $) NIL (|has| |#2| (-1099)))) (-3015 (((-112) $) NIL (|has| |#2| (-131)))) (-3047 (($ (-921)) 65 (|has| |#2| (-1049)))) (-2518 (((-1269) $ (-566) (-566)) NIL (|has| $ (-6 -4415)))) (-4385 (($ $ $) 70 (|has| |#2| (-793)))) (-4014 (((-3 $ "failed") $ $) 57 (|has| |#2| (-131)))) (-1574 (((-112) $ (-771)) 17)) (-4070 (((-771)) NIL (|has| |#2| (-370)))) (-2899 (((-566) $) NIL (|has| |#2| (-848)))) (-3916 ((|#2| $ (-566) |#2|) NIL (|has| $ (-6 -4415)))) (-3877 (($) NIL T CONST)) (-3066 (((-3 (-566) "failed") $) NIL (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099)))) (((-3 (-409 (-566)) "failed") $) NIL (-12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) (((-3 |#2| "failed") $) 34 (|has| |#2| (-1099)))) (-1867 (((-566) $) NIL (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099)))) (((-409 (-566)) $) NIL (-12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) ((|#2| $) 32 (|has| |#2| (-1099)))) (-2210 (((-689 (-566)) (-689 $)) NIL (-12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049)))) (((-2 (|:| -4193 (-689 (-566))) (|:| |vec| (-1264 (-566)))) (-689 $) (-1264 $)) NIL (-12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049)))) (((-2 (|:| -4193 (-689 |#2|)) (|:| |vec| (-1264 |#2|))) (-689 $) (-1264 $)) NIL (|has| |#2| (-1049))) (((-689 |#2|) (-689 $)) NIL (|has| |#2| (-1049)))) (-2928 (((-3 $ "failed") $) 61 (|has| |#2| (-726)))) (-1618 (($) NIL (|has| |#2| (-370)))) (-3128 ((|#2| $ (-566) |#2|) NIL (|has| $ (-6 -4415)))) (-3059 ((|#2| $ (-566)) 59)) (-1533 (((-112) $) NIL (|has| |#2| (-848)))) (-3799 (((-644 |#2|) $) 15 (|has| $ (-6 -4414)))) (-3466 (((-112) $) NIL (|has| |#2| (-726)))) (-2917 (((-112) $) NIL (|has| |#2| (-848)))) (-3501 (((-112) $ (-771)) NIL)) (-2712 (((-566) $) 20 (|has| (-566) (-850)))) (-1945 (($ $ $) NIL (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-3276 (((-644 |#2|) $) NIL (|has| $ (-6 -4414)))) (-2183 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4414)) (|has| |#2| (-1099))))) (-2579 (((-566) $) 58 (|has| (-566) (-850)))) (-2709 (($ $ $) NIL (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-3117 (($ (-1 |#2| |#2|) $) NIL (|has| $ (-6 -4415)))) (-3152 (($ (-1 |#2| |#2|) $) 47)) (-1299 (((-921) $) NIL (|has| |#2| (-370)))) (-3582 (((-112) $ (-771)) NIL)) (-2402 (((-1157) $) NIL (|has| |#2| (-1099)))) (-2140 (((-644 (-566)) $) NIL)) (-3935 (((-112) (-566) $) NIL)) (-2208 (($ (-921)) NIL (|has| |#2| (-370)))) (-4056 (((-1119) $) NIL (|has| |#2| (-1099)))) (-4101 ((|#2| $) NIL (|has| (-566) (-850)))) (-3750 (($ $ |#2|) NIL (|has| $ (-6 -4415)))) (-3044 (((-112) (-1 (-112) |#2|) $) 24 (|has| $ (-6 -4414)))) (-2095 (($ $ (-644 (-295 |#2|))) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (($ $ (-295 |#2|)) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (($ $ |#2| |#2|) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (($ $ (-644 |#2|) (-644 |#2|)) NIL (-12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))))) (-4372 (((-112) $ $) NIL)) (-2298 (((-112) |#2| $) NIL (-12 (|has| $ (-6 -4414)) (|has| |#2| (-1099))))) (-2684 (((-644 |#2|) $) NIL)) (-3461 (((-112) $) NIL)) (-1793 (($) NIL)) (-4393 ((|#2| $ (-566) |#2|) NIL) ((|#2| $ (-566)) 21)) (-4086 ((|#2| $ $) NIL (|has| |#2| (-1049)))) (-2512 (($ (-1264 |#2|)) 18)) (-2012 (((-134)) NIL (|has| |#2| (-365)))) (-2578 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1049)))) (($ $ (-771)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1049)))) (($ $ (-1175)) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-644 (-1175))) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-1175) (-771)) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-644 (-1175)) (-644 (-771))) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-1 |#2| |#2|) (-771)) NIL (|has| |#2| (-1049))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1049)))) (-4067 (((-771) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4414))) (((-771) |#2| $) NIL (-12 (|has| $ (-6 -4414)) (|has| |#2| (-1099))))) (-3940 (($ $) NIL)) (-3780 (((-1264 |#2|) $) 10) (($ (-566)) NIL (-2805 (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049)))) (($ (-409 (-566))) NIL (-12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) (($ |#2|) 13 (|has| |#2| (-1099))) (((-862) $) NIL (|has| |#2| (-613 (-862))))) (-3996 (((-771)) NIL (|has| |#2| (-1049)) CONST)) (-3801 (((-112) $ $) NIL (|has| |#2| (-1099)))) (-1583 (((-112) (-1 (-112) |#2|) $) NIL (|has| $ (-6 -4414)))) (-3333 (($ $) NIL (|has| |#2| (-848)))) (-2493 (($) 40 (|has| |#2| (-131)) CONST)) (-4333 (($) 44 (|has| |#2| (-726)) CONST)) (-2876 (($ $) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1049)))) (($ $ (-771)) NIL (-12 (|has| |#2| (-233)) (|has| |#2| (-1049)))) (($ $ (-1175)) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-644 (-1175))) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-1175) (-771)) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-644 (-1175)) (-644 (-771))) NIL (-12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) (($ $ (-1 |#2| |#2|) (-771)) NIL (|has| |#2| (-1049))) (($ $ (-1 |#2| |#2|)) NIL (|has| |#2| (-1049)))) (-3010 (((-112) $ $) NIL (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-2984 (((-112) $ $) NIL (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-2950 (((-112) $ $) 31 (|has| |#2| (-1099)))) (-2999 (((-112) $ $) NIL (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-2972 (((-112) $ $) 68 (-2805 (|has| |#2| (-793)) (|has| |#2| (-848))))) (-3062 (($ $ |#2|) NIL (|has| |#2| (-365)))) (-3051 (($ $ $) NIL (|has| |#2| (-1049))) (($ $) NIL (|has| |#2| (-1049)))) (-3040 (($ $ $) 38 (|has| |#2| (-25)))) (** (($ $ (-771)) NIL (|has| |#2| (-726))) (($ $ (-921)) NIL (|has| |#2| (-726)))) (* (($ (-566) $) NIL (|has| |#2| (-1049))) (($ $ $) 50 (|has| |#2| (-726))) (($ $ |#2|) 48 (|has| |#2| (-726))) (($ |#2| $) 49 (|has| |#2| (-726))) (($ (-771) $) NIL (|has| |#2| (-131))) (($ (-921) $) NIL (|has| |#2| (-25)))) (-3020 (((-771) $) NIL (|has| $ (-6 -4414))))) +((-3764 (*1 *1 *2) (-12 (-5 *2 (-1264 *4)) (-4 *4 (-1214)) (-4 *1 (-238 *3 *4)))) (-4348 (*1 *1 *2) (-12 (-5 *2 (-921)) (-4 *1 (-238 *3 *4)) (-4 *4 (-1049)) (-4 *4 (-1214)))) (-4280 (*1 *2 *1 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1214)) (-4 *2 (-1049)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1214)) (-4 *2 (-726)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-238 *3 *2)) (-4 *2 (-1214)) (-4 *2 (-726))))) +(-13 (-604 (-566) |t#2|) (-613 (-1264 |t#2|)) (-10 -8 (-6 -4414) (-15 -3764 ($ (-1264 |t#2|))) (IF (|has| |t#2| (-1099)) (-6 (-413 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-1049)) (PROGN (-6 (-111 |t#2| |t#2|)) (-6 (-231 |t#2|)) (-6 (-379 |t#2|)) (-15 -4348 ($ (-921))) (-15 -4280 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-726)) (PROGN (-6 (-726)) (-15 * ($ |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 -4411)) (-6 -4411) |%noBranch|) (IF (|has| |t#2| (-848)) (-6 (-848)) |%noBranch|) (IF (|has| |t#2| (-793)) (-6 (-793)) |%noBranch|) (IF (|has| |t#2| (-365)) (-6 (-1271 |t#2|)) |%noBranch|))) +(((-21) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-23) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2809 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2809 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-616 #0=(-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-616 (-566)) -2809 (|has| |#2| (-1049)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-616 |#2|) -2809 (|has| |#2| (-1099)) (|has| |#2| (-172))) ((-613 (-862)) -2809 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-613 (-862))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-613 (-1264 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1049)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1049))) ((-287 #1=(-566) |#2|) . T) ((-289 #1# |#2|) . T) ((-310 |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-370) |has| |#2| (-370)) ((-379 |#2|) |has| |#2| (-1049)) ((-413 |#2|) |has| |#2| (-1099)) ((-491 |#2|) . T) ((-604 #1# |#2|) . T) ((-516 |#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((-646 (-566)) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 |#2|) -2809 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 $) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-648 |#2|) -2809 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-648 $) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-640 |#2|) -2809 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-639 (-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049))) ((-639 |#2|) |has| |#2| (-1049)) ((-717 |#2|) -2809 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-726) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-791) |has| |#2| (-848)) ((-792) -2809 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-793) |has| |#2| (-793)) ((-794) -2809 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-795) -2809 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-848) |has| |#2| (-848)) ((-850) -2809 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-900 (-1175)) -12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049))) ((-1038 #0#) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099))) ((-1038 (-566)) -12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) ((-1038 |#2|) |has| |#2| (-1099)) ((-1051 |#2|) -2809 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1056 |#2|) -2809 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1056 $) |has| |#2| (-172)) ((-1049) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2809 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2809 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1214) . T) ((-1271 |#2|) |has| |#2| (-365))) +((-3795 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1676 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-1301 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3795 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1676 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1301 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1214) (-1214)) (T -239)) +((-1301 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *7 (-1214)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1676 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *2 (-1214)) (-5 *1 (-239 *5 *6 *2)))) (-3795 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1214)) (-4 *5 (-1214)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-640 #0#) |has| |#1| (-38 (-409 (-566)))) ((-640 |#1|) |has| |#1| (-172)) ((-640 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-639 (-566)) |has| |#1| (-639 (-566))) ((-639 |#1|) . T) ((-717 #0#) |has| |#1| (-38 (-409 (-566)))) ((-717 |#1|) |has| |#1| (-172)) ((-717 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-726) . T) ((-900 (-1175)) |has| |#1| (-900 (-1175))) ((-900 |#3|) . T) ((-886 (-381)) -12 (|has| |#1| (-886 (-381))) (|has| |#3| (-886 (-381)))) ((-886 (-566)) -12 (|has| |#1| (-886 (-566))) (|has| |#3| (-886 (-566)))) ((-949 |#1| |#4| |#3|) . T) ((-909) |has| |#1| (-909)) ((-1038 (-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((-1038 (-566)) |has| |#1| (-1038 (-566))) ((-1038 |#1|) . T) ((-1038 |#2|) . T) ((-1038 |#3|) . T) ((-1051 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1051 |#1|) . T) ((-1051 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1056 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . T) ((-1218) |has| |#1| (-909))) -((-3009 (((-112) $ $) 19 (|has| |#1| (-1099)))) (-4175 ((|#1| $) 55)) (-3918 ((|#1| $) 45)) (-1574 (((-112) $ (-771)) 8)) (-3877 (($) 7 T CONST)) (-2547 (($ $) 61)) (-3416 (($ $) 49)) (-3082 ((|#1| |#1| $) 47)) (-3827 ((|#1| $) 46)) (-3799 (((-644 |#1|) $) 31 (|has| $ (-6 -4414)))) (-3501 (((-112) $ (-771)) 9)) (-3276 (((-644 |#1|) $) 30 (|has| $ (-6 -4414)))) (-2183 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1099)) (|has| $ (-6 -4414))))) (-3117 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4415)))) (-3152 (($ (-1 |#1| |#1|) $) 36)) (-3582 (((-112) $ (-771)) 10)) (-3945 (((-771) $) 62)) (-2402 (((-1157) $) 22 (|has| |#1| (-1099)))) (-3765 ((|#1| $) 40)) (-4044 ((|#1| |#1| $) 53)) (-4296 ((|#1| |#1| $) 52)) (-2903 (($ |#1| $) 41)) (-3906 (((-771) $) 56)) (-4056 (((-1119) $) 21 (|has| |#1| (-1099)))) (-1763 ((|#1| $) 63)) (-1820 ((|#1| $) 51)) (-3641 ((|#1| $) 50)) (-3852 ((|#1| $) 42)) (-3044 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4414)))) (-2095 (($ $ (-644 (-295 |#1|))) 27 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ (-295 |#1|)) 26 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ (-644 |#1|) (-644 |#1|)) 24 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))))) (-4372 (((-112) $ $) 14)) (-3894 ((|#1| |#1| $) 59)) (-3461 (((-112) $) 11)) (-1793 (($) 12)) (-2069 ((|#1| $) 60)) (-4353 (($) 58) (($ (-644 |#1|)) 57)) (-1677 (((-771) $) 44)) (-4067 (((-771) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4414))) (((-771) |#1| $) 29 (-12 (|has| |#1| (-1099)) (|has| $ (-6 -4414))))) (-3940 (($ $) 13)) (-3780 (((-862) $) 18 (|has| |#1| (-613 (-862))))) (-2682 ((|#1| $) 54)) (-3801 (((-112) $ $) 23 (|has| |#1| (-1099)))) (-2926 (($ (-644 |#1|)) 43)) (-1980 ((|#1| $) 64)) (-1583 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4414)))) (-2950 (((-112) $ $) 20 (|has| |#1| (-1099)))) (-3020 (((-771) $) 6 (|has| $ (-6 -4414))))) +((-4151 (*1 *2 *3) (-12 (-4 *4 (-1049)) (-4 *3 (-850)) (-4 *5 (-267 *3)) (-4 *6 (-793)) (-5 *2 (-1 *1 (-771))) (-4 *1 (-254 *4 *3 *5 *6)))) (-4110 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-644 *4)))) (-3254 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1049)) (-4 *3 (-850)) (-4 *5 (-267 *3)) (-4 *6 (-793)) (-5 *2 (-771)))) (-3254 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-771)))) (-3636 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1049)) (-4 *3 (-850)) (-4 *5 (-267 *3)) (-4 *6 (-793)) (-5 *2 (-771)))) (-2430 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-644 (-771))))) (-1617 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-771)))) (-2430 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1049)) (-4 *3 (-850)) (-4 *5 (-267 *3)) (-4 *6 (-793)) (-5 *2 (-644 (-771))))) (-1617 (*1 *2 *1 *3) (-12 (-4 *1 (-254 *4 *3 *5 *6)) (-4 *4 (-1049)) (-4 *3 (-850)) (-4 *5 (-267 *3)) (-4 *6 (-793)) (-5 *2 (-771)))) (-3843 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *5 *6)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-112)))) (-2886 (*1 *2 *1) (-12 (-4 *1 (-254 *3 *4 *2 *5)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-793)) (-4 *2 (-267 *4)))) (-2780 (*1 *1 *1) (-12 (-4 *1 (-254 *2 *3 *4 *5)) (-4 *2 (-1049)) (-4 *3 (-850)) (-4 *4 (-267 *3)) (-4 *5 (-793)))) (-1644 (*1 *1 *1) (-12 (-4 *1 (-254 *2 *3 *4 *5)) (-4 *2 (-1049)) (-4 *3 (-850)) (-4 *4 (-267 *3)) (-4 *5 (-793)))) (-4151 (*1 *2 *1) (-12 (-4 *3 (-233)) (-4 *3 (-1049)) (-4 *4 (-850)) (-4 *5 (-267 *4)) (-4 *6 (-793)) (-5 *2 (-1 *1 (-771))) (-4 *1 (-254 *3 *4 *5 *6))))) +(-13 (-949 |t#1| |t#4| |t#3|) (-231 |t#1|) (-1038 |t#2|) (-10 -8 (-15 -4151 ((-1 $ (-771)) |t#2|)) (-15 -4110 ((-644 |t#2|) $)) (-15 -3254 ((-771) $ |t#2|)) (-15 -3254 ((-771) $)) (-15 -3636 ((-771) $ |t#2|)) (-15 -2430 ((-644 (-771)) $)) (-15 -1617 ((-771) $)) (-15 -2430 ((-644 (-771)) $ |t#2|)) (-15 -1617 ((-771) $ |t#2|)) (-15 -3843 ((-112) $)) (-15 -2886 (|t#3| $)) (-15 -2780 ($ $)) (-15 -1644 ($ $)) (IF (|has| |t#1| (-233)) (PROGN (-6 (-516 |t#2| |t#1|)) (-6 (-516 |t#2| $)) (-6 (-310 $)) (-15 -4151 ((-1 $ (-771)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-409 (-566)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #0#) -2809 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 |#1|) . T) ((-616 |#2|) . T) ((-616 |#3|) . T) ((-616 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-613 (-862)) . T) ((-172) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-614 (-538)) -12 (|has| |#1| (-614 (-538))) (|has| |#3| (-614 (-538)))) ((-614 (-892 (-381))) -12 (|has| |#1| (-614 (-892 (-381)))) (|has| |#3| (-614 (-892 (-381))))) ((-614 (-892 (-566))) -12 (|has| |#1| (-614 (-892 (-566)))) (|has| |#3| (-614 (-892 (-566))))) ((-231 |#1|) . T) ((-233) |has| |#1| (-233)) ((-291) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-310 $) . T) ((-327 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-454) -2809 (|has| |#1| (-909)) (|has| |#1| (-454))) ((-516 |#2| |#1|) |has| |#1| (-233)) ((-516 |#2| $) |has| |#1| (-233)) ((-516 |#3| |#1|) . T) ((-516 |#3| $) . T) ((-516 $ $) . T) ((-558) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-646 #0#) |has| |#1| (-38 (-409 (-566)))) ((-646 (-566)) . T) ((-646 |#1|) . T) ((-646 $) . T) ((-648 #0#) |has| |#1| (-38 (-409 (-566)))) ((-648 |#1|) . T) ((-648 $) . T) ((-640 #0#) |has| |#1| (-38 (-409 (-566)))) ((-640 |#1|) |has| |#1| (-172)) ((-640 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-639 (-566)) |has| |#1| (-639 (-566))) ((-639 |#1|) . T) ((-717 #0#) |has| |#1| (-38 (-409 (-566)))) ((-717 |#1|) |has| |#1| (-172)) ((-717 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-726) . T) ((-900 (-1175)) |has| |#1| (-900 (-1175))) ((-900 |#3|) . T) ((-886 (-381)) -12 (|has| |#1| (-886 (-381))) (|has| |#3| (-886 (-381)))) ((-886 (-566)) -12 (|has| |#1| (-886 (-566))) (|has| |#3| (-886 (-566)))) ((-949 |#1| |#4| |#3|) . T) ((-909) |has| |#1| (-909)) ((-1038 (-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((-1038 (-566)) |has| |#1| (-1038 (-566))) ((-1038 |#1|) . T) ((-1038 |#2|) . T) ((-1038 |#3|) . T) ((-1051 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1051 |#1|) . T) ((-1051 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1056 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . T) ((-1218) |has| |#1| (-909))) +((-3007 (((-112) $ $) 19 (|has| |#1| (-1099)))) (-2991 ((|#1| $) 55)) (-1825 ((|#1| $) 45)) (-2256 (((-112) $ (-771)) 8)) (-3012 (($) 7 T CONST)) (-2499 (($ $) 61)) (-3413 (($ $) 49)) (-2261 ((|#1| |#1| $) 47)) (-2008 ((|#1| $) 46)) (-3979 (((-644 |#1|) $) 31 (|has| $ (-6 -4414)))) (-2404 (((-112) $ (-771)) 9)) (-2329 (((-644 |#1|) $) 30 (|has| $ (-6 -4414)))) (-1916 (((-112) |#1| $) 28 (-12 (|has| |#1| (-1099)) (|has| $ (-6 -4414))))) (-2908 (($ (-1 |#1| |#1|) $) 35 (|has| $ (-6 -4415)))) (-1301 (($ (-1 |#1| |#1|) $) 36)) (-2603 (((-112) $ (-771)) 10)) (-4149 (((-771) $) 62)) (-4117 (((-1157) $) 22 (|has| |#1| (-1099)))) (-4039 ((|#1| $) 40)) (-1425 ((|#1| |#1| $) 53)) (-1463 ((|#1| |#1| $) 52)) (-3406 (($ |#1| $) 41)) (-2076 (((-771) $) 56)) (-4035 (((-1119) $) 21 (|has| |#1| (-1099)))) (-2303 ((|#1| $) 63)) (-3283 ((|#1| $) 51)) (-3181 ((|#1| $) 50)) (-2539 ((|#1| $) 42)) (-2692 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4414)))) (-2055 (($ $ (-644 (-295 |#1|))) 27 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ (-295 |#1|)) 26 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ |#1| |#1|) 25 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (($ $ (-644 |#1|) (-644 |#1|)) 24 (-12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))))) (-1932 (((-112) $ $) 14)) (-2364 ((|#1| |#1| $) 59)) (-3467 (((-112) $) 11)) (-1494 (($) 12)) (-1747 ((|#1| $) 60)) (-2675 (($) 58) (($ (-644 |#1|)) 57)) (-2266 (((-771) $) 44)) (-4045 (((-771) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4414))) (((-771) |#1| $) 29 (-12 (|has| |#1| (-1099)) (|has| $ (-6 -4414))))) (-3940 (($ $) 13)) (-3783 (((-862) $) 18 (|has| |#1| (-613 (-862))))) (-2798 ((|#1| $) 54)) (-3117 (((-112) $ $) 23 (|has| |#1| (-1099)))) (-1748 (($ (-644 |#1|)) 43)) (-2745 ((|#1| $) 64)) (-1894 (((-112) (-1 (-112) |#1|) $) 34 (|has| $ (-6 -4414)))) (-2947 (((-112) $ $) 20 (|has| |#1| (-1099)))) (-3018 (((-771) $) 6 (|has| $ (-6 -4414))))) (((-255 |#1|) (-140) (-1214)) (T -255)) -((-4353 (*1 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-4353 (*1 *1 *2) (-12 (-5 *2 (-644 *3)) (-4 *3 (-1214)) (-4 *1 (-255 *3)))) (-3906 (*1 *2 *1) (-12 (-4 *1 (-255 *3)) (-4 *3 (-1214)) (-5 *2 (-771)))) (-4175 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-2682 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-4044 (*1 *2 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-4296 (*1 *2 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-1820 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-3641 (*1 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214)))) (-3416 (*1 *1 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214))))) -(-13 (-1120 |t#1|) (-995 |t#1|) (-10 -8 (-15 -4353 ($)) (-15 -4353 ($ (-644 |t#1|))) (-15 -3906 ((-771) $)) (-15 -4175 (|t#1| $)) (-15 -2682 (|t#1| $)) (-15 -4044 (|t#1| |t#1| $)) (-15 -4296 (|t#1| |t#1| $)) (-15 -1820 (|t#1| $)) (-15 -3641 (|t#1| $)) (-15 -3416 ($ $)))) -(((-34) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-409 (-566))) -2809 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-38 |#1|) . T) ((-38 $) -2809 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-102) . T) ((-111 #0# #0#) -2809 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2809 (|has| |#1| (-351)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-616 #0#) -2809 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-351)) (|has| |#1| (-365))) ((-616 (-566)) . T) ((-616 |#1|) . T) ((-616 $) -2809 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-613 (-862)) . T) ((-172) . T) ((-614 |#2|) . 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T) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-365)) ((-646 $) . T) ((-648 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-648 |#1|) . T) ((-648 |#2|) |has| |#1| (-365)) ((-648 $) . T) ((-640 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-640 |#1|) |has| |#1| (-172)) ((-640 |#2|) |has| |#1| (-365)) ((-640 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-639 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-639 (-566)))) ((-639 |#2|) |has| |#1| (-365)) ((-717 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-717 |#1|) |has| |#1| (-172)) ((-717 |#2|) |has| |#1| (-365)) ((-717 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-726) . T) ((-791) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-792) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-794) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-795) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-820) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-848) -12 (|has| |#1| (-365)) (|has| |#2| (-820))) ((-850) -2805 (-12 (|has| |#1| (-365)) (|has| |#2| (-850))) (-12 (|has| |#1| (-365)) (|has| |#2| (-820)))) ((-900 (-1175)) -2805 (-12 (|has| |#1| (-365)) (|has| |#2| (-900 (-1175)))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175))))) ((-886 (-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-381)))) ((-886 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-566)))) ((-884 |#2|) |has| |#1| (-365)) ((-909) -12 (|has| |#1| (-365)) (|has| |#2| (-909))) ((-973 |#1| #0# (-1081)) . T) ((-920) |has| |#1| (-365)) ((-992 |#2|) |has| |#1| (-365)) ((-1002) |has| |#1| (-38 (-409 (-566)))) ((-1022) -12 (|has| |#1| (-365)) (|has| |#2| (-1022))) ((-1038 (-409 (-566))) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-566)))) ((-1038 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-566)))) ((-1038 #2#) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-1175)))) ((-1038 |#2|) . T) ((-1051 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1051 |#1|) . T) ((-1051 |#2|) |has| |#1| (-365)) ((-1051 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1056 #1#) -2805 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1056 |#1|) . T) ((-1056 |#2|) |has| |#1| (-365)) ((-1056 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . T) ((-1150) -12 (|has| |#1| (-365)) (|has| |#2| (-1150))) ((-1199) |has| |#1| (-38 (-409 (-566)))) ((-1202) |has| |#1| (-38 (-409 (-566)))) ((-1214) |has| |#1| (-365)) ((-1218) |has| |#1| (-365)) ((-1224 |#1|) . T) ((-1242 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-566)) . T) ((-25) . T) ((-38 #1=(-409 (-566))) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 |#2|) |has| |#1| (-365)) ((-38 $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-409 (-566)))) ((-95) |has| |#1| (-38 (-409 (-566)))) ((-102) . T) ((-111 #1# #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-365)) ((-111 $ $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) -2809 (-12 (|has| |#1| (-365)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-147) -2809 (-12 (|has| |#1| (-365)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-616 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 #2=(-1175)) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-1175)))) ((-616 |#1|) |has| |#1| (-172)) ((-616 |#2|) . 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T) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-365)) ((-646 $) . T) ((-648 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-648 |#1|) . T) ((-648 |#2|) |has| |#1| (-365)) ((-648 $) . T) ((-640 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-640 |#1|) |has| |#1| (-172)) ((-640 |#2|) |has| |#1| (-365)) ((-640 $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-639 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-639 (-566)))) ((-639 |#2|) |has| |#1| (-365)) ((-717 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-717 |#1|) |has| |#1| (-172)) ((-717 |#2|) |has| |#1| (-365)) ((-717 $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-726) . 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T) ((-920) |has| |#1| (-365)) ((-992 |#2|) |has| |#1| (-365)) ((-1002) |has| |#1| (-38 (-409 (-566)))) ((-1022) -12 (|has| |#1| (-365)) (|has| |#2| (-1022))) ((-1038 (-409 (-566))) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-566)))) ((-1038 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-566)))) ((-1038 #2#) -12 (|has| |#1| (-365)) (|has| |#2| (-1038 (-1175)))) ((-1038 |#2|) . T) ((-1051 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1051 |#1|) . T) ((-1051 |#2|) |has| |#1| (-365)) ((-1051 $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1056 #1#) -2809 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1056 |#1|) . T) ((-1056 |#2|) |has| |#1| (-365)) ((-1056 $) -2809 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . 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T) ((-1051 #1#) |has| |#1| (-38 (-409 (-566)))) ((-1051 |#1|) . T) ((-1051 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1056 #1#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . 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T) ((-23) . T) ((-47 |#1| #0=(-771)) . T) ((-25) . T) ((-38 #1=(-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-409 (-566)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #1#) -2809 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 #2=(-1081)) . T) ((-616 |#1|) . T) ((-616 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-613 (-862)) . T) ((-172) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-614 (-538)) -12 (|has| (-1081) (-614 (-538))) (|has| |#1| (-614 (-538)))) ((-614 (-892 (-381))) -12 (|has| (-1081) (-614 (-892 (-381)))) (|has| |#1| (-614 (-892 (-381))))) ((-614 (-892 (-566))) -12 (|has| (-1081) (-614 (-892 (-566)))) (|has| |#1| (-614 (-892 (-566))))) ((-231 |#1|) . T) ((-233) . T) ((-287 (-409 $) (-409 $)) |has| |#1| (-558)) ((-287 |#1| |#1|) . T) ((-287 $ $) . T) ((-291) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-310 $) . T) ((-327 |#1| #0#) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-454) -2809 (|has| |#1| (-909)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-516 #2# |#1|) . T) ((-516 #2# $) . T) ((-516 $ $) . T) ((-558) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-646 #1#) |has| |#1| (-38 (-409 (-566)))) ((-646 (-566)) . T) ((-646 |#1|) . T) ((-646 $) . T) ((-648 #1#) |has| |#1| (-38 (-409 (-566)))) ((-648 |#1|) . T) ((-648 $) . T) ((-640 #1#) |has| |#1| (-38 (-409 (-566)))) ((-640 |#1|) |has| |#1| (-172)) ((-640 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-639 (-566)) |has| |#1| (-639 (-566))) ((-639 |#1|) . T) ((-717 #1#) |has| |#1| (-38 (-409 (-566)))) ((-717 |#1|) |has| |#1| (-172)) ((-717 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-726) . T) ((-900 #2#) . T) ((-900 (-1175)) |has| |#1| (-900 (-1175))) ((-886 (-381)) -12 (|has| (-1081) (-886 (-381))) (|has| |#1| (-886 (-381)))) ((-886 (-566)) -12 (|has| (-1081) (-886 (-566))) (|has| |#1| (-886 (-566)))) ((-949 |#1| #0# #2#) . T) ((-909) |has| |#1| (-909)) ((-920) |has| |#1| (-365)) ((-1038 (-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((-1038 (-566)) |has| |#1| (-1038 (-566))) ((-1038 #2#) . T) ((-1038 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-409 (-566)))) ((-1051 |#1|) . T) ((-1051 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1056 #1#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2809 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . T) ((-1150) |has| |#1| (-1150)) ((-1218) |has| |#1| (-909))) +((-3863 (((-644 (-1081)) $) 34)) (-1786 (($ $) 31)) (-3840 (($ |#2| |#3|) NIL) (($ $ (-1081) |#3|) 28) (($ $ (-644 (-1081)) (-644 |#3|)) 27)) (-1749 (($ $) 14)) (-1763 ((|#2| $) 12)) (-3636 ((|#3| $) 10))) +(((-1241 |#1| |#2| |#3|) (-10 -8 (-15 -3863 ((-644 (-1081)) |#1|)) (-15 -3840 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -3840 (|#1| |#1| (-1081) |#3|)) (-15 -1786 (|#1| |#1|)) (-15 -3840 (|#1| |#2| |#3|)) (-15 -3636 (|#3| |#1|)) (-15 -1749 (|#1| |#1|)) (-15 -1763 (|#2| |#1|))) (-1242 |#2| |#3|) (-1049) (-792)) (T -1241)) +NIL +(-10 -8 (-15 -3863 ((-644 (-1081)) |#1|)) (-15 -3840 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -3840 (|#1| |#1| (-1081) |#3|)) (-15 -1786 (|#1| |#1|)) (-15 -3840 (|#1| |#2| |#3|)) (-15 -3636 (|#3| |#1|)) (-15 -1749 (|#1| |#1|)) (-15 -1763 (|#2| |#1|))) +((-3007 (((-112) $ $) 7)) (-1788 (((-112) $) 17)) (-3863 (((-644 (-1081)) $) 86)) (-1385 (((-1175) $) 115)) (-1860 (((-2 (|:| -3002 $) (|:| 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NIL 2945436 NIL) (-1217 2943917 2943963 2944058 "UFD-" 2944063 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2942999 2943182 2943398 "UDVO" 2943723 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2940815 2941224 2941695 "UDPO" 2942563 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2940748 2940753 2940783 "TYPE" 2940788 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940508 2940703 2940734 "TYPEAST" 2940739 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939479 2939681 2939921 "TWOFACT" 2940302 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938502 2938888 2939123 "TUPLE" 2939279 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936193 2936712 2937251 "TUBETOOL" 2937985 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935042 2935247 2935488 "TUBE" 2935986 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2929771 2934014 2934297 "TS" 2934794 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918411 2922530 2922627 "TSETCAT" 2927896 NIL TSETCAT (NIL T T T T) -9 NIL 2929427 NIL) (-1206 2913143 2914743 2916634 "TSETCAT-" 2916639 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2907782 2908629 2909558 "TRMANIP" 2912279 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907223 2907286 2907449 "TRIMAT" 2907714 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905089 2905326 2905683 "TRIGMNIP" 2906972 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2904609 2904722 2904752 "TRIGCAT" 2904965 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904278 2904357 2904498 "TRIGCAT-" 2904503 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901123 2903136 2903417 "TREE" 2904032 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900397 2900925 2900955 "TRANFUN" 2900990 T TRANFUN (NIL) -9 NIL 2901056 NIL) (-1198 2899676 2899867 2900147 "TRANFUN-" 2900152 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899480 2899512 2899573 "TOPSP" 2899637 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2898828 2898943 2899097 "TOOLSIGN" 2899361 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897462 2898005 2898244 "TEXTFILE" 2898611 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895374 2895915 2896344 "TEX" 2897055 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895155 2895186 2895258 "TEX1" 2895337 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2894803 2894866 2894956 "TEMUTL" 2895087 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2892957 2893237 2893562 "TBCMPPK" 2894526 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2884734 2891117 2891173 "TBAGG" 2891573 NIL TBAGG (NIL T T) -9 NIL 2891784 NIL) (-1189 2879804 2881292 2883046 "TBAGG-" 2883051 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879188 2879295 2879440 "TANEXP" 2879693 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872578 2879045 2879138 "TABLE" 2879143 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2871990 2872089 2872227 "TABLEAU" 2872475 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2866598 2867818 2869066 "TABLBUMP" 2870776 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2865820 2865967 2866148 "SYSTEM" 2866439 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862279 2862978 2863761 "SYSSOLP" 2865071 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861323 2861828 2861947 "SYSNNI" 2862133 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862218) (-1181 2860630 2861089 2861168 "SYSINT" 2861228 NIL SYSINT (NIL NIL) -8 NIL NIL 2861273) (-1180 2856962 2857908 2858618 "SYNTAX" 2859942 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854120 2854722 2855354 "SYMTAB" 2856352 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849369 2850271 2851254 "SYMS" 2853159 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2846604 2848827 2849057 "SYMPOLY" 2849174 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846121 2846196 2846319 "SYMFUNC" 2846516 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842140 2843433 2844246 "SYMBOL" 2845330 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2835679 2837368 2839088 "SWITCH" 2840442 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2828913 2834500 2834803 "SUTS" 2835434 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2820979 2828160 2828433 "SUPXS" 2828698 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2812738 2820597 2820723 "SUP" 2820888 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2811897 2812024 2812241 "SUPFRACF" 2812606 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811518 2811577 2811690 "SUP2" 2811832 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2809966 2810240 2810596 "SUMRF" 2811217 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809301 2809367 2809559 "SUMFS" 2809887 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793268 2808478 2808729 "SULS" 2809108 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2792870 2793090 2793160 "SUCHTAST" 2793220 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792165 2792395 2792535 "SUCH" 2792778 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786031 2787071 2788030 "SUBSPACE" 2791253 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785461 2785551 2785715 "SUBRESP" 2785919 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2778826 2780126 2781437 "STTF" 2784197 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2772999 2774119 2775266 "STTFNC" 2777726 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764309 2766181 2767975 "STTAYLOR" 2771240 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757439 2764173 2764256 "STRTBL" 2764261 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2752803 2757394 2757425 "STRING" 2757430 T STRING (NIL) -8 NIL NIL NIL) (-1156 2747664 2752176 2752206 "STRICAT" 2752265 T STRICAT (NIL) -9 NIL 2752327 NIL) (-1155 2740417 2745283 2745894 "STREAM" 2747088 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2739927 2740004 2740148 "STREAM3" 2740334 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2738909 2739092 2739327 "STREAM2" 2739740 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2738597 2738649 2738742 "STREAM1" 2738851 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2737613 2737794 2738025 "STINPROD" 2738413 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737165 2737375 2737405 "STEP" 2737485 T STEP (NIL) -9 NIL 2737563 NIL) (-1149 2730597 2737064 2737141 "STBL" 2737146 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2725723 2729818 2729861 "STAGG" 2730014 NIL STAGG (NIL T) -9 NIL 2730103 NIL) (-1147 2723425 2724027 2724899 "STAGG-" 2724904 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721572 2723195 2723287 "STACK" 2723368 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714267 2719713 2720169 "SREGSET" 2721202 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2706692 2708061 2709574 "SRDCMPK" 2712873 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2699609 2704132 2704162 "SRAGG" 2705465 T SRAGG (NIL) -9 NIL 2706073 NIL) (-1142 2698626 2698881 2699260 "SRAGG-" 2699265 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693086 2697573 2697994 "SQMATRIX" 2698252 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2686771 2689804 2690531 "SPLTREE" 2692431 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2682734 2683427 2684073 "SPLNODE" 2686197 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2681781 2682014 2682044 "SPFCAT" 2682488 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680518 2680728 2680992 "SPECOUT" 2681539 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672144 2673914 2673944 "SPADXPT" 2678336 T SPADXPT (NIL) -9 NIL 2680370 NIL) (-1135 2671905 2671945 2672014 "SPADPRSR" 2672097 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670060 2671860 2671891 "SPADAST" 2671896 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662005 2663778 2663821 "SPACEC" 2668194 NIL SPACEC (NIL T) -9 NIL 2670010 NIL) (-1132 2660135 2661937 2661986 "SPACE3" 2661991 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2658887 2659058 2659349 "SORTPAK" 2659940 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2656979 2657282 2657694 "SOLVETRA" 2658551 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656029 2656251 2656512 "SOLVESER" 2656752 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651333 2652221 2653216 "SOLVERAD" 2655081 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647148 2647757 2648486 "SOLVEFOR" 2650700 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641418 2646497 2646594 "SNTSCAT" 2646599 NIL SNTSCAT (NIL T T T T) -9 NIL 2646669 NIL) (-1125 2635524 2639741 2640132 "SMTS" 2641108 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630208 2635412 2635489 "SMP" 2635494 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628367 2628668 2629066 "SMITH" 2629905 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621080 2625276 2625379 "SMATCAT" 2626730 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627280 NIL) (-1121 2618020 2618843 2620021 "SMATCAT-" 2620026 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2615686 2617256 2617299 "SKAGG" 2617560 NIL SKAGG (NIL T) -9 NIL 2617695 NIL) (-1119 2611997 2615102 2615297 "SINT" 2615484 T SINT (NIL) -8 NIL NIL 2615657) (-1118 2611769 2611807 2611873 "SIMPAN" 2611953 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611048 2611304 2611444 "SIG" 2611651 T SIG (NIL) -8 NIL NIL NIL) (-1116 2609886 2610107 2610382 "SIGNRF" 2610807 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2608719 2608870 2609154 "SIGNEF" 2609715 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608025 2608302 2608426 "SIGAST" 2608617 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2605714 2606169 2606675 "SHP" 2607566 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599566 2605615 2605691 "SHDP" 2605696 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599139 2599331 2599361 "SGROUP" 2599454 T SGROUP (NIL) -9 NIL 2599516 NIL) (-1110 2598997 2599023 2599096 "SGROUP-" 2599101 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2595832 2596530 2597253 "SGCF" 2598296 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590200 2595279 2595376 "SFRTCAT" 2595381 NIL SFRTCAT (NIL T T T T) -9 NIL 2595420 NIL) (-1107 2583621 2584639 2585775 "SFRGCD" 2589183 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2576747 2577820 2579006 "SFQCMPK" 2582554 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576367 2576456 2576567 "SFORT" 2576688 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575485 2576207 2576328 "SEXOF" 2576333 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574592 2575366 2575434 "SEX" 2575439 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570105 2570820 2570915 "SEXCAT" 2573852 NIL SEXCAT (NIL T T T T T) -9 NIL 2574430 NIL) (-1101 2567258 2570039 2570087 "SET" 2570092 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565482 2565971 2566276 "SETMN" 2566999 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2564978 2565130 2565160 "SETCAT" 2565336 T SETCAT (NIL) -9 NIL 2565446 NIL) (-1098 2564670 2564748 2564878 "SETCAT-" 2564883 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561031 2563131 2563174 "SETAGG" 2564044 NIL SETAGG (NIL T) -9 NIL 2564384 NIL) (-1096 2560489 2560605 2560842 "SETAGG-" 2560847 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2559932 2560185 2560286 "SEQAST" 2560410 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559131 2559425 2559486 "SEGXCAT" 2559772 NIL SEGXCAT (NIL T T) -9 NIL 2559892 NIL) (-1093 2558137 2558797 2558979 "SEG" 2558984 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557116 2557330 2557373 "SEGCAT" 2557895 NIL SEGCAT (NIL T) -9 NIL 2558116 NIL) (-1091 2556117 2556495 2556695 "SEGBIND" 2556951 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2555738 2555797 2555910 "SEGBIND2" 2556052 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555311 2555539 2555616 "SEGAST" 2555683 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554530 2554656 2554860 "SEG2" 2555155 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2553940 2554465 2554512 "SDVAR" 2554517 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546467 2553710 2553840 "SDPOL" 2553845 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545060 2545326 2545645 "SCPKG" 2546182 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544224 2544396 2544588 "SCOPE" 2544890 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543444 2543578 2543757 "SCACHE" 2544079 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543090 2543276 2543306 "SASTCAT" 2543311 T SASTCAT (NIL) -9 NIL 2543324 NIL) (-1081 2542577 2542925 2543001 "SAOS" 2543036 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542142 2542177 2542350 "SAERFFC" 2542536 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536081 2542039 2542119 "SAE" 2542124 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2535674 2535709 2535868 "SAEFACT" 2536040 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2533995 2534309 2534710 "RURPK" 2535340 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2532632 2532938 2533243 "RULESET" 2533829 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2529855 2530385 2530843 "RULE" 2532313 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529467 2529649 2529732 "RULECOLD" 2529807 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529257 2529285 2529356 "RTVALUE" 2529418 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2528728 2528974 2529068 "RSTRCAST" 2529185 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523576 2524371 2525291 "RSETGCD" 2527927 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2512806 2517885 2517982 "RSETCAT" 2522101 NIL RSETCAT (NIL T T T T) -9 NIL 2523198 NIL) (-1069 2510733 2511272 2512096 "RSETCAT-" 2512101 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503118 2504495 2506015 "RSDCMPK" 2509332 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501097 2501564 2501638 "RRCC" 2502724 NIL RRCC (NIL T T) -9 NIL 2503068 NIL) (-1066 2500448 2500622 2500901 "RRCC-" 2500906 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2499891 2500144 2500245 "RPTAST" 2500369 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2473742 2483099 2483166 "RPOLCAT" 2493830 NIL RPOLCAT (NIL T T T) -9 NIL 2496989 NIL) (-1063 2465240 2467580 2470702 "RPOLCAT-" 2470707 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456171 2463451 2463933 "ROUTINE" 2464780 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2452969 2455797 2455937 "ROMAN" 2456053 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451213 2451829 2452089 "ROIRC" 2452774 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447445 2449729 2449759 "RNS" 2450063 T RNS (NIL) -9 NIL 2450337 NIL) (-1058 2445954 2446337 2446871 "RNS-" 2446946 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445357 2445765 2445795 "RNG" 2445800 T RNG (NIL) -9 NIL 2445821 NIL) (-1056 2444756 2445144 2445187 "RMODULE" 2445192 NIL RMODULE (NIL T) -9 NIL 2445219 NIL) (-1055 2443592 2443686 2444022 "RMCAT2" 2444657 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440442 2442938 2443235 "RMATRIX" 2443354 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433269 2435529 2435644 "RMATCAT" 2439003 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2439985 NIL) (-1052 2432644 2432791 2433098 "RMATCAT-" 2433103 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432045 2432266 2432309 "RLINSET" 2432503 NIL RLINSET (NIL T) -9 NIL 2432594 NIL) (-1050 2431612 2431687 2431815 "RINTERP" 2431964 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2430670 2431224 2431254 "RING" 2431310 T RING (NIL) -9 NIL 2431402 NIL) (-1048 2430462 2430506 2430603 "RING-" 2430608 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429303 2429540 2429798 "RIDIST" 2430226 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420592 2428771 2428977 "RGCHAIN" 2429151 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2419942 2420348 2420389 "RGBCSPC" 2420447 NIL RGBCSPC (NIL T) -9 NIL 2420499 NIL) (-1044 2419100 2419481 2419522 "RGBCMDL" 2419754 NIL RGBCMDL (NIL T) -9 NIL 2419868 NIL) (-1043 2416094 2416708 2417378 "RF" 2418464 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2415740 2415803 2415906 "RFFACTOR" 2416025 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415465 2415500 2415597 "RFFACT" 2415699 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413582 2413946 2414328 "RFDIST" 2415105 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413035 2413127 2413290 "RETSOL" 2413484 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2412671 2412751 2412794 "RETRACT" 2412927 NIL RETRACT (NIL T) -9 NIL 2413014 NIL) (-1037 2412520 2412545 2412632 "RETRACT-" 2412637 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412122 2412342 2412412 "RETAST" 2412472 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2404860 2411775 2411902 "RESULT" 2412017 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403451 2404129 2404328 "RESRING" 2404763 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403087 2403136 2403234 "RESLATC" 2403388 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2402792 2402827 2402934 "REPSQ" 2403046 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400214 2400794 2401396 "REP" 2402212 T REP (NIL) -7 NIL NIL NIL) (-1030 2399911 2399946 2400057 "REPDB" 2400173 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2393811 2395200 2396423 "REP2" 2398723 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390188 2390869 2391677 "REP1" 2393038 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2382884 2388329 2388785 "REGSET" 2389818 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2381649 2382032 2382282 "REF" 2382669 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381026 2381129 2381296 "REDORDER" 2381533 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2376994 2380239 2380466 "RECLOS" 2380854 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376046 2376227 2376442 "REALSOLV" 2376801 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2375892 2375933 2375963 "REAL" 2375968 T REAL (NIL) -9 NIL 2376003 NIL) (-1021 2372375 2373177 2374061 "REAL0Q" 2375057 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2367976 2368964 2370025 "REAL0" 2371356 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367447 2367693 2367787 "RDUCEAST" 2367904 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2366852 2366924 2367131 "RDIV" 2367369 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2365920 2366094 2366307 "RDIST" 2366674 NIL RDIST (NIL T) -7 NIL NIL NIL) 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NIL NIL) (-1004 2338531 2344248 2344558 "RADIX" 2345139 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330150 2338373 2338503 "RADFF" 2338508 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1002 2329797 2329872 2329902 "RADCAT" 2330062 T RADCAT (NIL) -9 NIL NIL NIL) (-1001 2329579 2329627 2329727 "RADCAT-" 2329732 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1000 2327679 2329351 2329442 "QUEUE" 2329523 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-999 2324220 2327616 2327661 "QUAT" 2327666 NIL QUAT (NIL T) -8 NIL NIL NIL) (-998 2323858 2323901 2324028 "QUATCT2" 2324171 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2317320 2320665 2320705 "QUATCAT" 2321485 NIL QUATCAT (NIL T) -9 NIL 2322251 NIL) (-996 2313464 2314501 2315888 "QUATCAT-" 2315982 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-995 2310937 2312548 2312589 "QUAGG" 2312964 NIL QUAGG (NIL T) -9 NIL 2313139 NIL) (-994 2310542 2310762 2310830 "QQUTAST" 2310889 T QQUTAST (NIL) -8 NIL NIL NIL) (-993 2309440 2309940 2310112 "QFORM" 2310414 NIL QFORM (NIL 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2276045 "PTFUNC2" 2276184 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-980 2270356 2274751 2274792 "PTCAT" 2275088 NIL PTCAT (NIL T) -9 NIL 2275241 NIL) (-979 2270014 2270049 2270173 "PSQFR" 2270315 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-978 2268609 2268907 2269241 "PSEUDLIN" 2269712 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-977 2255372 2257743 2260067 "PSETPK" 2266369 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-976 2248390 2251130 2251226 "PSETCAT" 2254247 NIL PSETCAT (NIL T T T T) -9 NIL 2255061 NIL) (-975 2246226 2246860 2247681 "PSETCAT-" 2247686 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-974 2245575 2245740 2245768 "PSCURVE" 2246036 T PSCURVE (NIL) -9 NIL 2246203 NIL) (-973 2241573 2243089 2243154 "PSCAT" 2243998 NIL PSCAT (NIL T T T) -9 NIL 2244238 NIL) (-972 2240636 2240852 2241252 "PSCAT-" 2241257 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-971 2239341 2240001 2240206 "PRTITION" 2240451 T PRTITION (NIL) -8 NIL NIL NIL) (-970 2238816 2239062 2239154 "PRTDAST" 2239269 T PRTDAST 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2069926 "PDEPROB" 2070617 T PDEPROB (NIL) -8 NIL NIL NIL) (-897 2066025 2066529 2067084 "PDEPACK" 2067945 T PDEPACK (NIL) -7 NIL NIL NIL) (-896 2064937 2065127 2065378 "PDECOMP" 2065824 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-895 2062516 2063359 2063387 "PDECAT" 2064174 T PDECAT (NIL) -9 NIL 2064887 NIL) (-894 2062267 2062300 2062390 "PCOMP" 2062477 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-893 2060445 2061068 2061365 "PBWLB" 2061996 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-892 2052918 2054518 2055856 "PATTERN" 2059128 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-891 2052550 2052607 2052716 "PATTERN2" 2052855 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-890 2050307 2050695 2051152 "PATTERN1" 2052139 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-889 2047675 2048256 2048737 "PATRES" 2049872 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-888 2047239 2047306 2047438 "PATRES2" 2047602 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-887 2045122 2045527 2045934 "PATMATCH" 2046906 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-886 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NIL) (-874 2036015 2036359 2036587 "PALETTE" 2037030 T PALETTE (NIL) -8 NIL NIL NIL) (-873 2034408 2035020 2035380 "PAIR" 2035701 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-872 2028278 2033667 2033861 "PADICRC" 2034263 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-871 2021507 2027624 2027808 "PADICRAT" 2028126 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-870 2019822 2021444 2021489 "PADIC" 2021494 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-869 2016932 2018496 2018536 "PADICCT" 2019117 NIL PADICCT (NIL NIL) -9 NIL 2019399 NIL) (-868 2015889 2016089 2016357 "PADEPAC" 2016719 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-867 2015101 2015234 2015440 "PADE" 2015751 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-866 2013488 2014309 2014589 "OWP" 2014905 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-865 2012981 2013194 2013291 "OVERSET" 2013411 T OVERSET (NIL) -8 NIL NIL NIL) (-864 2012027 2012586 2012758 "OVAR" 2012849 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-863 2011291 2011412 2011573 "OUT" 2011886 T OUT (NIL) -7 NIL NIL NIL) (-862 2000163 2002400 2004600 "OUTFORM" 2009111 T OUTFORM (NIL) -8 NIL NIL NIL) (-861 1999499 1999760 1999887 "OUTBFILE" 2000056 T OUTBFILE (NIL) -8 NIL NIL NIL) (-860 1998806 1998971 1998999 "OUTBCON" 1999317 T OUTBCON (NIL) -9 NIL 1999483 NIL) (-859 1998407 1998519 1998676 "OUTBCON-" 1998681 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1997787 1998136 1998225 "OSI" 1998338 T OSI (NIL) -8 NIL NIL NIL) (-857 1997317 1997655 1997683 "OSGROUP" 1997688 T OSGROUP (NIL) -9 NIL 1997710 NIL) (-856 1996062 1996289 1996574 "ORTHPOL" 1997064 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1993613 1995897 1996018 "OREUP" 1996023 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991016 1993304 1993431 "ORESUP" 1993555 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988544 1989044 1989605 "OREPCTO" 1990505 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982230 1984431 1984472 "OREPCAT" 1986820 NIL OREPCAT (NIL T) -9 NIL 1987924 NIL) (-851 1979377 1980159 1981217 "OREPCAT-" 1981222 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978528 1978826 1978854 "ORDSET" 1979163 T ORDSET (NIL) -9 NIL 1979327 NIL) (-849 1977959 1978107 1978331 "ORDSET-" 1978336 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976524 1977315 1977343 "ORDRING" 1977545 T ORDRING (NIL) -9 NIL 1977670 NIL) (-847 1976169 1976263 1976407 "ORDRING-" 1976412 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975549 1976012 1976040 "ORDMON" 1976045 T ORDMON (NIL) -9 NIL 1976066 NIL) (-845 1974711 1974858 1975053 "ORDFUNS" 1975398 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974049 1974468 1974496 "ORDFIN" 1974561 T ORDFIN (NIL) -9 NIL 1974635 NIL) (-843 1970608 1972635 1973044 "ORDCOMP" 1973673 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1969874 1970001 1970187 "ORDCOMP2" 1970468 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966455 1967365 1968179 "OPTPROB" 1969080 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963257 1963896 1964600 "OPTPACK" 1965771 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1960944 1961710 1961738 "OPTCAT" 1962557 T OPTCAT (NIL) -9 NIL 1963207 NIL) (-838 1960328 1960621 1960726 "OPSIG" 1960859 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960096 1960135 1960201 "OPQUERY" 1960282 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957227 1958407 1958911 "OP" 1959625 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1956601 1956827 1956868 "OPERCAT" 1957080 NIL OPERCAT (NIL T) -9 NIL 1957177 NIL) (-834 1956356 1956412 1956529 "OPERCAT-" 1956534 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953169 1955153 1955522 "ONECOMP" 1956020 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952474 1952589 1952763 "ONECOMP2" 1953041 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1951893 1951999 1952129 "OMSERVER" 1952364 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1948755 1951333 1951373 "OMSAGG" 1951434 NIL OMSAGG (NIL T) -9 NIL 1951498 NIL) (-829 1947378 1947641 1947923 "OMPKG" 1948493 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1946808 1946911 1946939 "OM" 1947238 T OM (NIL) -9 NIL NIL NIL) (-827 1945355 1946357 1946526 "OMLO" 1946689 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944315 1944462 1944682 "OMEXPR" 1945181 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1943606 1943861 1943997 "OMERR" 1944199 T OMERR (NIL) -8 NIL NIL NIL) (-824 1942757 1943027 1943187 "OMERRK" 1943466 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942208 1942434 1942542 "OMENC" 1942669 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936103 1937288 1938459 "OMDEV" 1941057 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935172 1935343 1935537 "OMCONN" 1935929 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1933693 1934669 1934697 "OINTDOM" 1934702 T OINTDOM (NIL) -9 NIL 1934723 NIL) (-819 1929472 1930683 1931399 "OFMONOID" 1933009 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1928883 1929409 1929454 "ODVAR" 1929459 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926306 1928628 1928783 "ODR" 1928788 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1918887 1926082 1926208 "ODPOL" 1926213 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1912709 1918759 1918864 "ODP" 1918869 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911475 1911690 1911965 "ODETOOLS" 1912483 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908442 1909100 1909816 "ODESYS" 1910808 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903324 1904232 1905257 "ODERTRIC" 1907517 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1902750 1902832 1903026 "ODERED" 1903236 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1899638 1900186 1900863 "ODERAT" 1902173 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1896595 1897062 1897659 "ODEPRRIC" 1899167 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894538 1895134 1895620 "ODEPROB" 1896129 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891058 1891543 1892190 "ODEPRIM" 1894017 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890307 1890409 1890669 "ODEPAL" 1890950 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886469 1887260 1888124 "ODEPACK" 1889463 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885530 1885637 1885859 "ODEINT" 1886358 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1879631 1881056 1882503 "ODEIFTBL" 1884103 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875029 1875815 1876767 "ODEEF" 1878790 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874378 1874467 1874690 "ODECONST" 1874934 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872503 1873164 1873192 "ODECAT" 1873797 T ODECAT (NIL) -9 NIL 1874328 NIL) (-799 1869375 1872215 1872334 "OCT" 1872416 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869013 1869056 1869183 "OCTCT2" 1869326 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1863662 1866097 1866137 "OC" 1867234 NIL OC (NIL T) -9 NIL 1868092 NIL) (-796 1860889 1861637 1862627 "OC-" 1862721 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860241 1860709 1860737 "OCAMON" 1860742 T OCAMON (NIL) -9 NIL 1860763 NIL) (-794 1859772 1860113 1860141 "OASGP" 1860146 T OASGP (NIL) -9 NIL 1860166 NIL) (-793 1859033 1859522 1859550 "OAMONS" 1859590 T OAMONS (NIL) -9 NIL 1859633 NIL) (-792 1858447 1858880 1858908 "OAMON" 1858913 T OAMON (NIL) -9 NIL 1858933 NIL) (-791 1857705 1858223 1858251 "OAGROUP" 1858256 T OAGROUP (NIL) -9 NIL 1858276 NIL) (-790 1857395 1857445 1857533 "NUMTUBE" 1857649 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1850968 1852486 1854022 "NUMQUAD" 1855879 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1846724 1847712 1848737 "NUMODE" 1849963 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844079 1844959 1844987 "NUMINT" 1845910 T NUMINT (NIL) -9 NIL 1846674 NIL) (-786 1843027 1843224 1843442 "NUMFMT" 1843881 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829386 1832331 1834863 "NUMERIC" 1840534 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1823756 1828835 1828930 "NTSCAT" 1828935 NIL NTSCAT (NIL T T T T) -9 NIL 1828974 NIL) (-783 1822950 1823115 1823308 "NTPOLFN" 1823595 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811027 1819775 1820587 "NSUP" 1822171 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1810659 1810716 1810825 "NSUP2" 1810964 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1800887 1810433 1810566 "NSMP" 1810571 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799319 1799620 1799977 "NREP" 1800575 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1797910 1798162 1798520 "NPCOEF" 1799062 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1796976 1797091 1797307 "NORMRETR" 1797791 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795017 1795307 1795716 "NORMPK" 1796684 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1794702 1794730 1794854 "NORMMA" 1794983 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794502 1794659 1794688 "NONE" 1794693 T NONE (NIL) -8 NIL NIL NIL) (-773 1794291 1794320 1794389 "NONE1" 1794466 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1793788 1793850 1794029 "NODE1" 1794223 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792073 1792924 1793179 "NNI" 1793526 T NNI (NIL) -8 NIL NIL 1793761) (-770 1790493 1790806 1791170 "NLINSOL" 1791741 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1786734 1787729 1788628 "NIPROB" 1789614 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785491 1785725 1786027 "NFINTBAS" 1786496 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1784665 1785141 1785182 "NETCLT" 1785354 NIL NETCLT (NIL T) -9 NIL 1785436 NIL) (-766 1783373 1783604 1783885 "NCODIV" 1784433 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783135 1783172 1783247 "NCNTFRAC" 1783330 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781315 1781679 1782099 "NCEP" 1782760 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780166 1780939 1780967 "NASRING" 1781077 T NASRING (NIL) -9 NIL 1781157 NIL) (-762 1779961 1780005 1780099 "NASRING-" 1780104 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779068 1779593 1779621 "NARNG" 1779738 T NARNG (NIL) -9 NIL 1779829 NIL) (-760 1778760 1778827 1778961 "NARNG-" 1778966 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1777639 1777846 1778081 "NAGSP" 1778545 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1768911 1770595 1772268 "NAGS" 1775986 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767459 1767767 1768098 "NAGF07" 1768600 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1761997 1763288 1764595 "NAGF04" 1766172 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1754965 1756579 1758212 "NAGF02" 1760384 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750189 1751289 1752406 "NAGF01" 1753868 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1743817 1745383 1746968 "NAGE04" 1748624 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1734986 1737107 1739237 "NAGE02" 1741707 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1730939 1731886 1732850 "NAGE01" 1734042 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1728734 1729268 1729826 "NAGD03" 1730401 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720484 1722412 1724366 "NAGD02" 1726800 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714295 1715720 1717160 "NAGD01" 1719064 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710504 1711326 1712163 "NAGC06" 1713478 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1708969 1709301 1709657 "NAGC05" 1710168 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708345 1708464 1708608 "NAGC02" 1708845 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707304 1707887 1707927 "NAALG" 1708006 NIL NAALG (NIL T) -9 NIL 1708067 NIL) (-743 1707139 1707168 1707258 "NAALG-" 1707263 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701089 1702197 1703384 "MULTSQFR" 1706035 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700408 1700483 1700667 "MULTFACT" 1701001 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693132 1697045 1697098 "MTSCAT" 1698168 NIL MTSCAT (NIL T T) -9 NIL 1698683 NIL) (-739 1692844 1692898 1692990 "MTHING" 1693072 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1692636 1692669 1692729 "MSYSCMD" 1692804 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1688718 1691391 1691711 "MSET" 1692349 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1685787 1688279 1688320 "MSETAGG" 1688325 NIL MSETAGG (NIL T) -9 NIL 1688359 NIL) (-735 1681628 1683166 1683911 "MRING" 1685087 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681194 1681261 1681392 "MRF2" 1681555 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1680812 1680847 1680991 "MRATFAC" 1681153 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678424 1678719 1679150 "MPRFF" 1680517 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1672721 1678278 1678375 "MPOLY" 1678380 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672211 1672246 1672454 "MPCPF" 1672680 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1671725 1671768 1671952 "MPC3" 1672162 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1670920 1671001 1671222 "MPC2" 1671640 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669221 1669558 1669948 "MONOTOOL" 1670580 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668446 1668763 1668791 "MONOID" 1669010 T MONOID (NIL) -9 NIL 1669157 NIL) (-725 1667992 1668111 1668292 "MONOID-" 1668297 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658467 1664418 1664477 "MONOGEN" 1665151 NIL MONOGEN (NIL T T) -9 NIL 1665607 NIL) (-723 1655685 1656420 1657420 "MONOGEN-" 1657539 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654518 1654964 1654992 "MONADWU" 1655384 T MONADWU (NIL) -9 NIL 1655622 NIL) (-721 1653890 1654049 1654297 "MONADWU-" 1654302 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653249 1653493 1653521 "MONAD" 1653728 T MONAD (NIL) -9 NIL 1653840 NIL) (-719 1652934 1653012 1653144 "MONAD-" 1653149 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651223 1651847 1652126 "MOEBIUS" 1652687 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650501 1650905 1650945 "MODULE" 1650950 NIL MODULE (NIL T) -9 NIL 1650989 NIL) (-716 1650069 1650165 1650355 "MODULE-" 1650360 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1647749 1648433 1648760 "MODRING" 1649893 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1644693 1645854 1646375 "MODOP" 1647278 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643281 1643760 1644037 "MODMONOM" 1644556 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633322 1641572 1641986 "MODMON" 1642918 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630478 1632166 1632442 "MODFIELD" 1633197 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629455 1629759 1629949 "MMLFORM" 1630308 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1628981 1629024 1629203 "MMAP" 1629406 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627060 1627827 1627868 "MLO" 1628291 NIL MLO (NIL T) -9 NIL 1628533 NIL) (-707 1624426 1624942 1625544 "MLIFT" 1626541 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1623817 1623901 1624055 "MKUCFUNC" 1624337 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623416 1623486 1623609 "MKRECORD" 1623740 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622463 1622625 1622853 "MKFUNC" 1623227 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1621851 1621955 1622111 "MKFLCFN" 1622346 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621128 1621230 1621415 "MKBCFUNC" 1621744 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1617835 1620682 1620818 "MINT" 1621012 T MINT (NIL) -8 NIL NIL NIL) (-700 1616647 1616890 1617167 "MHROWRED" 1617590 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612026 1615182 1615587 "MFLOAT" 1616262 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611383 1611459 1611630 "MFINFACT" 1611938 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1607698 1608546 1609430 "MESH" 1610519 T MESH (NIL) -7 NIL NIL NIL) (-696 1606088 1606400 1606753 "MDDFACT" 1607385 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1602883 1605247 1605288 "MDAGG" 1605543 NIL MDAGG (NIL T) -9 NIL 1605686 NIL) (-694 1592623 1602176 1602383 "MCMPLX" 1602696 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1591764 1591910 1592110 "MCDEN" 1592472 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1589654 1589924 1590304 "MCALCFN" 1591494 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588579 1588819 1589052 "MAYBE" 1589460 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586191 1586714 1587276 "MATSTOR" 1588050 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582148 1585563 1585811 "MATRIX" 1585976 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1577912 1578621 1579357 "MATLIN" 1581505 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568018 1571204 1571281 "MATCAT" 1576161 NIL MATCAT (NIL T T T) -9 NIL 1577578 NIL) (-686 1564374 1565395 1566751 "MATCAT-" 1566756 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1562968 1563121 1563454 "MATCAT2" 1564209 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561080 1561404 1561788 "MAPPKG3" 1562643 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560061 1560234 1560456 "MAPPKG2" 1560904 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558560 1558844 1559171 "MAPPKG1" 1559767 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1557639 1557966 1558143 "MAPPAST" 1558403 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557250 1557308 1557431 "MAPHACK3" 1557575 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1556842 1556903 1557017 "MAPHACK2" 1557182 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556279 1556383 1556525 "MAPHACK1" 1556733 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554358 1554979 1555283 "MAGMA" 1556007 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1553837 1554082 1554173 "MACROAST" 1554287 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550255 1552076 1552537 "M3D" 1553409 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544361 1548624 1548665 "LZSTAGG" 1549447 NIL LZSTAGG (NIL T) -9 NIL 1549742 NIL) (-673 1540318 1541492 1542949 "LZSTAGG-" 1542954 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537405 1538209 1538696 "LWORD" 1539863 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1536981 1537209 1537284 "LSTAST" 1537350 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530147 1536752 1536886 "LSQM" 1536891 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529371 1529510 1529738 "LSPP" 1530002 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527183 1527484 1527940 "LSMP" 1529060 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1523962 1524636 1525366 "LSMP1" 1526485 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1517839 1523129 1523170 "LSAGG" 1523232 NIL LSAGG (NIL T) -9 NIL 1523310 NIL) (-665 1514534 1515458 1516671 "LSAGG-" 1516676 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512133 1513678 1513927 "LPOLY" 1514329 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1511715 1511800 1511923 "LPEFRAC" 1512042 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510036 1510809 1511062 "LO" 1511547 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1509688 1509800 1509828 "LOGIC" 1509939 T LOGIC (NIL) -9 NIL 1510020 NIL) (-660 1509550 1509573 1509644 "LOGIC-" 1509649 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1508743 1508883 1509076 "LODOOPS" 1509406 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506166 1508659 1508725 "LODO" 1508730 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1504704 1504939 1505292 "LODOF" 1505913 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1500922 1503353 1503394 "LODOCAT" 1503832 NIL LODOCAT (NIL T) -9 NIL 1504043 NIL) (-655 1500655 1500713 1500840 "LODOCAT-" 1500845 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1497975 1500496 1500614 "LODO2" 1500619 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495410 1497912 1497957 "LODO1" 1497962 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494291 1494456 1494761 "LODEEF" 1495233 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489530 1492421 1492462 "LNAGG" 1493409 NIL LNAGG (NIL T) -9 NIL 1493853 NIL) (-650 1488677 1488891 1489233 "LNAGG-" 1489238 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1484813 1485602 1486241 "LMOPS" 1488092 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484216 1484604 1484645 "LMODULE" 1484650 NIL LMODULE (NIL T) -9 NIL 1484676 NIL) (-647 1481414 1483861 1483984 "LMDICT" 1484126 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1480820 1481041 1481082 "LLINSET" 1481273 NIL LLINSET (NIL T) -9 NIL 1481364 NIL) (-645 1480519 1480728 1480788 "LITERAL" 1480793 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1473702 1479465 1479763 "LIST" 1480254 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473227 1473301 1473440 "LIST3" 1473622 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472234 1472412 1472640 "LIST2" 1473045 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470368 1470680 1471079 "LIST2MAP" 1471881 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1469964 1470201 1470242 "LINSET" 1470247 NIL LINSET (NIL T) -9 NIL 1470281 NIL) (-639 1468625 1469295 1469336 "LINEXP" 1469591 NIL LINEXP (NIL T) -9 NIL 1469740 NIL) (-638 1467272 1467532 1467829 "LINDEP" 1468377 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464039 1464758 1465535 "LIMITRF" 1466527 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462342 1462638 1463047 "LIMITPS" 1463734 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1456770 1461853 1462081 "LIE" 1462163 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1455718 1456187 1456227 "LIECAT" 1456367 NIL LIECAT (NIL T) -9 NIL 1456518 NIL) (-633 1455559 1455586 1455674 "LIECAT-" 1455679 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448055 1455008 1455173 "LIB" 1455414 T LIB (NIL) -8 NIL NIL NIL) (-631 1443690 1444573 1445508 "LGROBP" 1447172 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1441688 1441962 1442312 "LF" 1443411 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440528 1441220 1441248 "LFCAT" 1441455 T LFCAT (NIL) -9 NIL 1441594 NIL) (-628 1437430 1438060 1438748 "LEXTRIPK" 1439892 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434174 1435000 1435503 "LEXP" 1437010 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1433650 1433895 1433987 "LETAST" 1434102 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432048 1432361 1432762 "LEADCDET" 1433332 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431238 1431312 1431541 "LAZM3PK" 1431969 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426155 1429315 1429853 "LAUPOL" 1430750 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1425734 1425778 1425939 "LAPLACE" 1426105 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1423673 1424835 1425086 "LA" 1425567 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1422667 1423251 1423292 "LALG" 1423354 NIL LALG (NIL T) -9 NIL 1423413 NIL) (-619 1422381 1422440 1422576 "LALG-" 1422581 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422216 1422240 1422281 "KVTFROM" 1422343 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421139 1421583 1421768 "KTVLOGIC" 1422051 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1420974 1420998 1421039 "KRCFROM" 1421101 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1419878 1420065 1420364 "KOVACIC" 1420774 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1419713 1419737 1419778 "KONVERT" 1419840 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419548 1419572 1419613 "KOERCE" 1419675 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417378 1418141 1418518 "KERNEL" 1419204 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1416874 1416955 1417087 "KERNEL2" 1417292 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1410644 1415413 1415467 "KDAGG" 1415844 NIL KDAGG (NIL T T) -9 NIL 1416050 NIL) (-609 1410173 1410297 1410502 "KDAGG-" 1410507 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403321 1409834 1409989 "KAFILE" 1410051 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1397749 1402832 1403060 "JORDAN" 1403142 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397128 1397398 1397519 "JOINAST" 1397648 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1396974 1397033 1397088 "JAVACODE" 1397093 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393226 1395179 1395233 "IXAGG" 1396162 NIL IXAGG (NIL T T) -9 NIL 1396621 NIL) (-603 1392145 1392451 1392870 "IXAGG-" 1392875 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1387675 1392067 1392126 "IVECTOR" 1392131 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386441 1386678 1386944 "ITUPLE" 1387442 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1384943 1385120 1385415 "ITRIGMNP" 1386263 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1383688 1383892 1384175 "ITFUN3" 1384719 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383320 1383377 1383486 "ITFUN2" 1383625 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381122 1382182 1382481 "ITAYLOR" 1383054 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370067 1375259 1376422 "ISUPS" 1379992 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369171 1369311 1369547 "ISUMP" 1369914 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364385 1368972 1369051 "ISTRING" 1369124 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1363861 1364106 1364198 "ISAST" 1364313 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363070 1363152 1363368 "IRURPK" 1363775 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362006 1362207 1362447 "IRSN" 1362850 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360077 1360432 1360861 "IRRF2F" 1361644 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1359824 1359862 1359938 "IRREDFFX" 1360033 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358439 1358698 1358997 "IROOT" 1359557 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355043 1356123 1356815 "IR" 1357779 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1352656 1353151 1353717 "IR2" 1354521 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1351756 1351869 1352083 "IR2F" 1352539 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351547 1351581 1351641 "IPRNTPK" 1351716 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348126 1351436 1351505 "IPF" 1351510 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346453 1348051 1348108 "IPADIC" 1348113 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1345765 1346013 1346143 "IP4ADDR" 1346343 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345238 1345469 1345579 "IOMODE" 1345675 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344311 1344835 1344962 "IOBFILE" 1345131 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1343799 1344215 1344243 "IOBCON" 1344248 T IOBCON (NIL) -9 NIL 1344269 NIL) (-577 1343310 1343368 1343551 "INVLAPLA" 1343735 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1332958 1335312 1337698 "INTTR" 1340974 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329293 1330035 1330900 "INTTOOLS" 1332143 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1328879 1328970 1329087 "INTSLPE" 1329196 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1326832 1328802 1328861 "INTRVL" 1328866 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324434 1324946 1325521 "INTRF" 1326317 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1323845 1323942 1324084 "INTRET" 1324332 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1321842 1322231 1322701 "INTRAT" 1323453 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319105 1319688 1320307 "INTPM" 1321327 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1315850 1316449 1317187 "INTPAF" 1318491 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311029 1311991 1313042 "INTPACK" 1314819 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1307909 1310758 1310885 "INT" 1310922 T INT (NIL) -8 NIL NIL NIL) (-565 1307161 1307313 1307521 "INTHERTR" 1307751 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1306600 1306680 1306868 "INTHERAL" 1307075 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304446 1304889 1305346 "INTHEORY" 1306163 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1295852 1297473 1299245 "INTG0" 1302798 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276425 1281215 1286025 "INTFTBL" 1291062 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1275674 1275812 1275985 "INTFACT" 1276284 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273101 1273547 1274104 "INTEF" 1275228 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271468 1272207 1272235 "INTDOM" 1272536 T INTDOM (NIL) -9 NIL 1272743 NIL) (-557 1270837 1271011 1271253 "INTDOM-" 1271258 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267225 1269153 1269207 "INTCAT" 1270006 NIL INTCAT (NIL T) -9 NIL 1270327 NIL) (-555 1266697 1266800 1266928 "INTBIT" 1267117 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265396 1265550 1265857 "INTALG" 1266542 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1264879 1264969 1265126 "INTAF" 1265300 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258222 1264689 1264829 "INTABL" 1264834 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257563 1258029 1258094 "INT8" 1258128 T INT8 (NIL) -8 NIL NIL 1258173) (-550 1256903 1257369 1257434 "INT64" 1257468 T INT64 (NIL) -8 NIL NIL 1257513) (-549 1256243 1256709 1256774 "INT32" 1256808 T INT32 (NIL) -8 NIL NIL 1256853) (-548 1255583 1256049 1256114 "INT16" 1256148 T INT16 (NIL) -8 NIL NIL 1256193) (-547 1250493 1253206 1253234 "INS" 1254168 T INS (NIL) -9 NIL 1254833 NIL) (-546 1247733 1248504 1249478 "INS-" 1249551 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246508 1246735 1247033 "INPSIGN" 1247486 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1245626 1245743 1245940 "INPRODPF" 1246388 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244520 1244637 1244874 "INPRODFF" 1245506 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243520 1243672 1243932 "INNMFACT" 1244356 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1242717 1242814 1243002 "INMODGCD" 1243419 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241225 1241470 1241794 "INFSP" 1242462 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240409 1240526 1240709 "INFPROD0" 1241105 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237264 1238474 1238989 "INFORM" 1239902 T INFORM (NIL) -8 NIL NIL NIL) (-537 1236874 1236934 1237032 "INFORM1" 1237199 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236397 1236486 1236600 "INFINITY" 1236780 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235573 1236117 1236218 "INETCLTS" 1236316 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234189 1234439 1234760 "INEP" 1235321 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233438 1234086 1234151 "INDE" 1234156 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233002 1233070 1233187 "INCRMAPS" 1233365 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1231820 1232271 1232477 "INBFILE" 1232816 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227119 1228056 1229000 "INBFF" 1230908 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226027 1226296 1226324 "INBCON" 1226837 T INBCON (NIL) -9 NIL 1227103 NIL) (-528 1225279 1225502 1225778 "INBCON-" 1225783 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1224758 1225003 1225094 "INAST" 1225208 T INAST (NIL) -8 NIL NIL NIL) (-526 1224185 1224437 1224543 "IMPTAST" 1224672 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1220631 1224029 1224133 "IMATRIX" 1224138 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219343 1219466 1219781 "IMATQF" 1220487 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217563 1217790 1218127 "IMATLIN" 1219099 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212141 1217487 1217545 "ILIST" 1217550 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210046 1212001 1212114 "IIARRAY2" 1212119 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205444 1209957 1210021 "IFF" 1210026 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1204791 1205061 1205177 "IFAST" 1205348 T IFAST (NIL) -8 NIL NIL NIL) (-518 1199786 1204083 1204271 "IFARRAY" 1204648 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1198966 1199690 1199763 "IFAMON" 1199768 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198550 1198615 1198669 "IEVALAB" 1198876 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198225 1198293 1198453 "IEVALAB-" 1198458 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1197856 1198139 1198202 "IDPO" 1198207 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197106 1197745 1197820 "IDPOAMS" 1197825 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196413 1196995 1197070 "IDPOAM" 1197075 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195472 1195748 1195801 "IDPC" 1196214 NIL IDPC (NIL T T) -9 NIL 1196363 NIL) (-510 1194941 1195364 1195437 "IDPAM" 1195442 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194317 1194833 1194906 "IDPAG" 1194911 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1193962 1194153 1194228 "IDENT" 1194262 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190217 1191065 1191960 "IDECOMP" 1193119 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183055 1184140 1185187 "IDEAL" 1189253 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182219 1182331 1182530 "ICDEN" 1182939 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181290 1181699 1181846 "ICARD" 1182092 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179350 1179663 1180068 "IBPTOOLS" 1180967 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1174957 1178970 1179083 "IBITS" 1179269 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1171680 1172256 1172951 "IBATOOL" 1174374 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169459 1169921 1170454 "IBACHIN" 1171215 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167288 1169305 1169408 "IARRAY2" 1169413 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163394 1167214 1167271 "IARRAY1" 1167276 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157503 1161806 1162287 "IAN" 1162933 T IAN (NIL) -8 NIL NIL NIL) (-496 1157014 1157071 1157244 "IALGFACT" 1157440 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156542 1156655 1156683 "HYPCAT" 1156890 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156080 1156197 1156383 "HYPCAT-" 1156388 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1155675 1155875 1155958 "HOSTNAME" 1156017 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155520 1155557 1155598 "HOMOTOP" 1155603 NIL HOMOTOP (NIL T) -9 NIL 1155636 NIL) (-491 1152152 1153530 1153571 "HOAGG" 1154552 NIL HOAGG (NIL T) -9 NIL 1155231 NIL) (-490 1150746 1151145 1151671 "HOAGG-" 1151676 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1144750 1150341 1150490 "HEXADEC" 1150617 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143497 1143720 1143983 "HEUGCD" 1144527 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142573 1143334 1143464 "HELLFDIV" 1143469 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1140752 1142350 1142438 "HEAP" 1142517 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140015 1140304 1140438 "HEADAST" 1140638 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1133881 1139930 1139992 "HDP" 1139997 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1127869 1133516 1133668 "HDMP" 1133782 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127193 1127333 1127497 "HB" 1127725 T HB (NIL) -7 NIL NIL NIL) (-481 1120579 1127039 1127143 "HASHTBL" 1127148 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120055 1120300 1120392 "HASAST" 1120507 T HASAST (NIL) -8 NIL NIL NIL) (-479 1117833 1119677 1119859 "HACKPI" 1119893 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113501 1117686 1117799 "GTSET" 1117804 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1106916 1113379 1113477 "GSTBL" 1113482 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099194 1105947 1106212 "GSERIES" 1106707 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098335 1098752 1098780 "GROUP" 1098983 T GROUP (NIL) -9 NIL 1099117 NIL) (-474 1097701 1097860 1098111 "GROUP-" 1098116 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096068 1096389 1096776 "GROEBSOL" 1097378 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1094982 1095270 1095321 "GRMOD" 1095850 NIL GRMOD (NIL T T) -9 NIL 1096018 NIL) (-471 1094750 1094786 1094914 "GRMOD-" 1094919 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090040 1091104 1092104 "GRIMAGE" 1093770 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088506 1088767 1089091 "GRDEF" 1089736 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1087950 1088066 1088207 "GRAY" 1088385 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087137 1087543 1087594 "GRALG" 1087747 NIL GRALG (NIL T T) -9 NIL 1087840 NIL) (-466 1086798 1086871 1087034 "GRALG-" 1087039 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083575 1086383 1086561 "GPOLSET" 1086705 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1082929 1082986 1083244 "GOSPER" 1083512 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1078661 1079367 1079893 "GMODPOL" 1082628 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1077666 1077850 1078088 "GHENSEL" 1078473 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1071822 1072665 1073685 "GENUPS" 1076750 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071519 1071570 1071659 "GENUFACT" 1071765 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1070931 1071008 1071173 "GENPGCD" 1071437 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070405 1070440 1070653 "GENMFACT" 1070890 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1068971 1069228 1069535 "GENEEZ" 1070148 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063117 1068582 1068744 "GDMP" 1068894 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052459 1056888 1057994 "GCNAALG" 1062100 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1050786 1051648 1051676 "GCDDOM" 1051931 T GCDDOM (NIL) -9 NIL 1052088 NIL) (-453 1050256 1050383 1050598 "GCDDOM-" 1050603 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1048928 1049113 1049417 "GB" 1050035 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037544 1039874 1042266 "GBINTERN" 1046619 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035381 1035673 1036094 "GBF" 1037219 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034162 1034327 1034594 "GBEUCLID" 1035197 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033511 1033636 1033785 "GAUSSFAC" 1034033 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1031878 1032180 1032494 "GALUTIL" 1033230 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030186 1030460 1030784 "GALPOLYU" 1031605 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027551 1027841 1028248 "GALFACTU" 1029883 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019356 1020856 1022464 "GALFACT" 1025983 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1016744 1017402 1017430 "FVFUN" 1018586 T FVFUN (NIL) -9 NIL 1019306 NIL) (-442 1016010 1016192 1016220 "FVC" 1016511 T FVC (NIL) -9 NIL 1016694 NIL) (-441 1015653 1015835 1015903 "FUNDESC" 1015962 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015268 1015450 1015531 "FUNCTION" 1015605 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013012 1013590 1014056 "FT" 1014822 T FT (NIL) -8 NIL NIL NIL) (-438 1011803 1012313 1012516 "FTEM" 1012829 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010094 1010383 1010780 "FSUPFACT" 1011494 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008491 1008780 1009112 "FST" 1009782 T FST (NIL) -8 NIL NIL NIL) (-435 1007690 1007796 1007984 "FSRED" 1008373 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006389 1006645 1006992 "FSPRMELT" 1007405 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1003695 1004133 1004619 "FSPECF" 1005952 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985333 993664 993705 "FS" 997589 NIL FS (NIL T) -9 NIL 999878 NIL) (-431 973976 976969 981026 "FS-" 981326 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973504 973558 973728 "FSINT" 973917 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 971796 972497 972800 "FSERIES" 973283 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 970838 970954 971178 "FSCINT" 971676 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967046 969782 969823 "FSAGG" 970193 NIL FSAGG (NIL T) -9 NIL 970452 NIL) (-426 964808 965409 966205 "FSAGG-" 966300 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 963850 963993 964220 "FSAGG2" 964661 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961532 961812 962359 "FS2UPS" 963568 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961166 961209 961338 "FS2" 961483 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960044 960215 960517 "FS2EXPXP" 960991 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959470 959585 959737 "FRUTIL" 959924 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 950883 954965 956323 "FR" 958144 NIL FR (NIL T) -8 NIL NIL NIL) (-419 945852 948526 948566 "FRNAALG" 949962 NIL FRNAALG (NIL T) -9 NIL 950569 NIL) (-418 941525 942601 943876 "FRNAALG-" 944626 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941163 941206 941333 "FRNAAF2" 941476 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939543 940017 940312 "FRMOD" 940975 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937294 937926 938243 "FRIDEAL" 939334 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936489 936576 936865 "FRIDEAL2" 937201 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935622 936036 936077 "FRETRCT" 936082 NIL FRETRCT (NIL T) -9 NIL 936258 NIL) (-412 934734 934965 935316 "FRETRCT-" 935321 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 931822 933032 933091 "FRAMALG" 933973 NIL FRAMALG (NIL T T) -9 NIL 934265 NIL) (-410 929956 930411 931041 "FRAMALG-" 931264 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 923877 929431 929707 "FRAC" 929712 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923513 923570 923677 "FRAC2" 923814 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923149 923206 923313 "FR2" 923450 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 917662 920555 920583 "FPS" 921702 T FPS (NIL) -9 NIL 922259 NIL) (-405 917111 917220 917384 "FPS-" 917530 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914413 916082 916110 "FPC" 916335 T FPC (NIL) -9 NIL 916477 NIL) (-403 914206 914246 914343 "FPC-" 914348 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 912996 913694 913735 "FPATMAB" 913740 NIL FPATMAB (NIL T) -9 NIL 913892 NIL) (-401 910669 911172 911598 "FPARFRAC" 912633 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906062 906561 907243 "FORTRAN" 910101 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 903778 904278 904817 "FORT" 905543 T FORT (NIL) -7 NIL NIL NIL) (-398 901454 902016 902044 "FORTFN" 903104 T FORTFN (NIL) -9 NIL 903728 NIL) (-397 901218 901268 901296 "FORTCAT" 901355 T FORTCAT (NIL) -9 NIL 901417 NIL) (-396 899324 899834 900224 "FORMULA" 900848 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899112 899142 899211 "FORMULA1" 899288 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 898635 898687 898860 "FORDER" 899054 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 897731 897895 898088 "FOP" 898462 T FOP (NIL) -7 NIL NIL NIL) (-392 896312 897011 897185 "FNLA" 897613 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895041 895456 895484 "FNCAT" 895944 T FNCAT (NIL) -9 NIL 896204 NIL) (-390 894580 895000 895028 "FNAME" 895033 T FNAME (NIL) -8 NIL NIL NIL) (-389 893143 894106 894134 "FMTC" 894139 T FMTC (NIL) -9 NIL 894175 NIL) (-388 889476 890666 891295 "FMONOID" 892547 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 888668 889218 889367 "FM" 889372 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886092 886738 886766 "FMFUN" 887910 T FMFUN (NIL) -9 NIL 888618 NIL) (-385 885361 885542 885570 "FMC" 885860 T FMC (NIL) -9 NIL 886042 NIL) (-384 882440 883300 883354 "FMCAT" 884549 NIL FMCAT (NIL T T) -9 NIL 885044 NIL) (-383 881306 882206 882306 "FM1" 882385 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879080 879496 879990 "FLOATRP" 880857 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872655 876809 877430 "FLOAT" 878479 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870093 870593 871171 "FLOATCP" 872122 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 868833 869671 869712 "FLINEXP" 869717 NIL FLINEXP (NIL T) -9 NIL 869810 NIL) (-378 867987 868222 868550 "FLINEXP-" 868555 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867063 867207 867431 "FLASORT" 867839 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864179 865047 865099 "FLALG" 866326 NIL FLALG (NIL T T) -9 NIL 866793 NIL) (-375 857915 861665 861706 "FLAGG" 862968 NIL FLAGG (NIL T) -9 NIL 863620 NIL) (-374 856641 856980 857470 "FLAGG-" 857475 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855683 855826 856053 "FLAGG2" 856494 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852534 853542 853601 "FINRALG" 854729 NIL FINRALG (NIL T T) -9 NIL 855237 NIL) (-371 851694 851923 852262 "FINRALG-" 852267 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851074 851313 851341 "FINITE" 851537 T FINITE (NIL) -9 NIL 851644 NIL) (-369 843431 845618 845658 "FINAALG" 849325 NIL FINAALG (NIL T) -9 NIL 850778 NIL) (-368 838763 839813 840957 "FINAALG-" 842336 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838131 838518 838621 "FILE" 838693 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 836789 837127 837181 "FILECAT" 837865 NIL FILECAT (NIL T T) -9 NIL 838081 NIL) (-365 834505 836033 836061 "FIELD" 836101 T FIELD (NIL) -9 NIL 836181 NIL) (-364 833125 833510 834021 "FIELD-" 834026 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 830975 831760 832107 "FGROUP" 832811 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830065 830229 830449 "FGLMICPK" 830807 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 825897 829990 830047 "FFX" 830052 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825498 825559 825694 "FFSLPE" 825830 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821487 822270 823066 "FFPOLY" 824734 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 820991 821027 821236 "FFPOLY2" 821445 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 816834 820910 820973 "FFP" 820978 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812232 816745 816809 "FF" 816814 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807358 811575 811765 "FFNBX" 812086 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802287 806493 806751 "FFNBP" 807212 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 796920 801571 801782 "FFNB" 802120 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795752 795950 796265 "FFINTBAS" 796717 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 791821 794041 794069 "FFIELDC" 794689 T FFIELDC (NIL) -9 NIL 795065 NIL) (-350 790483 790854 791351 "FFIELDC-" 791356 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790052 790098 790222 "FFHOM" 790425 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787747 788234 788751 "FFF" 789567 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783365 787489 787590 "FFCGX" 787690 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 778986 783097 783204 "FFCGP" 783308 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774169 778713 778821 "FFCG" 778922 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755565 764646 764732 "FFCAT" 769897 NIL FFCAT (NIL T T T) -9 NIL 771348 NIL) (-343 750763 751810 753124 "FFCAT-" 754354 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750174 750217 750452 "FFCAT2" 750714 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739495 743146 744366 "FEXPR" 749026 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738495 738930 738971 "FEVALAB" 739055 NIL FEVALAB (NIL T) -9 NIL 739316 NIL) (-339 737654 737864 738202 "FEVALAB-" 738207 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736220 737037 737240 "FDIV" 737553 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733240 733981 734096 "FDIVCAT" 735664 NIL FDIVCAT (NIL T T T T) -9 NIL 736101 NIL) (-336 733002 733029 733199 "FDIVCAT-" 733204 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732222 732309 732586 "FDIV2" 732909 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731224 731538 731733 "FCTRDATA" 732047 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 729910 730169 730458 "FCPAK1" 730955 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729009 729410 729551 "FCOMP" 729801 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712711 716159 719697 "FC" 725491 T FC (NIL) -8 NIL NIL NIL) (-330 705074 709102 709142 "FAXF" 710944 NIL FAXF (NIL T) -9 NIL 711636 NIL) (-329 702350 703008 703833 "FAXF-" 704298 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697402 701726 701902 "FARRAY" 702207 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692296 694363 694416 "FAMR" 695439 NIL FAMR (NIL T T) -9 NIL 695899 NIL) (-326 691186 691488 691923 "FAMR-" 691928 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690355 691108 691161 "FAMONOID" 691166 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688141 688851 688904 "FAMONC" 689845 NIL FAMONC (NIL T T) -9 NIL 690231 NIL) (-323 686805 687895 688032 "FAGROUP" 688037 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684600 684919 685322 "FACUTIL" 686486 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683699 683884 684106 "FACTFUNC" 684410 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676121 683002 683201 "EXPUPXS" 683555 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673604 674144 674730 "EXPRTUBE" 675555 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 669875 670467 671197 "EXPRODE" 672943 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655360 668524 668953 "EXPR" 669479 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 649914 650501 651307 "EXPR2UPS" 654658 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649546 649603 649712 "EXPR2" 649851 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 640936 648699 648989 "EXPEXPAN" 649383 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640736 640893 640922 "EXIT" 640927 T EXIT (NIL) -8 NIL NIL NIL) (-312 640216 640460 640551 "EXITAST" 640665 T EXITAST (NIL) -8 NIL NIL NIL) (-311 639843 639905 640018 "EVALCYC" 640148 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639384 639502 639543 "EVALAB" 639713 NIL EVALAB (NIL T) -9 NIL 639817 NIL) (-309 638865 638987 639208 "EVALAB-" 639213 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636233 637535 637563 "EUCDOM" 638118 T EUCDOM (NIL) -9 NIL 638468 NIL) (-307 634638 635080 635670 "EUCDOM-" 635675 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622176 624936 627686 "ESTOOLS" 631908 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621808 621865 621974 "ESTOOLS2" 622113 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621559 621601 621681 "ESTOOLS1" 621760 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615596 617204 617232 "ES" 620000 T ES (NIL) -9 NIL 621410 NIL) (-302 610543 611830 613647 "ES-" 613811 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 606917 607678 608458 "ESCONT" 609783 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606662 606694 606776 "ESCONT1" 606879 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606337 606387 606487 "ES2" 606606 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 605967 606025 606134 "ES1" 606273 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605183 605312 605488 "ERROR" 605811 T ERROR (NIL) -7 NIL NIL NIL) (-296 598575 605042 605133 "EQTBL" 605138 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591078 593889 595338 "EQ" 597159 NIL -2114 (NIL T) -8 NIL NIL NIL) (-294 590710 590767 590876 "EQ2" 591015 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 585999 587048 588141 "EP" 589649 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584599 584890 585196 "ENV" 585713 T ENV (NIL) -8 NIL NIL NIL) (-291 583693 584247 584275 "ENTIRER" 584280 T ENTIRER (NIL) -9 NIL 584326 NIL) (-290 580160 581648 582018 "EMR" 583492 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579304 579489 579543 "ELTAGG" 579923 NIL ELTAGG (NIL T T) -9 NIL 580134 NIL) (-288 579023 579085 579226 "ELTAGG-" 579231 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 578812 578841 578895 "ELTAB" 578979 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 577938 578084 578283 "ELFUTS" 578663 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577680 577736 577764 "ELEMFUN" 577869 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577550 577571 577639 "ELEMFUN-" 577644 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572394 575650 575691 "ELAGG" 576631 NIL ELAGG (NIL T) -9 NIL 577094 NIL) (-282 570679 571113 571776 "ELAGG-" 571781 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569344 569622 569915 "ELABEXPR" 570406 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562208 564011 564838 "EFUPXS" 568620 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555658 557459 558269 "EFULS" 561484 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553143 553501 553973 "EFSTRUC" 555290 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 542934 544500 546048 "EF" 551658 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542008 542419 542568 "EAB" 542805 T EAB (NIL) -8 NIL NIL NIL) (-275 541190 541967 541995 "E04UCFA" 542000 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540372 541149 541177 "E04NAFA" 541182 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539554 540331 540359 "E04MBFA" 540364 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538736 539513 539541 "E04JAFA" 539546 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 537920 538695 538723 "E04GCFA" 538728 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537104 537879 537907 "E04FDFA" 537912 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536286 537063 537091 "E04DGFA" 537096 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530459 531811 533175 "E04AGNT" 534942 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529139 529645 529685 "DVARCAT" 530160 NIL DVARCAT (NIL T) -9 NIL 530359 NIL) (-266 528343 528555 528869 "DVARCAT-" 528874 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521480 528142 528271 "DSMP" 528276 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516261 517425 518493 "DROPT" 520432 T DROPT (NIL) -8 NIL NIL NIL) (-263 515926 515985 516083 "DROPT1" 516196 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511041 512167 513304 "DROPT0" 514809 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509386 509711 510097 "DRAWPT" 510675 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 503973 504896 505975 "DRAW" 508360 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503606 503659 503777 "DRAWHACK" 503914 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502337 502606 502897 "DRAWCX" 503335 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 501852 501921 502072 "DRAWCURV" 502263 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492320 494282 496397 "DRAWCFUN" 499757 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489086 491015 491056 "DQAGG" 491685 NIL DQAGG (NIL T) -9 NIL 491958 NIL) (-254 477210 483679 483762 "DPOLCAT" 485614 NIL DPOLCAT (NIL T T T T) -9 NIL 486159 NIL) (-253 472046 473395 475353 "DPOLCAT-" 475358 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465168 471907 472005 "DPMO" 472010 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458193 464948 465115 "DPMM" 465120 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457671 457885 457983 "DOMTMPLT" 458115 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457104 457473 457553 "DOMCTOR" 457611 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456372 456626 456763 "DOMAIN" 456987 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450360 456007 456159 "DMP" 456273 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 449960 450016 450160 "DLP" 450298 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443782 449287 449477 "DLIST" 449802 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440579 442635 442676 "DLAGG" 443226 NIL DLAGG (NIL T) -9 NIL 443456 NIL) (-243 439255 439919 439947 "DIVRING" 440039 T DIVRING (NIL) -9 NIL 440122 NIL) (-242 438492 438682 438982 "DIVRING-" 438987 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436594 436951 437357 "DISPLAY" 438106 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430482 436508 436571 "DIRPROD" 436576 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429330 429533 429798 "DIRPROD2" 430275 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418105 424111 424164 "DIRPCAT" 424574 NIL DIRPCAT (NIL NIL T) -9 NIL 425414 NIL) (-237 415431 416073 416954 "DIRPCAT-" 417291 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414718 414878 415064 "DIOSP" 415265 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411373 413630 413671 "DIOPS" 414105 NIL DIOPS (NIL T) -9 NIL 414334 NIL) (-234 410922 411036 411227 "DIOPS-" 411232 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409745 410373 410401 "DIFRING" 410588 T DIFRING (NIL) -9 NIL 410698 NIL) (-232 409391 409468 409620 "DIFRING-" 409625 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407127 408399 408440 "DIFEXT" 408803 NIL DIFEXT (NIL T) -9 NIL 409097 NIL) (-230 405412 405840 406506 "DIFEXT-" 406511 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402687 404944 404985 "DIAGG" 404990 NIL DIAGG (NIL T) -9 NIL 405010 NIL) (-228 402071 402228 402480 "DIAGG-" 402485 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397488 401030 401307 "DHMATRIX" 401840 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393100 394009 395019 "DFSFUN" 396498 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388178 392031 392343 "DFLOAT" 392808 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386441 386722 387111 "DFINTTLS" 387886 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383470 384462 384862 "DERHAM" 386107 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381271 383245 383334 "DEQUEUE" 383414 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380525 380658 380841 "DEGRED" 381133 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 376955 377700 378546 "DEFINTRF" 379753 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374510 374979 375571 "DEFINTEF" 376474 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373860 374130 374245 "DEFAST" 374415 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367864 373455 373604 "DECIMAL" 373731 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365376 365834 366340 "DDFACT" 367408 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 364972 365015 365166 "DBLRESP" 365327 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362844 363205 363565 "DBASE" 364739 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362086 362324 362470 "DATAARY" 362743 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361192 362045 362073 "D03FAFA" 362078 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360299 361151 361179 "D03EEFA" 361184 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358249 358715 359204 "D03AGNT" 359830 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357538 358208 358236 "D02EJFA" 358241 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356827 357497 357525 "D02CJFA" 357530 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356116 356786 356814 "D02BHFA" 356819 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355405 356075 356103 "D02BBFA" 356108 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348602 350191 351797 "D02AGNT" 353819 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346370 346893 347439 "D01WGTS" 348076 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345437 346329 346357 "D01TRNS" 346362 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344505 345396 345424 "D01GBFA" 345429 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343573 344464 344492 "D01FCFA" 344497 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342641 343532 343560 "D01ASFA" 343565 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341709 342600 342628 "D01AQFA" 342633 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340777 341668 341696 "D01APFA" 341701 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339845 340736 340764 "D01ANFA" 340769 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338913 339804 339832 "D01AMFA" 339837 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337981 338872 338900 "D01ALFA" 338905 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337049 337940 337968 "D01AKFA" 337973 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336117 337008 337036 "D01AJFA" 337041 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329412 330965 332526 "D01AGNT" 334576 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328749 328877 329029 "CYCLOTOM" 329280 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325483 326197 326924 "CYCLES" 328042 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324795 324929 325100 "CVMP" 325344 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322636 322894 323263 "CTRIGMNP" 324523 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322072 322430 322503 "CTOR" 322583 T CTOR (NIL) -8 NIL NIL NIL) (-186 321581 321803 321904 "CTORKIND" 321991 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320872 321188 321216 "CTORCAT" 321398 T CTORCAT (NIL) -9 NIL 321511 NIL) (-184 320470 320581 320740 "CTORCAT-" 320745 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319959 320173 320271 "CTORCALL" 320392 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319333 319432 319585 "CSTTOOLS" 319856 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315132 315789 316547 "CRFP" 318645 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314607 314853 314945 "CRCEAST" 315060 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313654 313839 314067 "CRAPACK" 314411 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313038 313139 313343 "CPMATCH" 313530 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312763 312791 312897 "CPIMA" 313004 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309111 309783 310502 "COORDSYS" 312098 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308523 308644 308786 "CONTOUR" 308989 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304414 306526 307018 "CONTFRAC" 308063 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304294 304315 304343 "CONDUIT" 304380 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303382 303936 303964 "COMRING" 303969 T COMRING (NIL) -9 NIL 304021 NIL) (-171 302436 302740 302924 "COMPPROP" 303218 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302097 302132 302260 "COMPLPAT" 302395 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292388 301906 302015 "COMPLEX" 302020 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292024 292081 292188 "COMPLEX2" 292325 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291742 291777 291875 "COMPFACT" 291983 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275822 285816 285856 "COMPCAT" 286860 NIL COMPCAT (NIL T) -9 NIL 288208 NIL) (-165 265334 268261 271888 "COMPCAT-" 272244 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265063 265091 265194 "COMMUPC" 265300 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264857 264891 264950 "COMMONOP" 265024 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264413 264608 264695 "COMM" 264790 T COMM (NIL) -8 NIL NIL NIL) (-161 263989 264217 264292 "COMMAAST" 264358 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263238 263432 263460 "COMBOPC" 263798 T COMBOPC (NIL) -9 NIL 263973 NIL) (-159 262134 262344 262586 "COMBINAT" 263028 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258591 259165 259792 "COMBF" 261556 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257349 257707 257942 "COLOR" 258376 T COLOR (NIL) -8 NIL NIL NIL) (-156 256825 257070 257162 "COLONAST" 257277 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256465 256512 256637 "CMPLXRT" 256772 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255913 256165 256264 "CLLCTAST" 256386 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251411 252443 253523 "CLIP" 254853 T CLIP (NIL) -7 NIL NIL NIL) (-152 249757 250517 250756 "CLIF" 251238 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245932 247903 247944 "CLAGG" 248873 NIL CLAGG (NIL T) -9 NIL 249409 NIL) (-150 244354 244811 245394 "CLAGG-" 245399 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243898 243983 244123 "CINTSLPE" 244263 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241399 241870 242418 "CHVAR" 243426 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240573 241127 241155 "CHARZ" 241160 T CHARZ (NIL) -9 NIL 241175 NIL) (-146 240327 240367 240445 "CHARPOL" 240527 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239385 239972 240000 "CHARNZ" 240047 T CHARNZ (NIL) -9 NIL 240103 NIL) (-144 237351 238075 238410 "CHAR" 239070 T CHAR (NIL) -8 NIL NIL NIL) (-143 237077 237138 237166 "CFCAT" 237277 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236322 236433 236615 "CDEN" 236961 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232287 235475 235755 "CCLASS" 236062 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231594 231737 231900 "CATEGORY" 232144 T -10 (NIL) -8 NIL NIL NIL) (-139 231167 231513 231561 "CATCTOR" 231566 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230618 230870 230968 "CATAST" 231089 T CATAST (NIL) -8 NIL NIL NIL) (-137 230094 230339 230431 "CASEAST" 230546 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225103 226123 226876 "CARTEN" 229397 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224211 224359 224580 "CARTEN2" 224950 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222527 223361 223618 "CARD" 223974 T CARD (NIL) -8 NIL NIL NIL) (-133 222103 222331 222406 "CAPSLAST" 222472 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221607 221815 221843 "CACHSET" 221975 T CACHSET (NIL) -9 NIL 222053 NIL) (-131 221077 221399 221427 "CABMON" 221477 T CABMON (NIL) -9 NIL 221533 NIL) (-130 220550 220781 220891 "BYTEORD" 220987 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220084 220226 "BYTE" 220389 T BYTE (NIL) -8 NIL NIL 220511) (-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 3221085 3221090 3221095 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3221070 3221075 3221080 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3221055 3221060 3221065 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3221040 3221045 3221050 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1292 3220183 3220915 3220992 "ZMOD" 3220997 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1291 3219293 3219457 3219666 "ZLINDEP" 3220015 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1290 3208593 3210361 3212333 "ZDSOLVE" 3217423 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1289 3207839 3207980 3208169 "YSTREAM" 3208439 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1288 3205613 3207140 3207344 "XRPOLY" 3207682 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3202166 3203484 3204059 "XPR" 3205085 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1286 3199887 3201497 3201701 "XPOLY" 3201997 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1285 3197540 3198908 3198963 "XPOLYC" 3199251 NIL XPOLYC (NIL T T) -9 NIL 3199364 NIL) (-1284 3193915 3196057 3196445 "XPBWPOLY" 3197198 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1283 3189610 3191905 3191947 "XF" 3192568 NIL XF (NIL T) -9 NIL 3192968 NIL) (-1282 3189231 3189319 3189488 "XF-" 3189493 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1281 3184427 3185716 3185771 "XFALG" 3187943 NIL XFALG (NIL T T) -9 NIL 3188732 NIL) (-1280 3183560 3183664 3183869 "XEXPPKG" 3184319 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1279 3181669 3183410 3183506 "XDPOLY" 3183511 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3180476 3181076 3181119 "XALG" 3181124 NIL XALG (NIL T) -9 NIL 3181235 NIL) (-1277 3173918 3178453 3178947 "WUTSET" 3180068 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1276 3172174 3172970 3173293 "WP" 3173729 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1275 3171776 3171996 3172066 "WHILEAST" 3172126 T WHILEAST (NIL) -8 NIL NIL NIL) (-1274 3171248 3171493 3171587 "WHEREAST" 3171704 T WHEREAST (NIL) -8 NIL NIL NIL) (-1273 3170134 3170332 3170627 "WFFINTBS" 3171045 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1272 3168038 3168465 3168927 "WEIER" 3169706 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1271 3167084 3167534 3167576 "VSPACE" 3167712 NIL VSPACE (NIL T) -9 NIL 3167786 NIL) (-1270 3166922 3166949 3167040 "VSPACE-" 3167045 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1269 3166730 3166773 3166841 "VOID" 3166876 T VOID (NIL) -8 NIL NIL NIL) (-1268 3164866 3165225 3165631 "VIEW" 3166346 T VIEW (NIL) -7 NIL NIL NIL) (-1267 3161290 3161929 3162666 "VIEWDEF" 3164151 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1266 3150594 3152838 3155011 "VIEW3D" 3159139 T VIEW3D (NIL) -8 NIL NIL NIL) (-1265 3142845 3144505 3146084 "VIEW2D" 3149037 T VIEW2D (NIL) -8 NIL NIL NIL) (-1264 3138197 3142615 3142707 "VECTOR" 3142788 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1263 3136774 3137033 3137351 "VECTOR2" 3137927 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1262 3130248 3134555 3134598 "VECTCAT" 3135593 NIL VECTCAT (NIL T) -9 NIL 3136180 NIL) (-1261 3129262 3129516 3129906 "VECTCAT-" 3129911 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1260 3128716 3128913 3129033 "VARIABLE" 3129177 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1259 3128649 3128654 3128684 "UTYPE" 3128689 T UTYPE (NIL) -9 NIL NIL NIL) (-1258 3127479 3127633 3127895 "UTSODETL" 3128475 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1257 3124919 3125379 3125903 "UTSODE" 3127020 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1256 3116756 3122545 3123034 "UTS" 3124488 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3107630 3112997 3113040 "UTSCAT" 3114152 NIL UTSCAT (NIL T) -9 NIL 3114910 NIL) (-1254 3104977 3105700 3106689 "UTSCAT-" 3106694 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104604 3104647 3104780 "UTS2" 3104928 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3098830 3101442 3101485 "URAGG" 3103555 NIL URAGG (NIL T) -9 NIL 3104278 NIL) (-1251 3095769 3096632 3097755 "URAGG-" 3097760 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1250 3091478 3094404 3094869 "UPXSSING" 3095433 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1249 3083544 3090725 3090998 "UPXS" 3091263 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3076617 3083448 3083520 "UPXSCONS" 3083525 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1247 3066362 3073155 3073217 "UPXSCCA" 3073791 NIL UPXSCCA (NIL T T) -9 NIL 3074024 NIL) (-1246 3066000 3066085 3066259 "UPXSCCA-" 3066264 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1245 3055597 3062163 3062206 "UPXSCAT" 3062854 NIL UPXSCAT (NIL T) -9 NIL 3063463 NIL) (-1244 3055027 3055106 3055285 "UPXS2" 3055512 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 3053681 3053934 3054285 "UPSQFREE" 3054770 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1242 3047102 3050159 3050214 "UPSCAT" 3051375 NIL UPSCAT (NIL T T) -9 NIL 3052149 NIL) (-1241 3046306 3046513 3046840 "UPSCAT-" 3046845 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1240 3031961 3039729 3039772 "UPOLYC" 3041873 NIL UPOLYC (NIL T) -9 NIL 3043094 NIL) (-1239 3023289 3025715 3028862 "UPOLYC-" 3028867 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1238 3022916 3022959 3023092 "UPOLYC2" 3023240 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1237 3014727 3022599 3022728 "UP" 3022835 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1236 3014066 3014173 3014337 "UPMP" 3014616 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1235 3013619 3013700 3013839 "UPDIVP" 3013979 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1234 3012187 3012436 3012752 "UPDECOMP" 3013368 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1233 3011422 3011534 3011719 "UPCDEN" 3012071 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1232 3010941 3011010 3011159 "UP2" 3011347 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1231 3009408 3010145 3010422 "UNISEG" 3010699 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1230 3008623 3008750 3008955 "UNISEG2" 3009251 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1229 3007683 3007863 3008089 "UNIFACT" 3008439 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1228 2991615 3006860 3007111 "ULS" 3007490 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1227 2979613 2991519 2991591 "ULSCONS" 2991596 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1226 2961632 2973617 2973679 "ULSCCAT" 2974317 NIL ULSCCAT (NIL T T) -9 NIL 2974605 NIL) (-1225 2960682 2960927 2961315 "ULSCCAT-" 2961320 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1224 2950056 2956536 2956579 "ULSCAT" 2957442 NIL ULSCAT (NIL T) -9 NIL 2958173 NIL) (-1223 2949486 2949565 2949744 "ULS2" 2949971 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1222 2948613 2949123 2949230 "UINT8" 2949341 T UINT8 (NIL) -8 NIL NIL 2949426) (-1221 2947739 2948249 2948356 "UINT64" 2948467 T UINT64 (NIL) -8 NIL NIL 2948552) (-1220 2946865 2947375 2947482 "UINT32" 2947593 T UINT32 (NIL) -8 NIL NIL 2947678) (-1219 2945991 2946501 2946608 "UINT16" 2946719 T UINT16 (NIL) -8 NIL NIL 2946804) (-1218 2944294 2945251 2945281 "UFD" 2945493 T UFD (NIL) -9 NIL 2945607 NIL) (-1217 2944088 2944134 2944229 "UFD-" 2944234 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2943170 2943353 2943569 "UDVO" 2943894 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2940986 2941395 2941866 "UDPO" 2942734 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2940919 2940924 2940954 "TYPE" 2940959 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940679 2940874 2940905 "TYPEAST" 2940910 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939650 2939852 2940092 "TWOFACT" 2940473 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938673 2939059 2939294 "TUPLE" 2939450 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936364 2936883 2937422 "TUBETOOL" 2938156 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935213 2935418 2935659 "TUBE" 2936157 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2929942 2934185 2934468 "TS" 2934965 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918582 2922701 2922798 "TSETCAT" 2928067 NIL TSETCAT (NIL T T T T) -9 NIL 2929598 NIL) (-1206 2913314 2914914 2916805 "TSETCAT-" 2916810 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2907953 2908800 2909729 "TRMANIP" 2912450 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907394 2907457 2907620 "TRIMAT" 2907885 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905260 2905497 2905854 "TRIGMNIP" 2907143 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2904780 2904893 2904923 "TRIGCAT" 2905136 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904449 2904528 2904669 "TRIGCAT-" 2904674 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901294 2903307 2903588 "TREE" 2904203 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900568 2901096 2901126 "TRANFUN" 2901161 T TRANFUN (NIL) -9 NIL 2901227 NIL) (-1198 2899847 2900038 2900318 "TRANFUN-" 2900323 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899651 2899683 2899744 "TOPSP" 2899808 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2898999 2899114 2899268 "TOOLSIGN" 2899532 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897633 2898176 2898415 "TEXTFILE" 2898782 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895545 2896086 2896515 "TEX" 2897226 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895326 2895357 2895429 "TEX1" 2895508 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2894974 2895037 2895127 "TEMUTL" 2895258 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2893128 2893408 2893733 "TBCMPPK" 2894697 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2884905 2891288 2891344 "TBAGG" 2891744 NIL TBAGG (NIL T T) -9 NIL 2891955 NIL) (-1189 2879975 2881463 2883217 "TBAGG-" 2883222 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879359 2879466 2879611 "TANEXP" 2879864 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872749 2879216 2879309 "TABLE" 2879314 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2872161 2872260 2872398 "TABLEAU" 2872646 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2866769 2867989 2869237 "TABLBUMP" 2870947 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2865991 2866138 2866319 "SYSTEM" 2866610 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862450 2863149 2863932 "SYSSOLP" 2865242 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861494 2861999 2862118 "SYSNNI" 2862304 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862389) (-1181 2860801 2861260 2861339 "SYSINT" 2861399 NIL SYSINT (NIL NIL) -8 NIL NIL 2861444) (-1180 2857133 2858079 2858789 "SYNTAX" 2860113 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854291 2854893 2855525 "SYMTAB" 2856523 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849540 2850442 2851425 "SYMS" 2853330 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2846775 2848998 2849228 "SYMPOLY" 2849345 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846292 2846367 2846490 "SYMFUNC" 2846687 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842311 2843604 2844417 "SYMBOL" 2845501 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2835850 2837539 2839259 "SWITCH" 2840613 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829084 2834671 2834974 "SUTS" 2835605 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821150 2828331 2828604 "SUPXS" 2828869 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2812909 2820768 2820894 "SUP" 2821059 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812068 2812195 2812412 "SUPFRACF" 2812777 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811689 2811748 2811861 "SUP2" 2812003 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810137 2810411 2810767 "SUMRF" 2811388 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809472 2809538 2809730 "SUMFS" 2810058 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793439 2808649 2808900 "SULS" 2809279 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793041 2793261 2793331 "SUCHTAST" 2793391 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792336 2792566 2792706 "SUCH" 2792949 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786202 2787242 2788201 "SUBSPACE" 2791424 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785632 2785722 2785886 "SUBRESP" 2786090 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2778997 2780297 2781608 "STTF" 2784368 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773170 2774290 2775437 "STTFNC" 2777897 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764480 2766352 2768146 "STTAYLOR" 2771411 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757610 2764344 2764427 "STRTBL" 2764432 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2752974 2757565 2757596 "STRING" 2757601 T STRING (NIL) -8 NIL NIL NIL) (-1156 2747835 2752347 2752377 "STRICAT" 2752436 T STRICAT (NIL) -9 NIL 2752498 NIL) (-1155 2740588 2745454 2746065 "STREAM" 2747259 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740098 2740175 2740319 "STREAM3" 2740505 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739080 2739263 2739498 "STREAM2" 2739911 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2738768 2738820 2738913 "STREAM1" 2739022 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2737784 2737965 2738196 "STINPROD" 2738584 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737336 2737546 2737576 "STEP" 2737656 T STEP (NIL) -9 NIL 2737734 NIL) (-1149 2730768 2737235 2737312 "STBL" 2737317 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2725894 2729989 2730032 "STAGG" 2730185 NIL STAGG (NIL T) -9 NIL 2730274 NIL) (-1147 2723596 2724198 2725070 "STAGG-" 2725075 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721743 2723366 2723458 "STACK" 2723539 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714438 2719884 2720340 "SREGSET" 2721373 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2706863 2708232 2709745 "SRDCMPK" 2713044 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2699780 2704303 2704333 "SRAGG" 2705636 T SRAGG (NIL) -9 NIL 2706244 NIL) (-1142 2698797 2699052 2699431 "SRAGG-" 2699436 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693257 2697744 2698165 "SQMATRIX" 2698423 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2686942 2689975 2690702 "SPLTREE" 2692602 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2682905 2683598 2684244 "SPLNODE" 2686368 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2681952 2682185 2682215 "SPFCAT" 2682659 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680689 2680899 2681163 "SPECOUT" 2681710 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672315 2674085 2674115 "SPADXPT" 2678507 T SPADXPT (NIL) -9 NIL 2680541 NIL) (-1135 2672076 2672116 2672185 "SPADPRSR" 2672268 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670231 2672031 2672062 "SPADAST" 2672067 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662176 2663949 2663992 "SPACEC" 2668365 NIL SPACEC (NIL T) -9 NIL 2670181 NIL) (-1132 2660306 2662108 2662157 "SPACE3" 2662162 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659058 2659229 2659520 "SORTPAK" 2660111 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657150 2657453 2657865 "SOLVETRA" 2658722 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656200 2656422 2656683 "SOLVESER" 2656923 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651504 2652392 2653387 "SOLVERAD" 2655252 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647319 2647928 2648657 "SOLVEFOR" 2650871 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641589 2646668 2646765 "SNTSCAT" 2646770 NIL SNTSCAT (NIL T T T T) -9 NIL 2646840 NIL) (-1125 2635695 2639912 2640303 "SMTS" 2641279 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630379 2635583 2635660 "SMP" 2635665 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628538 2628839 2629237 "SMITH" 2630076 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621251 2625447 2625550 "SMATCAT" 2626901 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627451 NIL) (-1121 2618191 2619014 2620192 "SMATCAT-" 2620197 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2615857 2617427 2617470 "SKAGG" 2617731 NIL SKAGG (NIL T) -9 NIL 2617866 NIL) (-1119 2612168 2615273 2615468 "SINT" 2615655 T SINT (NIL) -8 NIL NIL 2615828) (-1118 2611940 2611978 2612044 "SIMPAN" 2612124 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611219 2611475 2611615 "SIG" 2611822 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610057 2610278 2610553 "SIGNRF" 2610978 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2608890 2609041 2609325 "SIGNEF" 2609886 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608196 2608473 2608597 "SIGAST" 2608788 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2605885 2606340 2606846 "SHP" 2607737 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599737 2605786 2605862 "SHDP" 2605867 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599310 2599502 2599532 "SGROUP" 2599625 T SGROUP (NIL) -9 NIL 2599687 NIL) (-1110 2599168 2599194 2599267 "SGROUP-" 2599272 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596003 2596701 2597424 "SGCF" 2598467 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590371 2595450 2595547 "SFRTCAT" 2595552 NIL SFRTCAT (NIL T T T T) -9 NIL 2595591 NIL) (-1107 2583792 2584810 2585946 "SFRGCD" 2589354 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2576918 2577991 2579177 "SFQCMPK" 2582725 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576538 2576627 2576738 "SFORT" 2576859 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575656 2576378 2576499 "SEXOF" 2576504 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574763 2575537 2575605 "SEX" 2575610 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570276 2570991 2571086 "SEXCAT" 2574023 NIL SEXCAT (NIL T T T T T) -9 NIL 2574601 NIL) (-1101 2567429 2570210 2570258 "SET" 2570263 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565653 2566142 2566447 "SETMN" 2567170 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565149 2565301 2565331 "SETCAT" 2565507 T SETCAT (NIL) -9 NIL 2565617 NIL) (-1098 2564841 2564919 2565049 "SETCAT-" 2565054 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561202 2563302 2563345 "SETAGG" 2564215 NIL SETAGG (NIL T) -9 NIL 2564555 NIL) (-1096 2560660 2560776 2561013 "SETAGG-" 2561018 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560103 2560356 2560457 "SEQAST" 2560581 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559302 2559596 2559657 "SEGXCAT" 2559943 NIL SEGXCAT (NIL T T) -9 NIL 2560063 NIL) (-1093 2558308 2558968 2559150 "SEG" 2559155 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557287 2557501 2557544 "SEGCAT" 2558066 NIL SEGCAT (NIL T) -9 NIL 2558287 NIL) (-1091 2556288 2556666 2556866 "SEGBIND" 2557122 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2555909 2555968 2556081 "SEGBIND2" 2556223 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555482 2555710 2555787 "SEGAST" 2555854 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554701 2554827 2555031 "SEG2" 2555326 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554111 2554636 2554683 "SDVAR" 2554688 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546638 2553881 2554011 "SDPOL" 2554016 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545231 2545497 2545816 "SCPKG" 2546353 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544395 2544567 2544759 "SCOPE" 2545061 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543615 2543749 2543928 "SCACHE" 2544250 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543261 2543447 2543477 "SASTCAT" 2543482 T SASTCAT (NIL) -9 NIL 2543495 NIL) (-1081 2542748 2543096 2543172 "SAOS" 2543207 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542313 2542348 2542521 "SAERFFC" 2542707 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536252 2542210 2542290 "SAE" 2542295 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2535845 2535880 2536039 "SAEFACT" 2536211 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534166 2534480 2534881 "RURPK" 2535511 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2532803 2533109 2533414 "RULESET" 2534000 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530026 2530556 2531014 "RULE" 2532484 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529638 2529820 2529903 "RULECOLD" 2529978 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529428 2529456 2529527 "RTVALUE" 2529589 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2528899 2529145 2529239 "RSTRCAST" 2529356 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523747 2524542 2525462 "RSETGCD" 2528098 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2512977 2518056 2518153 "RSETCAT" 2522272 NIL RSETCAT (NIL T T T T) -9 NIL 2523369 NIL) (-1069 2510904 2511443 2512267 "RSETCAT-" 2512272 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503289 2504666 2506186 "RSDCMPK" 2509503 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501268 2501735 2501809 "RRCC" 2502895 NIL RRCC (NIL T T) -9 NIL 2503239 NIL) (-1066 2500619 2500793 2501072 "RRCC-" 2501077 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500062 2500315 2500416 "RPTAST" 2500540 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2473913 2483270 2483337 "RPOLCAT" 2494001 NIL RPOLCAT (NIL T T T) -9 NIL 2497160 NIL) (-1063 2465411 2467751 2470873 "RPOLCAT-" 2470878 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456342 2463622 2464104 "ROUTINE" 2464951 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453140 2455968 2456108 "ROMAN" 2456224 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451384 2452000 2452260 "ROIRC" 2452945 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447616 2449900 2449930 "RNS" 2450234 T RNS (NIL) -9 NIL 2450508 NIL) (-1058 2446125 2446508 2447042 "RNS-" 2447117 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445528 2445936 2445966 "RNG" 2445971 T RNG (NIL) -9 NIL 2445992 NIL) (-1056 2444927 2445315 2445358 "RMODULE" 2445363 NIL RMODULE (NIL T) -9 NIL 2445390 NIL) (-1055 2443763 2443857 2444193 "RMCAT2" 2444828 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440613 2443109 2443406 "RMATRIX" 2443525 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433440 2435700 2435815 "RMATCAT" 2439174 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440156 NIL) (-1052 2432815 2432962 2433269 "RMATCAT-" 2433274 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432216 2432437 2432480 "RLINSET" 2432674 NIL RLINSET (NIL T) -9 NIL 2432765 NIL) (-1050 2431783 2431858 2431986 "RINTERP" 2432135 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2430841 2431395 2431425 "RING" 2431481 T RING (NIL) -9 NIL 2431573 NIL) (-1048 2430633 2430677 2430774 "RING-" 2430779 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429474 2429711 2429969 "RIDIST" 2430397 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420763 2428942 2429148 "RGCHAIN" 2429322 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420113 2420519 2420560 "RGBCSPC" 2420618 NIL RGBCSPC (NIL T) -9 NIL 2420670 NIL) (-1044 2419271 2419652 2419693 "RGBCMDL" 2419925 NIL RGBCMDL (NIL T) -9 NIL 2420039 NIL) (-1043 2416265 2416879 2417549 "RF" 2418635 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2415911 2415974 2416077 "RFFACTOR" 2416196 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415636 2415671 2415768 "RFFACT" 2415870 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413753 2414117 2414499 "RFDIST" 2415276 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413206 2413298 2413461 "RETSOL" 2413655 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2412842 2412922 2412965 "RETRACT" 2413098 NIL RETRACT (NIL T) -9 NIL 2413185 NIL) (-1037 2412691 2412716 2412803 "RETRACT-" 2412808 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412293 2412513 2412583 "RETAST" 2412643 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405031 2411946 2412073 "RESULT" 2412188 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403622 2404300 2404499 "RESRING" 2404934 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403258 2403307 2403405 "RESLATC" 2403559 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2402963 2402998 2403105 "REPSQ" 2403217 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400385 2400965 2401567 "REP" 2402383 T REP (NIL) -7 NIL NIL NIL) (-1030 2400082 2400117 2400228 "REPDB" 2400344 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2393982 2395371 2396594 "REP2" 2398894 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390359 2391040 2391848 "REP1" 2393209 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383055 2388500 2388956 "REGSET" 2389989 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2381820 2382203 2382453 "REF" 2382840 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381197 2381300 2381467 "REDORDER" 2381704 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377165 2380410 2380637 "RECLOS" 2381025 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376217 2376398 2376613 "REALSOLV" 2376972 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376063 2376104 2376134 "REAL" 2376139 T REAL (NIL) -9 NIL 2376174 NIL) (-1021 2372546 2373348 2374232 "REAL0Q" 2375228 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368147 2369135 2370196 "REAL0" 2371527 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367618 2367864 2367958 "RDUCEAST" 2368075 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367023 2367095 2367302 "RDIV" 2367540 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366091 2366265 2366478 "RDIST" 2366845 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364688 2364975 2365347 "RDETRS" 2365799 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362500 2362954 2363492 "RDETR" 2364230 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2361125 2361403 2361800 "RDEEFS" 2362216 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 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1998578 1998690 1998847 "OUTBCON-" 1998852 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1997958 1998307 1998396 "OSI" 1998509 T OSI (NIL) -8 NIL NIL NIL) (-857 1997488 1997826 1997854 "OSGROUP" 1997859 T OSGROUP (NIL) -9 NIL 1997881 NIL) (-856 1996233 1996460 1996745 "ORTHPOL" 1997235 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1993784 1996068 1996189 "OREUP" 1996194 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991187 1993475 1993602 "ORESUP" 1993726 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988715 1989215 1989776 "OREPCTO" 1990676 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982401 1984602 1984643 "OREPCAT" 1986991 NIL OREPCAT (NIL T) -9 NIL 1988095 NIL) (-851 1979548 1980330 1981388 "OREPCAT-" 1981393 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978699 1978997 1979025 "ORDSET" 1979334 T ORDSET (NIL) -9 NIL 1979498 NIL) (-849 1978130 1978278 1978502 "ORDSET-" 1978507 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976695 1977486 1977514 "ORDRING" 1977716 T ORDRING (NIL) -9 NIL 1977841 NIL) (-847 1976340 1976434 1976578 "ORDRING-" 1976583 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975720 1976183 1976211 "ORDMON" 1976216 T ORDMON (NIL) -9 NIL 1976237 NIL) (-845 1974882 1975029 1975224 "ORDFUNS" 1975569 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974220 1974639 1974667 "ORDFIN" 1974732 T ORDFIN (NIL) -9 NIL 1974806 NIL) (-843 1970779 1972806 1973215 "ORDCOMP" 1973844 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1970045 1970172 1970358 "ORDCOMP2" 1970639 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966626 1967536 1968350 "OPTPROB" 1969251 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963428 1964067 1964771 "OPTPACK" 1965942 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961115 1961881 1961909 "OPTCAT" 1962728 T OPTCAT (NIL) -9 NIL 1963378 NIL) (-838 1960499 1960792 1960897 "OPSIG" 1961030 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960267 1960306 1960372 "OPQUERY" 1960453 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957398 1958578 1959082 "OP" 1959796 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1956772 1956998 1957039 "OPERCAT" 1957251 NIL OPERCAT (NIL T) -9 NIL 1957348 NIL) (-834 1956527 1956583 1956700 "OPERCAT-" 1956705 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953340 1955324 1955693 "ONECOMP" 1956191 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952645 1952760 1952934 "ONECOMP2" 1953212 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952064 1952170 1952300 "OMSERVER" 1952535 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1948926 1951504 1951544 "OMSAGG" 1951605 NIL OMSAGG (NIL T) -9 NIL 1951669 NIL) (-829 1947549 1947812 1948094 "OMPKG" 1948664 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1946979 1947082 1947110 "OM" 1947409 T OM (NIL) -9 NIL NIL NIL) (-827 1945526 1946528 1946697 "OMLO" 1946860 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944486 1944633 1944853 "OMEXPR" 1945352 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1943777 1944032 1944168 "OMERR" 1944370 T OMERR (NIL) -8 NIL NIL NIL) (-824 1942928 1943198 1943358 "OMERRK" 1943637 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942379 1942605 1942713 "OMENC" 1942840 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936274 1937459 1938630 "OMDEV" 1941228 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935343 1935514 1935708 "OMCONN" 1936100 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1933864 1934840 1934868 "OINTDOM" 1934873 T OINTDOM (NIL) -9 NIL 1934894 NIL) (-819 1929643 1930854 1931570 "OFMONOID" 1933180 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929054 1929580 1929625 "ODVAR" 1929630 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926477 1928799 1928954 "ODR" 1928959 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919058 1926253 1926379 "ODPOL" 1926384 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1912880 1918930 1919035 "ODP" 1919040 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911646 1911861 1912136 "ODETOOLS" 1912654 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908613 1909271 1909987 "ODESYS" 1910979 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903495 1904403 1905428 "ODERTRIC" 1907688 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1902921 1903003 1903197 "ODERED" 1903407 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1899809 1900357 1901034 "ODERAT" 1902344 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1896766 1897233 1897830 "ODEPRRIC" 1899338 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894709 1895305 1895791 "ODEPROB" 1896300 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891229 1891714 1892361 "ODEPRIM" 1894188 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890478 1890580 1890840 "ODEPAL" 1891121 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886640 1887431 1888295 "ODEPACK" 1889634 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885701 1885808 1886030 "ODEINT" 1886529 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1879802 1881227 1882674 "ODEIFTBL" 1884274 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875200 1875986 1876938 "ODEEF" 1878961 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874549 1874638 1874861 "ODECONST" 1875105 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872674 1873335 1873363 "ODECAT" 1873968 T ODECAT (NIL) -9 NIL 1874499 NIL) (-799 1869546 1872386 1872505 "OCT" 1872587 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869184 1869227 1869354 "OCTCT2" 1869497 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1863833 1866268 1866308 "OC" 1867405 NIL OC (NIL T) -9 NIL 1868263 NIL) (-796 1861060 1861808 1862798 "OC-" 1862892 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860412 1860880 1860908 "OCAMON" 1860913 T OCAMON (NIL) -9 NIL 1860934 NIL) (-794 1859943 1860284 1860312 "OASGP" 1860317 T OASGP (NIL) -9 NIL 1860337 NIL) (-793 1859204 1859693 1859721 "OAMONS" 1859761 T OAMONS (NIL) -9 NIL 1859804 NIL) (-792 1858618 1859051 1859079 "OAMON" 1859084 T OAMON (NIL) -9 NIL 1859104 NIL) (-791 1857876 1858394 1858422 "OAGROUP" 1858427 T OAGROUP (NIL) -9 NIL 1858447 NIL) (-790 1857566 1857616 1857704 "NUMTUBE" 1857820 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851139 1852657 1854193 "NUMQUAD" 1856050 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1846895 1847883 1848908 "NUMODE" 1850134 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844250 1845130 1845158 "NUMINT" 1846081 T NUMINT (NIL) -9 NIL 1846845 NIL) (-786 1843198 1843395 1843613 "NUMFMT" 1844052 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829557 1832502 1835034 "NUMERIC" 1840705 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1823927 1829006 1829101 "NTSCAT" 1829106 NIL NTSCAT (NIL T T T T) -9 NIL 1829145 NIL) (-783 1823121 1823286 1823479 "NTPOLFN" 1823766 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811198 1819946 1820758 "NSUP" 1822342 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1810830 1810887 1810996 "NSUP2" 1811135 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801058 1810604 1810737 "NSMP" 1810742 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799490 1799791 1800148 "NREP" 1800746 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798081 1798333 1798691 "NPCOEF" 1799233 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797147 1797262 1797478 "NORMRETR" 1797962 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795188 1795478 1795887 "NORMPK" 1796855 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1794873 1794901 1795025 "NORMMA" 1795154 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794673 1794830 1794859 "NONE" 1794864 T NONE (NIL) -8 NIL NIL NIL) (-773 1794462 1794491 1794560 "NONE1" 1794637 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1793959 1794021 1794200 "NODE1" 1794394 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792244 1793095 1793350 "NNI" 1793697 T NNI (NIL) -8 NIL NIL 1793932) (-770 1790664 1790977 1791341 "NLINSOL" 1791912 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1786905 1787900 1788799 "NIPROB" 1789785 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785662 1785896 1786198 "NFINTBAS" 1786667 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1784836 1785312 1785353 "NETCLT" 1785525 NIL NETCLT (NIL T) -9 NIL 1785607 NIL) (-766 1783544 1783775 1784056 "NCODIV" 1784604 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783306 1783343 1783418 "NCNTFRAC" 1783501 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781486 1781850 1782270 "NCEP" 1782931 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780337 1781110 1781138 "NASRING" 1781248 T NASRING (NIL) -9 NIL 1781328 NIL) (-762 1780132 1780176 1780270 "NASRING-" 1780275 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779239 1779764 1779792 "NARNG" 1779909 T NARNG (NIL) -9 NIL 1780000 NIL) (-760 1778931 1778998 1779132 "NARNG-" 1779137 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1777810 1778017 1778252 "NAGSP" 1778716 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769082 1770766 1772439 "NAGS" 1776157 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767630 1767938 1768269 "NAGF07" 1768771 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762168 1763459 1764766 "NAGF04" 1766343 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755136 1756750 1758383 "NAGF02" 1760555 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750360 1751460 1752577 "NAGF01" 1754039 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1743988 1745554 1747139 "NAGE04" 1748795 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735157 1737278 1739408 "NAGE02" 1741878 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731110 1732057 1733021 "NAGE01" 1734213 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1728905 1729439 1729997 "NAGD03" 1730572 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720655 1722583 1724537 "NAGD02" 1726971 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714466 1715891 1717331 "NAGD01" 1719235 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710675 1711497 1712334 "NAGC06" 1713649 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709140 1709472 1709828 "NAGC05" 1710339 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708516 1708635 1708779 "NAGC02" 1709016 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707475 1708058 1708098 "NAALG" 1708177 NIL NAALG (NIL T) -9 NIL 1708238 NIL) (-743 1707310 1707339 1707429 "NAALG-" 1707434 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701260 1702368 1703555 "MULTSQFR" 1706206 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700579 1700654 1700838 "MULTFACT" 1701172 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693303 1697216 1697269 "MTSCAT" 1698339 NIL MTSCAT (NIL T T) -9 NIL 1698854 NIL) (-739 1693015 1693069 1693161 "MTHING" 1693243 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1692807 1692840 1692900 "MSYSCMD" 1692975 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1688889 1691562 1691882 "MSET" 1692520 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1685958 1688450 1688491 "MSETAGG" 1688496 NIL MSETAGG (NIL T) -9 NIL 1688530 NIL) (-735 1681799 1683337 1684082 "MRING" 1685258 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681365 1681432 1681563 "MRF2" 1681726 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1680983 1681018 1681162 "MRATFAC" 1681324 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678595 1678890 1679321 "MPRFF" 1680688 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1672892 1678449 1678546 "MPOLY" 1678551 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672382 1672417 1672625 "MPCPF" 1672851 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1671896 1671939 1672123 "MPC3" 1672333 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671091 1671172 1671393 "MPC2" 1671811 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669392 1669729 1670119 "MONOTOOL" 1670751 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668617 1668934 1668962 "MONOID" 1669181 T MONOID (NIL) -9 NIL 1669328 NIL) (-725 1668163 1668282 1668463 "MONOID-" 1668468 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658638 1664589 1664648 "MONOGEN" 1665322 NIL MONOGEN (NIL T T) -9 NIL 1665778 NIL) (-723 1655856 1656591 1657591 "MONOGEN-" 1657710 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654689 1655135 1655163 "MONADWU" 1655555 T MONADWU (NIL) -9 NIL 1655793 NIL) (-721 1654061 1654220 1654468 "MONADWU-" 1654473 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653420 1653664 1653692 "MONAD" 1653899 T MONAD (NIL) -9 NIL 1654011 NIL) (-719 1653105 1653183 1653315 "MONAD-" 1653320 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651394 1652018 1652297 "MOEBIUS" 1652858 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650672 1651076 1651116 "MODULE" 1651121 NIL MODULE (NIL T) -9 NIL 1651160 NIL) (-716 1650240 1650336 1650526 "MODULE-" 1650531 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1647920 1648604 1648931 "MODRING" 1650064 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1644864 1646025 1646546 "MODOP" 1647449 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643452 1643931 1644208 "MODMONOM" 1644727 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633493 1641743 1642157 "MODMON" 1643089 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630649 1632337 1632613 "MODFIELD" 1633368 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629626 1629930 1630120 "MMLFORM" 1630479 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629152 1629195 1629374 "MMAP" 1629577 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627231 1627998 1628039 "MLO" 1628462 NIL MLO (NIL T) -9 NIL 1628704 NIL) (-707 1624597 1625113 1625715 "MLIFT" 1626712 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1623988 1624072 1624226 "MKUCFUNC" 1624508 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623587 1623657 1623780 "MKRECORD" 1623911 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622634 1622796 1623024 "MKFUNC" 1623398 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622022 1622126 1622282 "MKFLCFN" 1622517 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621299 1621401 1621586 "MKBCFUNC" 1621915 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618006 1620853 1620989 "MINT" 1621183 T MINT (NIL) -8 NIL NIL NIL) (-700 1616818 1617061 1617338 "MHROWRED" 1617761 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612197 1615353 1615758 "MFLOAT" 1616433 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611554 1611630 1611801 "MFINFACT" 1612109 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1607869 1608717 1609601 "MESH" 1610690 T MESH (NIL) -7 NIL NIL NIL) (-696 1606259 1606571 1606924 "MDDFACT" 1607556 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603054 1605418 1605459 "MDAGG" 1605714 NIL MDAGG (NIL T) -9 NIL 1605857 NIL) (-694 1592794 1602347 1602554 "MCMPLX" 1602867 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1591935 1592081 1592281 "MCDEN" 1592643 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1589825 1590095 1590475 "MCALCFN" 1591665 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588750 1588990 1589223 "MAYBE" 1589631 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586362 1586885 1587447 "MATSTOR" 1588221 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582319 1585734 1585982 "MATRIX" 1586147 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578083 1578792 1579528 "MATLIN" 1581676 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568189 1571375 1571452 "MATCAT" 1576332 NIL MATCAT (NIL T T T) -9 NIL 1577749 NIL) (-686 1564545 1565566 1566922 "MATCAT-" 1566927 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563139 1563292 1563625 "MATCAT2" 1564380 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561251 1561575 1561959 "MAPPKG3" 1562814 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560232 1560405 1560627 "MAPPKG2" 1561075 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558731 1559015 1559342 "MAPPKG1" 1559938 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1557810 1558137 1558314 "MAPPAST" 1558574 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557421 1557479 1557602 "MAPHACK3" 1557746 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557013 1557074 1557188 "MAPHACK2" 1557353 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556450 1556554 1556696 "MAPHACK1" 1556904 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554529 1555150 1555454 "MAGMA" 1556178 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554008 1554253 1554344 "MACROAST" 1554458 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550426 1552247 1552708 "M3D" 1553580 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544532 1548795 1548836 "LZSTAGG" 1549618 NIL LZSTAGG (NIL T) -9 NIL 1549913 NIL) (-673 1540489 1541663 1543120 "LZSTAGG-" 1543125 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537576 1538380 1538867 "LWORD" 1540034 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537152 1537380 1537455 "LSTAST" 1537521 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530318 1536923 1537057 "LSQM" 1537062 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529542 1529681 1529909 "LSPP" 1530173 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527354 1527655 1528111 "LSMP" 1529231 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524133 1524807 1525537 "LSMP1" 1526656 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518010 1523300 1523341 "LSAGG" 1523403 NIL LSAGG (NIL T) -9 NIL 1523481 NIL) (-665 1514705 1515629 1516842 "LSAGG-" 1516847 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512304 1513849 1514098 "LPOLY" 1514500 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1511886 1511971 1512094 "LPEFRAC" 1512213 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510207 1510980 1511233 "LO" 1511718 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1509859 1509971 1509999 "LOGIC" 1510110 T LOGIC (NIL) -9 NIL 1510191 NIL) (-660 1509721 1509744 1509815 "LOGIC-" 1509820 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1508914 1509054 1509247 "LODOOPS" 1509577 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506337 1508830 1508896 "LODO" 1508901 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1504875 1505110 1505463 "LODOF" 1506084 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501093 1503524 1503565 "LODOCAT" 1504003 NIL LODOCAT (NIL T) -9 NIL 1504214 NIL) (-655 1500826 1500884 1501011 "LODOCAT-" 1501016 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498146 1500667 1500785 "LODO2" 1500790 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495581 1498083 1498128 "LODO1" 1498133 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494462 1494627 1494932 "LODEEF" 1495404 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489701 1492592 1492633 "LNAGG" 1493580 NIL LNAGG (NIL T) -9 NIL 1494024 NIL) (-650 1488848 1489062 1489404 "LNAGG-" 1489409 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1484984 1485773 1486412 "LMOPS" 1488263 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484387 1484775 1484816 "LMODULE" 1484821 NIL LMODULE (NIL T) -9 NIL 1484847 NIL) (-647 1481585 1484032 1484155 "LMDICT" 1484297 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1480991 1481212 1481253 "LLINSET" 1481444 NIL LLINSET (NIL T) -9 NIL 1481535 NIL) (-645 1480690 1480899 1480959 "LITERAL" 1480964 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1473873 1479636 1479934 "LIST" 1480425 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473398 1473472 1473611 "LIST3" 1473793 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472405 1472583 1472811 "LIST2" 1473216 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470539 1470851 1471250 "LIST2MAP" 1472052 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470135 1470372 1470413 "LINSET" 1470418 NIL LINSET (NIL T) -9 NIL 1470452 NIL) (-639 1468796 1469466 1469507 "LINEXP" 1469762 NIL LINEXP (NIL T) -9 NIL 1469911 NIL) (-638 1467443 1467703 1468000 "LINDEP" 1468548 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464210 1464929 1465706 "LIMITRF" 1466698 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462513 1462809 1463218 "LIMITPS" 1463905 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1456941 1462024 1462252 "LIE" 1462334 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1455889 1456358 1456398 "LIECAT" 1456538 NIL LIECAT (NIL T) -9 NIL 1456689 NIL) (-633 1455730 1455757 1455845 "LIECAT-" 1455850 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448226 1455179 1455344 "LIB" 1455585 T LIB (NIL) -8 NIL NIL NIL) (-631 1443861 1444744 1445679 "LGROBP" 1447343 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1441859 1442133 1442483 "LF" 1443582 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440699 1441391 1441419 "LFCAT" 1441626 T LFCAT (NIL) -9 NIL 1441765 NIL) (-628 1437601 1438231 1438919 "LEXTRIPK" 1440063 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434345 1435171 1435674 "LEXP" 1437181 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1433821 1434066 1434158 "LETAST" 1434273 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432219 1432532 1432933 "LEADCDET" 1433503 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431409 1431483 1431712 "LAZM3PK" 1432140 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426326 1429486 1430024 "LAUPOL" 1430921 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1425905 1425949 1426110 "LAPLACE" 1426276 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1423844 1425006 1425257 "LA" 1425738 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1422838 1423422 1423463 "LALG" 1423525 NIL LALG (NIL T) -9 NIL 1423584 NIL) (-619 1422552 1422611 1422747 "LALG-" 1422752 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422387 1422411 1422452 "KVTFROM" 1422514 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421310 1421754 1421939 "KTVLOGIC" 1422222 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421145 1421169 1421210 "KRCFROM" 1421272 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420049 1420236 1420535 "KOVACIC" 1420945 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1419884 1419908 1419949 "KONVERT" 1420011 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419719 1419743 1419784 "KOERCE" 1419846 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417549 1418312 1418689 "KERNEL" 1419375 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417045 1417126 1417258 "KERNEL2" 1417463 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1410815 1415584 1415638 "KDAGG" 1416015 NIL KDAGG (NIL T T) -9 NIL 1416221 NIL) (-609 1410344 1410468 1410673 "KDAGG-" 1410678 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403492 1410005 1410160 "KAFILE" 1410222 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1397920 1403003 1403231 "JORDAN" 1403313 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397299 1397569 1397690 "JOINAST" 1397819 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397145 1397204 1397259 "JAVACODE" 1397264 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393397 1395350 1395404 "IXAGG" 1396333 NIL IXAGG (NIL T T) -9 NIL 1396792 NIL) (-603 1392316 1392622 1393041 "IXAGG-" 1393046 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1387846 1392238 1392297 "IVECTOR" 1392302 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386612 1386849 1387115 "ITUPLE" 1387613 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385114 1385291 1385586 "ITRIGMNP" 1386434 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1383859 1384063 1384346 "ITFUN3" 1384890 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383491 1383548 1383657 "ITFUN2" 1383796 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381293 1382353 1382652 "ITAYLOR" 1383225 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370238 1375430 1376593 "ISUPS" 1380163 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369342 1369482 1369718 "ISUMP" 1370085 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364556 1369143 1369222 "ISTRING" 1369295 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364032 1364277 1364369 "ISAST" 1364484 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363241 1363323 1363539 "IRURPK" 1363946 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362177 1362378 1362618 "IRSN" 1363021 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360248 1360603 1361032 "IRRF2F" 1361815 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1359995 1360033 1360109 "IRREDFFX" 1360204 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358610 1358869 1359168 "IROOT" 1359728 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355214 1356294 1356986 "IR" 1357950 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1352827 1353322 1353888 "IR2" 1354692 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1351927 1352040 1352254 "IR2F" 1352710 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351718 1351752 1351812 "IPRNTPK" 1351887 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348297 1351607 1351676 "IPF" 1351681 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346624 1348222 1348279 "IPADIC" 1348284 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1345936 1346184 1346314 "IP4ADDR" 1346514 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345409 1345640 1345750 "IOMODE" 1345846 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344482 1345006 1345133 "IOBFILE" 1345302 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1343970 1344386 1344414 "IOBCON" 1344419 T IOBCON (NIL) -9 NIL 1344440 NIL) (-577 1343481 1343539 1343722 "INVLAPLA" 1343906 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333129 1335483 1337869 "INTTR" 1341145 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329464 1330206 1331071 "INTTOOLS" 1332314 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329050 1329141 1329258 "INTSLPE" 1329367 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327003 1328973 1329032 "INTRVL" 1329037 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324605 1325117 1325692 "INTRF" 1326488 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324016 1324113 1324255 "INTRET" 1324503 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322013 1322402 1322872 "INTRAT" 1323624 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319276 1319859 1320478 "INTPM" 1321498 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316021 1316620 1317358 "INTPAF" 1318662 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311200 1312162 1313213 "INTPACK" 1314990 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308080 1310929 1311056 "INT" 1311093 T INT (NIL) -8 NIL NIL NIL) (-565 1307332 1307484 1307692 "INTHERTR" 1307922 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1306771 1306851 1307039 "INTHERAL" 1307246 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304617 1305060 1305517 "INTHEORY" 1306334 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296023 1297644 1299416 "INTG0" 1302969 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276596 1281386 1286196 "INTFTBL" 1291233 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1275845 1275983 1276156 "INTFACT" 1276455 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273272 1273718 1274275 "INTEF" 1275399 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271639 1272378 1272406 "INTDOM" 1272707 T INTDOM (NIL) -9 NIL 1272914 NIL) (-557 1271008 1271182 1271424 "INTDOM-" 1271429 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267396 1269324 1269378 "INTCAT" 1270177 NIL INTCAT (NIL T) -9 NIL 1270498 NIL) (-555 1266868 1266971 1267099 "INTBIT" 1267288 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265567 1265721 1266028 "INTALG" 1266713 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265050 1265140 1265297 "INTAF" 1265471 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258393 1264860 1265000 "INTABL" 1265005 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257734 1258200 1258265 "INT8" 1258299 T INT8 (NIL) -8 NIL NIL 1258344) (-550 1257074 1257540 1257605 "INT64" 1257639 T INT64 (NIL) -8 NIL NIL 1257684) (-549 1256414 1256880 1256945 "INT32" 1256979 T INT32 (NIL) -8 NIL NIL 1257024) (-548 1255754 1256220 1256285 "INT16" 1256319 T INT16 (NIL) -8 NIL NIL 1256364) (-547 1250664 1253377 1253405 "INS" 1254339 T INS (NIL) -9 NIL 1255004 NIL) (-546 1247904 1248675 1249649 "INS-" 1249722 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246679 1246906 1247204 "INPSIGN" 1247657 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1245797 1245914 1246111 "INPRODPF" 1246559 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244691 1244808 1245045 "INPRODFF" 1245677 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243691 1243843 1244103 "INNMFACT" 1244527 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1242888 1242985 1243173 "INMODGCD" 1243590 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241396 1241641 1241965 "INFSP" 1242633 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240580 1240697 1240880 "INFPROD0" 1241276 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237435 1238645 1239160 "INFORM" 1240073 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237045 1237105 1237203 "INFORM1" 1237370 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236568 1236657 1236771 "INFINITY" 1236951 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235744 1236288 1236389 "INETCLTS" 1236487 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234360 1234610 1234931 "INEP" 1235492 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233609 1234257 1234322 "INDE" 1234327 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233173 1233241 1233358 "INCRMAPS" 1233536 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1231991 1232442 1232648 "INBFILE" 1232987 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227290 1228227 1229171 "INBFF" 1231079 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226198 1226467 1226495 "INBCON" 1227008 T INBCON (NIL) -9 NIL 1227274 NIL) (-528 1225450 1225673 1225949 "INBCON-" 1225954 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1224929 1225174 1225265 "INAST" 1225379 T INAST (NIL) -8 NIL NIL NIL) (-526 1224356 1224608 1224714 "IMPTAST" 1224843 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1220802 1224200 1224304 "IMATRIX" 1224309 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219514 1219637 1219952 "IMATQF" 1220658 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217734 1217961 1218298 "IMATLIN" 1219270 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212312 1217658 1217716 "ILIST" 1217721 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210217 1212172 1212285 "IIARRAY2" 1212290 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205615 1210128 1210192 "IFF" 1210197 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1204962 1205232 1205348 "IFAST" 1205519 T IFAST (NIL) -8 NIL NIL NIL) (-518 1199957 1204254 1204442 "IFARRAY" 1204819 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199137 1199861 1199934 "IFAMON" 1199939 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198721 1198786 1198840 "IEVALAB" 1199047 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198396 1198464 1198624 "IEVALAB-" 1198629 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198027 1198310 1198373 "IDPO" 1198378 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197277 1197916 1197991 "IDPOAMS" 1197996 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196584 1197166 1197241 "IDPOAM" 1197246 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195643 1195919 1195972 "IDPC" 1196385 NIL IDPC (NIL T T) -9 NIL 1196534 NIL) (-510 1195112 1195535 1195608 "IDPAM" 1195613 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194488 1195004 1195077 "IDPAG" 1195082 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194133 1194324 1194399 "IDENT" 1194433 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190388 1191236 1192131 "IDECOMP" 1193290 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183226 1184311 1185358 "IDEAL" 1189424 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182390 1182502 1182701 "ICDEN" 1183110 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181461 1181870 1182017 "ICARD" 1182263 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179521 1179834 1180239 "IBPTOOLS" 1181138 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175128 1179141 1179254 "IBITS" 1179440 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1171851 1172427 1173122 "IBATOOL" 1174545 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169630 1170092 1170625 "IBACHIN" 1171386 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167459 1169476 1169579 "IARRAY2" 1169584 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163565 1167385 1167442 "IARRAY1" 1167447 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157674 1161977 1162458 "IAN" 1163104 T IAN (NIL) -8 NIL NIL NIL) (-496 1157185 1157242 1157415 "IALGFACT" 1157611 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156713 1156826 1156854 "HYPCAT" 1157061 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156251 1156368 1156554 "HYPCAT-" 1156559 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1155846 1156046 1156129 "HOSTNAME" 1156188 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155691 1155728 1155769 "HOMOTOP" 1155774 NIL HOMOTOP (NIL T) -9 NIL 1155807 NIL) (-491 1152323 1153701 1153742 "HOAGG" 1154723 NIL HOAGG (NIL T) -9 NIL 1155402 NIL) (-490 1150917 1151316 1151842 "HOAGG-" 1151847 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1144921 1150512 1150661 "HEXADEC" 1150788 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143668 1143891 1144154 "HEUGCD" 1144698 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142744 1143505 1143635 "HELLFDIV" 1143640 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1140923 1142521 1142609 "HEAP" 1142688 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140186 1140475 1140609 "HEADAST" 1140809 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134052 1140101 1140163 "HDP" 1140168 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128040 1133687 1133839 "HDMP" 1133953 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127364 1127504 1127668 "HB" 1127896 T HB (NIL) -7 NIL NIL NIL) (-481 1120750 1127210 1127314 "HASHTBL" 1127319 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120226 1120471 1120563 "HASAST" 1120678 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118004 1119848 1120030 "HACKPI" 1120064 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113672 1117857 1117970 "GTSET" 1117975 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107087 1113550 1113648 "GSTBL" 1113653 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099365 1106118 1106383 "GSERIES" 1106878 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098506 1098923 1098951 "GROUP" 1099154 T GROUP (NIL) -9 NIL 1099288 NIL) (-474 1097872 1098031 1098282 "GROUP-" 1098287 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096239 1096560 1096947 "GROEBSOL" 1097549 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095153 1095441 1095492 "GRMOD" 1096021 NIL GRMOD (NIL T T) -9 NIL 1096189 NIL) (-471 1094921 1094957 1095085 "GRMOD-" 1095090 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090211 1091275 1092275 "GRIMAGE" 1093941 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088677 1088938 1089262 "GRDEF" 1089907 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088121 1088237 1088378 "GRAY" 1088556 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087308 1087714 1087765 "GRALG" 1087918 NIL GRALG (NIL T T) -9 NIL 1088011 NIL) (-466 1086969 1087042 1087205 "GRALG-" 1087210 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083746 1086554 1086732 "GPOLSET" 1086876 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083100 1083157 1083415 "GOSPER" 1083683 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1078832 1079538 1080064 "GMODPOL" 1082799 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1077837 1078021 1078259 "GHENSEL" 1078644 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1071993 1072836 1073856 "GENUPS" 1076921 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071690 1071741 1071830 "GENUFACT" 1071936 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071102 1071179 1071344 "GENPGCD" 1071608 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070576 1070611 1070824 "GENMFACT" 1071061 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069142 1069399 1069706 "GENEEZ" 1070319 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063288 1068753 1068915 "GDMP" 1069065 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052630 1057059 1058165 "GCNAALG" 1062271 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1050957 1051819 1051847 "GCDDOM" 1052102 T GCDDOM (NIL) -9 NIL 1052259 NIL) (-453 1050427 1050554 1050769 "GCDDOM-" 1050774 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049099 1049284 1049588 "GB" 1050206 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037715 1040045 1042437 "GBINTERN" 1046790 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035552 1035844 1036265 "GBF" 1037390 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034333 1034498 1034765 "GBEUCLID" 1035368 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033682 1033807 1033956 "GAUSSFAC" 1034204 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032049 1032351 1032665 "GALUTIL" 1033401 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030357 1030631 1030955 "GALPOLYU" 1031776 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027722 1028012 1028419 "GALFACTU" 1030054 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019527 1021027 1022635 "GALFACT" 1026154 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1016915 1017573 1017601 "FVFUN" 1018757 T FVFUN (NIL) -9 NIL 1019477 NIL) (-442 1016181 1016363 1016391 "FVC" 1016682 T FVC (NIL) -9 NIL 1016865 NIL) (-441 1015824 1016006 1016074 "FUNDESC" 1016133 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015439 1015621 1015702 "FUNCTION" 1015776 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013183 1013761 1014227 "FT" 1014993 T FT (NIL) -8 NIL NIL NIL) (-438 1011974 1012484 1012687 "FTEM" 1013000 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010265 1010554 1010951 "FSUPFACT" 1011665 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008662 1008951 1009283 "FST" 1009953 T FST (NIL) -8 NIL NIL NIL) (-435 1007861 1007967 1008155 "FSRED" 1008544 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006560 1006816 1007163 "FSPRMELT" 1007576 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1003866 1004304 1004790 "FSPECF" 1006123 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985504 993835 993876 "FS" 997760 NIL FS (NIL T) -9 NIL 1000049 NIL) (-431 974147 977140 981197 "FS-" 981497 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973675 973729 973899 "FSINT" 974088 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 971967 972668 972971 "FSERIES" 973454 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971009 971125 971349 "FSCINT" 971847 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967217 969953 969994 "FSAGG" 970364 NIL FSAGG (NIL T) -9 NIL 970623 NIL) (-426 964979 965580 966376 "FSAGG-" 966471 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964021 964164 964391 "FSAGG2" 964832 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961703 961983 962530 "FS2UPS" 963739 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961337 961380 961509 "FS2" 961654 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960215 960386 960688 "FS2EXPXP" 961162 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959641 959756 959908 "FRUTIL" 960095 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951054 955136 956494 "FR" 958315 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946023 948697 948737 "FRNAALG" 950133 NIL FRNAALG (NIL T) -9 NIL 950740 NIL) (-418 941696 942772 944047 "FRNAALG-" 944797 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941334 941377 941504 "FRNAAF2" 941647 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939714 940188 940483 "FRMOD" 941146 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937465 938097 938414 "FRIDEAL" 939505 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936660 936747 937036 "FRIDEAL2" 937372 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935793 936207 936248 "FRETRCT" 936253 NIL FRETRCT (NIL T) -9 NIL 936429 NIL) (-412 934905 935136 935487 "FRETRCT-" 935492 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 931993 933203 933262 "FRAMALG" 934144 NIL FRAMALG (NIL T T) -9 NIL 934436 NIL) (-410 930127 930582 931212 "FRAMALG-" 931435 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924048 929602 929878 "FRAC" 929883 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923684 923741 923848 "FRAC2" 923985 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923320 923377 923484 "FR2" 923621 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 917833 920726 920754 "FPS" 921873 T FPS (NIL) -9 NIL 922430 NIL) (-405 917282 917391 917555 "FPS-" 917701 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914584 916253 916281 "FPC" 916506 T FPC (NIL) -9 NIL 916648 NIL) (-403 914377 914417 914514 "FPC-" 914519 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913167 913865 913906 "FPATMAB" 913911 NIL FPATMAB (NIL T) -9 NIL 914063 NIL) (-401 910840 911343 911769 "FPARFRAC" 912804 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906233 906732 907414 "FORTRAN" 910272 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 903949 904449 904988 "FORT" 905714 T FORT (NIL) -7 NIL NIL NIL) (-398 901625 902187 902215 "FORTFN" 903275 T FORTFN (NIL) -9 NIL 903899 NIL) (-397 901389 901439 901467 "FORTCAT" 901526 T FORTCAT (NIL) -9 NIL 901588 NIL) (-396 899495 900005 900395 "FORMULA" 901019 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899283 899313 899382 "FORMULA1" 899459 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 898806 898858 899031 "FORDER" 899225 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 897902 898066 898259 "FOP" 898633 T FOP (NIL) -7 NIL NIL NIL) (-392 896483 897182 897356 "FNLA" 897784 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895212 895627 895655 "FNCAT" 896115 T FNCAT (NIL) -9 NIL 896375 NIL) (-390 894751 895171 895199 "FNAME" 895204 T FNAME (NIL) -8 NIL NIL NIL) (-389 893314 894277 894305 "FMTC" 894310 T FMTC (NIL) -9 NIL 894346 NIL) (-388 889647 890837 891466 "FMONOID" 892718 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 888839 889389 889538 "FM" 889543 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886263 886909 886937 "FMFUN" 888081 T FMFUN (NIL) -9 NIL 888789 NIL) (-385 885532 885713 885741 "FMC" 886031 T FMC (NIL) -9 NIL 886213 NIL) (-384 882611 883471 883525 "FMCAT" 884720 NIL FMCAT (NIL T T) -9 NIL 885215 NIL) (-383 881477 882377 882477 "FM1" 882556 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879251 879667 880161 "FLOATRP" 881028 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872826 876980 877601 "FLOAT" 878650 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870264 870764 871342 "FLOATCP" 872293 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869004 869842 869883 "FLINEXP" 869888 NIL FLINEXP (NIL T) -9 NIL 869981 NIL) (-378 868158 868393 868721 "FLINEXP-" 868726 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867234 867378 867602 "FLASORT" 868010 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864350 865218 865270 "FLALG" 866497 NIL FLALG (NIL T T) -9 NIL 866964 NIL) (-375 858086 861836 861877 "FLAGG" 863139 NIL FLAGG (NIL T) -9 NIL 863791 NIL) (-374 856812 857151 857641 "FLAGG-" 857646 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855854 855997 856224 "FLAGG2" 856665 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852705 853713 853772 "FINRALG" 854900 NIL FINRALG (NIL T T) -9 NIL 855408 NIL) (-371 851865 852094 852433 "FINRALG-" 852438 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851245 851484 851512 "FINITE" 851708 T FINITE (NIL) -9 NIL 851815 NIL) (-369 843602 845789 845829 "FINAALG" 849496 NIL FINAALG (NIL T) -9 NIL 850949 NIL) (-368 838934 839984 841128 "FINAALG-" 842507 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838302 838689 838792 "FILE" 838864 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 836960 837298 837352 "FILECAT" 838036 NIL FILECAT (NIL T T) -9 NIL 838252 NIL) (-365 834676 836204 836232 "FIELD" 836272 T FIELD (NIL) -9 NIL 836352 NIL) (-364 833296 833681 834192 "FIELD-" 834197 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831146 831931 832278 "FGROUP" 832982 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830236 830400 830620 "FGLMICPK" 830978 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826068 830161 830218 "FFX" 830223 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825669 825730 825865 "FFSLPE" 826001 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821658 822441 823237 "FFPOLY" 824905 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821162 821198 821407 "FFPOLY2" 821616 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817005 821081 821144 "FFP" 821149 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812403 816916 816980 "FF" 816985 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807529 811746 811936 "FFNBX" 812257 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802458 806664 806922 "FFNBP" 807383 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797091 801742 801953 "FFNB" 802291 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795923 796121 796436 "FFINTBAS" 796888 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 791992 794212 794240 "FFIELDC" 794860 T FFIELDC (NIL) -9 NIL 795236 NIL) (-350 790654 791025 791522 "FFIELDC-" 791527 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790223 790269 790393 "FFHOM" 790596 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787918 788405 788922 "FFF" 789738 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783536 787660 787761 "FFCGX" 787861 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779157 783268 783375 "FFCGP" 783479 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774340 778884 778992 "FFCG" 779093 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755736 764817 764903 "FFCAT" 770068 NIL FFCAT (NIL T T T) -9 NIL 771519 NIL) (-343 750934 751981 753295 "FFCAT-" 754525 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750345 750388 750623 "FFCAT2" 750885 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739666 743317 744537 "FEXPR" 749197 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738666 739101 739142 "FEVALAB" 739226 NIL FEVALAB (NIL T) -9 NIL 739487 NIL) (-339 737825 738035 738373 "FEVALAB-" 738378 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736391 737208 737411 "FDIV" 737724 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733411 734152 734267 "FDIVCAT" 735835 NIL FDIVCAT (NIL T T T T) -9 NIL 736272 NIL) (-336 733173 733200 733370 "FDIVCAT-" 733375 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732393 732480 732757 "FDIV2" 733080 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731367 731688 731890 "FCTRDATA" 732211 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730053 730312 730601 "FCPAK1" 731098 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729152 729553 729694 "FCOMP" 729944 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712854 716302 719840 "FC" 725634 T FC (NIL) -8 NIL NIL NIL) (-330 705217 709245 709285 "FAXF" 711087 NIL FAXF (NIL T) -9 NIL 711779 NIL) (-329 702493 703151 703976 "FAXF-" 704441 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697545 701869 702045 "FARRAY" 702350 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692439 694506 694559 "FAMR" 695582 NIL FAMR (NIL T T) -9 NIL 696042 NIL) (-326 691329 691631 692066 "FAMR-" 692071 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690498 691251 691304 "FAMONOID" 691309 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688284 688994 689047 "FAMONC" 689988 NIL FAMONC (NIL T T) -9 NIL 690374 NIL) (-323 686948 688038 688175 "FAGROUP" 688180 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684743 685062 685465 "FACUTIL" 686629 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683842 684027 684249 "FACTFUNC" 684553 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676264 683145 683344 "EXPUPXS" 683698 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673747 674287 674873 "EXPRTUBE" 675698 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670018 670610 671340 "EXPRODE" 673086 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655503 668667 669096 "EXPR" 669622 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650057 650644 651450 "EXPR2UPS" 654801 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649689 649746 649855 "EXPR2" 649994 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641079 648842 649132 "EXPEXPAN" 649526 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640879 641036 641065 "EXIT" 641070 T EXIT (NIL) -8 NIL NIL NIL) (-312 640359 640603 640694 "EXITAST" 640808 T EXITAST (NIL) -8 NIL NIL NIL) (-311 639986 640048 640161 "EVALCYC" 640291 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639527 639645 639686 "EVALAB" 639856 NIL EVALAB (NIL T) -9 NIL 639960 NIL) (-309 639008 639130 639351 "EVALAB-" 639356 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636376 637678 637706 "EUCDOM" 638261 T EUCDOM (NIL) -9 NIL 638611 NIL) (-307 634781 635223 635813 "EUCDOM-" 635818 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622319 625079 627829 "ESTOOLS" 632051 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 621951 622008 622117 "ESTOOLS2" 622256 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621702 621744 621824 "ESTOOLS1" 621903 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615739 617347 617375 "ES" 620143 T ES (NIL) -9 NIL 621553 NIL) (-302 610686 611973 613790 "ES-" 613954 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607060 607821 608601 "ESCONT" 609926 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606805 606837 606919 "ESCONT1" 607022 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606480 606530 606630 "ES2" 606749 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606110 606168 606277 "ES1" 606416 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605326 605455 605631 "ERROR" 605954 T ERROR (NIL) -7 NIL NIL NIL) (-296 598718 605185 605276 "EQTBL" 605281 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591221 594032 595481 "EQ" 597302 NIL -2071 (NIL T) -8 NIL NIL NIL) (-294 590853 590910 591019 "EQ2" 591158 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586142 587191 588284 "EP" 589792 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584742 585033 585339 "ENV" 585856 T ENV (NIL) -8 NIL NIL NIL) (-291 583836 584390 584418 "ENTIRER" 584423 T ENTIRER (NIL) -9 NIL 584469 NIL) (-290 580303 581791 582161 "EMR" 583635 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579447 579632 579686 "ELTAGG" 580066 NIL ELTAGG (NIL T T) -9 NIL 580277 NIL) (-288 579166 579228 579369 "ELTAGG-" 579374 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 578955 578984 579038 "ELTAB" 579122 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578081 578227 578426 "ELFUTS" 578806 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577823 577879 577907 "ELEMFUN" 578012 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577693 577714 577782 "ELEMFUN-" 577787 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572537 575793 575834 "ELAGG" 576774 NIL ELAGG (NIL T) -9 NIL 577237 NIL) (-282 570822 571256 571919 "ELAGG-" 571924 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569483 569762 570056 "ELABEXPR" 570548 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562347 564150 564977 "EFUPXS" 568759 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555797 557598 558408 "EFULS" 561623 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553282 553640 554112 "EFSTRUC" 555429 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543073 544639 546187 "EF" 551797 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542147 542558 542707 "EAB" 542944 T EAB (NIL) -8 NIL NIL NIL) (-275 541329 542106 542134 "E04UCFA" 542139 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540511 541288 541316 "E04NAFA" 541321 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539693 540470 540498 "E04MBFA" 540503 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538875 539652 539680 "E04JAFA" 539685 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538059 538834 538862 "E04GCFA" 538867 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537243 538018 538046 "E04FDFA" 538051 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536425 537202 537230 "E04DGFA" 537235 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530598 531950 533314 "E04AGNT" 535081 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529278 529784 529824 "DVARCAT" 530299 NIL DVARCAT (NIL T) -9 NIL 530498 NIL) (-266 528482 528694 529008 "DVARCAT-" 529013 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521619 528281 528410 "DSMP" 528415 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516400 517564 518632 "DROPT" 520571 T DROPT (NIL) -8 NIL NIL NIL) (-263 516065 516124 516222 "DROPT1" 516335 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511180 512306 513443 "DROPT0" 514948 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509525 509850 510236 "DRAWPT" 510814 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504112 505035 506114 "DRAW" 508499 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503745 503798 503916 "DRAWHACK" 504053 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502476 502745 503036 "DRAWCX" 503474 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 501991 502060 502211 "DRAWCURV" 502402 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492459 494421 496536 "DRAWCFUN" 499896 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489225 491154 491195 "DQAGG" 491824 NIL DQAGG (NIL T) -9 NIL 492097 NIL) (-254 477349 483818 483901 "DPOLCAT" 485753 NIL DPOLCAT (NIL T T T T) -9 NIL 486298 NIL) (-253 472185 473534 475492 "DPOLCAT-" 475497 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465307 472046 472144 "DPMO" 472149 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458332 465087 465254 "DPMM" 465259 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457810 458024 458122 "DOMTMPLT" 458254 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457243 457612 457692 "DOMCTOR" 457750 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456455 456723 456874 "DOMAIN" 457112 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450443 456090 456242 "DMP" 456356 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450043 450099 450243 "DLP" 450381 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443865 449370 449560 "DLIST" 449885 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440662 442718 442759 "DLAGG" 443309 NIL DLAGG (NIL T) -9 NIL 443539 NIL) (-243 439338 440002 440030 "DIVRING" 440122 T DIVRING (NIL) -9 NIL 440205 NIL) (-242 438575 438765 439065 "DIVRING-" 439070 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436677 437034 437440 "DISPLAY" 438189 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430565 436591 436654 "DIRPROD" 436659 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429413 429616 429881 "DIRPROD2" 430358 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418188 424194 424247 "DIRPCAT" 424657 NIL DIRPCAT (NIL NIL T) -9 NIL 425497 NIL) (-237 415514 416156 417037 "DIRPCAT-" 417374 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414801 414961 415147 "DIOSP" 415348 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411456 413713 413754 "DIOPS" 414188 NIL DIOPS (NIL T) -9 NIL 414417 NIL) (-234 411005 411119 411310 "DIOPS-" 411315 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409828 410456 410484 "DIFRING" 410671 T DIFRING (NIL) -9 NIL 410781 NIL) (-232 409474 409551 409703 "DIFRING-" 409708 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407210 408482 408523 "DIFEXT" 408886 NIL DIFEXT (NIL T) -9 NIL 409180 NIL) (-230 405495 405923 406589 "DIFEXT-" 406594 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402770 405027 405068 "DIAGG" 405073 NIL DIAGG (NIL T) -9 NIL 405093 NIL) (-228 402154 402311 402563 "DIAGG-" 402568 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397571 401113 401390 "DHMATRIX" 401923 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393183 394092 395102 "DFSFUN" 396581 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388261 392114 392426 "DFLOAT" 392891 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386524 386805 387194 "DFINTTLS" 387969 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383553 384545 384945 "DERHAM" 386190 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381354 383328 383417 "DEQUEUE" 383497 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380608 380741 380924 "DEGRED" 381216 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377038 377783 378629 "DEFINTRF" 379836 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374593 375062 375654 "DEFINTEF" 376557 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373943 374213 374328 "DEFAST" 374498 T DEFAST (NIL) -8 NIL NIL NIL) (-217 367947 373538 373687 "DECIMAL" 373814 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365459 365917 366423 "DDFACT" 367491 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365055 365098 365249 "DBLRESP" 365410 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362927 363288 363648 "DBASE" 364822 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362169 362407 362553 "DATAARY" 362826 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361275 362128 362156 "D03FAFA" 362161 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360382 361234 361262 "D03EEFA" 361267 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358332 358798 359287 "D03AGNT" 359913 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357621 358291 358319 "D02EJFA" 358324 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356910 357580 357608 "D02CJFA" 357613 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356199 356869 356897 "D02BHFA" 356902 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355488 356158 356186 "D02BBFA" 356191 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348685 350274 351880 "D02AGNT" 353902 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346453 346976 347522 "D01WGTS" 348159 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345520 346412 346440 "D01TRNS" 346445 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344588 345479 345507 "D01GBFA" 345512 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343656 344547 344575 "D01FCFA" 344580 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342724 343615 343643 "D01ASFA" 343648 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341792 342683 342711 "D01AQFA" 342716 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340860 341751 341779 "D01APFA" 341784 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339928 340819 340847 "D01ANFA" 340852 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 338996 339887 339915 "D01AMFA" 339920 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338064 338955 338983 "D01ALFA" 338988 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337132 338023 338051 "D01AKFA" 338056 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336200 337091 337119 "D01AJFA" 337124 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329495 331048 332609 "D01AGNT" 334659 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328832 328960 329112 "CYCLOTOM" 329363 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325566 326280 327007 "CYCLES" 328125 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324878 325012 325183 "CVMP" 325427 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322719 322977 323346 "CTRIGMNP" 324606 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322155 322513 322586 "CTOR" 322666 T CTOR (NIL) -8 NIL NIL NIL) (-186 321664 321886 321987 "CTORKIND" 322074 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320955 321271 321299 "CTORCAT" 321481 T CTORCAT (NIL) -9 NIL 321594 NIL) (-184 320553 320664 320823 "CTORCAT-" 320828 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320015 320227 320335 "CTORCALL" 320477 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319389 319488 319641 "CSTTOOLS" 319912 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315188 315845 316603 "CRFP" 318701 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314663 314909 315001 "CRCEAST" 315116 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313710 313895 314123 "CRAPACK" 314467 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313094 313195 313399 "CPMATCH" 313586 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312819 312847 312953 "CPIMA" 313060 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309167 309839 310558 "COORDSYS" 312154 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308579 308700 308842 "CONTOUR" 309045 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304470 306582 307074 "CONTFRAC" 308119 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304350 304371 304399 "CONDUIT" 304436 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303438 303992 304020 "COMRING" 304025 T COMRING (NIL) -9 NIL 304077 NIL) (-171 302492 302796 302980 "COMPPROP" 303274 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302153 302188 302316 "COMPLPAT" 302451 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292444 301962 302071 "COMPLEX" 302076 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292080 292137 292244 "COMPLEX2" 292381 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291798 291833 291931 "COMPFACT" 292039 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275878 285872 285912 "COMPCAT" 286916 NIL COMPCAT (NIL T) -9 NIL 288264 NIL) (-165 265390 268317 271944 "COMPCAT-" 272300 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265119 265147 265250 "COMMUPC" 265356 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264913 264947 265006 "COMMONOP" 265080 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264469 264664 264751 "COMM" 264846 T COMM (NIL) -8 NIL NIL NIL) (-161 264045 264273 264348 "COMMAAST" 264414 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263294 263488 263516 "COMBOPC" 263854 T COMBOPC (NIL) -9 NIL 264029 NIL) (-159 262190 262400 262642 "COMBINAT" 263084 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258647 259221 259848 "COMBF" 261612 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257405 257763 257998 "COLOR" 258432 T COLOR (NIL) -8 NIL NIL NIL) (-156 256881 257126 257218 "COLONAST" 257333 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256521 256568 256693 "CMPLXRT" 256828 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255969 256221 256320 "CLLCTAST" 256442 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251467 252499 253579 "CLIP" 254909 T CLIP (NIL) -7 NIL NIL NIL) (-152 249813 250573 250812 "CLIF" 251294 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245988 247959 248000 "CLAGG" 248929 NIL CLAGG (NIL T) -9 NIL 249465 NIL) (-150 244410 244867 245450 "CLAGG-" 245455 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243954 244039 244179 "CINTSLPE" 244319 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241455 241926 242474 "CHVAR" 243482 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240629 241183 241211 "CHARZ" 241216 T CHARZ (NIL) -9 NIL 241231 NIL) (-146 240383 240423 240501 "CHARPOL" 240583 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239441 240028 240056 "CHARNZ" 240103 T CHARNZ (NIL) -9 NIL 240159 NIL) (-144 237407 238131 238466 "CHAR" 239126 T CHAR (NIL) -8 NIL NIL NIL) (-143 237133 237194 237222 "CFCAT" 237333 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236378 236489 236671 "CDEN" 237017 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232343 235531 235811 "CCLASS" 236118 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231594 231751 231928 "CATEGORY" 232186 T -10 (NIL) -8 NIL NIL NIL) (-139 231167 231513 231561 "CATCTOR" 231566 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230618 230870 230968 "CATAST" 231089 T CATAST (NIL) -8 NIL NIL NIL) (-137 230094 230339 230431 "CASEAST" 230546 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225103 226123 226876 "CARTEN" 229397 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224211 224359 224580 "CARTEN2" 224950 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222527 223361 223618 "CARD" 223974 T CARD (NIL) -8 NIL NIL NIL) (-133 222103 222331 222406 "CAPSLAST" 222472 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221607 221815 221843 "CACHSET" 221975 T CACHSET (NIL) -9 NIL 222053 NIL) (-131 221077 221399 221427 "CABMON" 221477 T CABMON (NIL) -9 NIL 221533 NIL) (-130 220550 220781 220891 "BYTEORD" 220987 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220084 220226 "BYTE" 220389 T BYTE (NIL) -8 NIL NIL 220511) (-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 diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 3f082283..abe4412c 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,5 +1,11 @@ -(732220 . 3453990497) +(732279 . 3454219024) +(((*1 *2 *1) + (-12 (-4 *4 (-1099)) (-5 *2 (-889 *3 *5)) (-5 *1 (-885 *3 *4 *5)) + (-4 *3 (-1099)) (-4 *5 (-666 *4))))) +(((*1 *2 *3 *3 *3 *4 *4 *3) + (-12 (-5 *3 (-566)) (-5 *4 (-689 (-225))) (-5 *2 (-1035)) + (-5 *1 (-755))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) (-4 *2 (-1214)))) ((*1 *1 *1) (-12 (-5 *1 (-672 *2)) (-4 *2 (-850)))) ((*1 *1 *1) (-12 (-5 *1 (-677 *2)) (-4 *2 (-850)))) @@ -8,6 +14,9 @@ ((*1 *2 *1) (-12 (-4 *2 (-13 (-848) (-365))) (-5 *1 (-1060 *2 *3)) (-4 *3 (-1240 *2))))) +(((*1 *2 *1) + (-12 (-5 *2 (-171)) (-5 *1 (-1163 *3 *4)) (-14 *3 (-921)) + (-4 *4 (-1049))))) (((*1 *2 *1 *3 *3 *2) (-12 (-5 *3 (-566)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1214)) (-4 *4 (-375 *2)) (-4 *5 (-375 *2)))) @@ -39,14 +48,14 @@ (-12 (-5 *3 (-1175)) (-5 *2 (-245 (-1157))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-850) - (-10 -8 (-15 -4393 ((-1157) $ *3)) (-15 -1736 ((-1269) $)) - (-15 -3018 ((-1269) $))))))) + (-10 -8 (-15 -4390 ((-1157) $ *3)) (-15 -1675 ((-1269) $)) + (-15 -3997 ((-1269) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-989)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-850) - (-10 -8 (-15 -4393 ((-1157) $ (-1175))) (-15 -1736 ((-1269) $)) - (-15 -3018 ((-1269) $))))))) + (-10 -8 (-15 -4390 ((-1157) $ (-1175))) (-15 -1675 ((-1269) $)) + (-15 -3997 ((-1269) $))))))) ((*1 *2 *1 *3) (-12 (-5 *3 "count") (-5 *2 (-771)) (-5 *1 (-245 *4)) (-4 *4 (-850)))) ((*1 *1 *1 *2) (-12 (-5 *2 "sort") (-5 *1 (-245 *3)) (-4 *3 (-850)))) @@ -133,54 +142,68 @@ (-12 (-5 *2 "rest") (-4 *1 (-1252 *3)) (-4 *3 (-1214)))) ((*1 *2 *1 *3) (-12 (-5 *3 "first") (-4 *1 (-1252 *2)) (-4 *2 (-1214))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-597 *3)) (-4 *3 (-1049)))) - ((*1 *2 *1) - (-12 (-4 *1 (-973 *3 *4 *5)) (-4 *3 (-1049)) (-4 *4 (-792)) - (-4 *5 (-850)) (-5 *2 (-112))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-771)) (-5 *3 (-943 *4)) (-4 *1 (-1133 *4)) + (-4 *4 (-1049)))) + ((*1 *2 *1 *3 *4) + (-12 (-5 *3 (-771)) (-5 *4 (-943 (-225))) (-5 *2 (-1269)) + (-5 *1 (-1266))))) +(((*1 *1 *1 *1 *2) + (-12 (-4 *1 (-1064 *3 *4 *2)) (-4 *3 (-1049)) (-4 *4 (-793)) + (-4 *2 (-850)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1064 *2 *3 *4)) (-4 *2 (-1049)) (-4 *3 (-793)) + (-4 *4 (-850))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1264 *4)) (-4 *4 (-639 (-566))) - (-5 *2 (-1264 (-409 (-566)))) (-5 *1 (-1291 *4))))) -(((*1 *2 *2 *3 *4) - (-12 (-5 *3 (-644 (-612 *2))) (-5 *4 (-644 (-1175))) - (-4 *2 (-13 (-432 (-169 *5)) (-1002) (-1199))) (-4 *5 (-558)) - (-5 *1 (-600 *5 *6 *2)) (-4 *6 (-13 (-432 *5) (-1002) (-1199)))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-1 *7 *7)) (-5 *5 (-644 (-409 *7))) - (-4 *7 (-1240 *6)) (-5 *3 (-409 *7)) (-4 *6 (-365)) - (-5 *2 - (-2 (|:| |mainpart| *3) - (|:| |limitedlogs| - (-644 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) - (-5 *1 (-576 *6 *7))))) -(((*1 *2 *2) - (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) - (-4 *2 (-13 (-432 *3) (-1002)))))) + (-12 (-5 *3 (-225)) (-5 *4 (-566)) (-5 *2 (-1035)) (-5 *1 (-758))))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-771)) (-4 *1 (-740 *4 *5)) (-4 *4 (-1049)) + (-4 *5 (-850)) (-5 *2 (-952 *4)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-771)) (-4 *1 (-740 *4 *5)) (-4 *4 (-1049)) + (-4 *5 (-850)) (-5 *2 (-952 *4)))) + ((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-771)) (-4 *1 (-1255 *4)) (-4 *4 (-1049)) + (-5 *2 (-952 *4)))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-771)) (-4 *1 (-1255 *4)) (-4 *4 (-1049)) + (-5 *2 (-952 *4))))) +(((*1 *2 *3 *3 *3 *4 *3 *5 *5 *3) + (-12 (-5 *3 (-566)) (-5 *5 (-689 (-225))) (-5 *4 (-225)) + (-5 *2 (-1035)) (-5 *1 (-756))))) +(((*1 *2 *1) (-12 (-5 *2 (-644 (-183 (-139)))) (-5 *1 (-140))))) (((*1 *2 *3) - (-12 (-5 *3 (-644 *2)) (-4 *2 (-432 *4)) (-5 *1 (-158 *4 *2)) - (-4 *4 (-558))))) -(((*1 *2) (-12 (-5 *2 (-381)) (-5 *1 (-1040))))) -(((*1 *2 *1) (-12 (-4 *1 (-556 *2)) (-4 *2 (-13 (-406) (-1199))))) - ((*1 *1 *1 *1) (-4 *1 (-793)))) -(((*1 *1 *2) (-12 (-5 *2 (-644 *3)) (-4 *3 (-850)) (-5 *1 (-126 *3))))) + (-12 (-4 *4 (-375 *2)) (-4 *5 (-375 *2)) (-4 *2 (-365)) + (-5 *1 (-523 *2 *4 *5 *3)) (-4 *3 (-687 *2 *4 *5)))) + ((*1 *2 *1) + (-12 (-4 *1 (-687 *2 *3 *4)) (-4 *3 (-375 *2)) (-4 *4 (-375 *2)) + (|has| *2 (-6 (-4416 "*"))) (-4 *2 (-1049)))) + ((*1 *2 *3) + (-12 (-4 *4 (-375 *2)) (-4 *5 (-375 *2)) (-4 *2 (-172)) + (-5 *1 (-688 *2 *4 *5 *3)) (-4 *3 (-687 *2 *4 *5)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1122 *3 *2 *4 *5)) (-4 *4 (-238 *3 *2)) + (-4 *5 (-238 *3 *2)) (|has| *2 (-6 (-4416 "*"))) (-4 *2 (-1049))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-225)) (-5 *4 (-566)) (-5 *2 (-1035)) (-5 *1 (-758))))) -(((*1 *2 *2) + (|partial| -12 (-5 *4 (-295 (-833 *3))) + (-4 *5 (-13 (-454) (-1038 (-566)) (-639 (-566)))) + (-5 *2 (-833 *3)) (-5 *1 (-636 *5 *3)) + (-4 *3 (-13 (-27) (-1199) (-432 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-295 (-833 (-952 *5)))) (-4 *5 (-454)) + (-5 *2 (-833 (-409 (-952 *5)))) (-5 *1 (-637 *5)) + (-5 *3 (-409 (-952 *5))))) + ((*1 *2 *3 *4) + (-12 (-5 *4 (-295 (-409 (-952 *5)))) (-5 *3 (-409 (-952 *5))) + (-4 *5 (-454)) (-5 *2 (-833 *3)) (-5 *1 (-637 *5))))) +(((*1 *2 *3) (-12 - (-5 *2 - (-506 (-409 (-566)) (-240 *4 (-771)) (-864 *3) - (-247 *3 (-409 (-566))))) - (-14 *3 (-644 (-1175))) (-14 *4 (-771)) (-5 *1 (-507 *3 *4))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *4 (-771)) (-4 *5 (-351)) (-4 *6 (-1240 *5)) - (-5 *2 - (-644 - (-2 (|:| -1575 (-689 *6)) (|:| |basisDen| *6) - (|:| |basisInv| (-689 *6))))) - (-5 *1 (-500 *5 *6 *7)) (-5 *3 - (-2 (|:| -1575 (-689 *6)) (|:| |basisDen| *6) - (|:| |basisInv| (-689 *6)))) - (-4 *7 (-1240 *6))))) + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1264 (-317 (-225)))) (|:| |yinit| (-644 (-225))) + (|:| |intvals| (-644 (-225))) (|:| |g| (-317 (-225))) + (|:| |abserr| (-225)) (|:| |relerr| (-225)))) + (-5 *2 (-381)) (-5 *1 (-205))))) (((*1 *1 *1) (-12 (-4 *1 (-119 *2)) 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*4) - (-12 (-5 *4 (-112)) (-4 *5 (-454)) (-4 *6 (-793)) (-4 *7 (-850)) - (-4 *8 (-1064 *5 *6 *7)) - (-5 *2 - (-2 (|:| |val| (-644 *8)) - (|:| |towers| (-644 (-1145 *5 *6 *7 *8))))) - (-5 *1 (-1145 *5 *6 *7 *8)) (-5 *3 (-644 *8))))) -(((*1 *2 *1) (-12 (-4 *1 (-132)) (-5 *2 (-771)))) - ((*1 *2 *3 *1 *2) - (-12 (-5 *2 (-566)) (-4 *1 (-375 *3)) (-4 *3 (-1214)) - (-4 *3 (-1099)))) - ((*1 *2 *3 *1) - (-12 (-4 *1 (-375 *3)) (-4 *3 (-1214)) (-4 *3 (-1099)) - (-5 *2 (-566)))) - ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 (-112) *4)) (-4 *1 (-375 *4)) (-4 *4 (-1214)) - (-5 *2 (-566)))) - ((*1 *2 *1) (-12 (-5 *2 (-1119)) (-5 *1 (-531)))) - ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1143)) (-5 *2 (-566)) (-5 *3 (-141)))) - ((*1 *2 *1 *1 *2) (-12 (-4 *1 (-1143)) (-5 *2 (-566))))) -(((*1 *1 *1 *1) (|partial| -4 *1 (-131)))) -(((*1 *1 *2 *2 *2) (-12 (-5 *1 (-882 *2)) (-4 *2 (-1214))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-547)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-983 *2)) (-4 *2 (-1199))))) -(((*1 *1 *1 *1) - (-12 (-5 *1 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+ (-13 (-850) + (-10 -8 (-15 -1348 ((-1175) $)) + (-15 -1385 ((-3 $ "failed") (-1175)))))) + (-4 *4 (-1049)) (-4 *5 (-793)) (-5 *1 (-984 *4 *5 *6 *2)) + (-4 *2 (-949 (-952 *4) *5 *6))))) (((*1 *2 *2) (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) (-4 *2 (-13 (-432 *3) (-1002))))) @@ -2386,77 +1703,68 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-409 (-566)))) (-4 *4 (-1224 *3)) (-5 *1 (-280 *3 *4 *2 *5)) (-4 *2 (-1247 *3 *4)) (-4 *5 (-983 *4)))) + ((*1 *1 *1) (-4 *1 (-495))) ((*1 *2 *2) (-12 (-5 *2 (-1155 *3)) (-4 *3 (-38 (-409 (-566)))) (-5 *1 (-1160 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1155 *3)) (-4 *3 (-38 (-409 (-566)))) - (-5 *1 (-1161 *3)))) - ((*1 *1 *1) (-4 *1 (-1202)))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-409 (-566))) (-5 *1 (-596 *3)) (-4 *3 (-38 *2)) - (-4 *3 (-1049))))) -(((*1 *2 *2) - (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) - (-4 *2 (-13 (-432 *3) (-1002)))))) -(((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1163 *3 *4)) (-14 *3 (-921)) - (-4 *4 (-1049))))) -(((*1 *2) (-12 (-5 *2 (-1146 (-1157))) (-5 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+ (-4 *6 (-1240 *5)) (-5 *2 (-689 *6)) (-5 *1 (-503 *5 *6 *7 *8)) + (-4 *7 (-1240 *6))))) (((*1 *1) (-5 *1 (-186)))) (((*1 *1 *2) (-12 (-5 *2 (-644 *3)) (-4 *3 (-1214)) (-4 *1 (-151 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-644 (-2 (|:| -2456 (-771)) (|:| -3174 *4) (|:| |num| *4)))) + (-5 *2 (-644 (-2 (|:| -2852 (-771)) (|:| -1320 *4) (|:| |num| *4)))) (-4 *4 (-1240 *3)) (-4 *3 (-13 (-365) (-147))) (-5 *1 (-401 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -1616 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -2895 "void"))) (-5 *3 (-644 (-952 (-566)))) (-5 *4 (-112)) (-5 *1 (-439)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -1616 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -2895 "void"))) (-5 *3 (-644 (-1175))) (-5 *4 (-112)) (-5 *1 (-439)))) ((*1 *2 *1) (-12 (-5 *2 (-1155 *3)) (-5 *1 (-601 *3)) (-4 *3 (-1214)))) @@ -3345,24 +3477,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-713 *2 *3 *4)) (-4 *2 (-850)) (-4 *3 (-1099)) (-14 *4 - (-1 (-112) (-2 (|:| -2208 *2) (|:| -2456 *3)) - (-2 (|:| -2208 *2) (|:| -2456 *3)))))) + (-1 (-112) (-2 (|:| -2178 *2) (|:| -2852 *3)) + (-2 (|:| -2178 *2) (|:| -2852 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-508)) (-5 *3 (-1117)) (-5 *1 (-838)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-873 *2 *3)) (-4 *2 (-1214)) (-4 *3 (-1214)))) ((*1 *1 *2) - (-12 (-5 *2 (-644 (-2 (|:| -2050 (-1175)) (|:| -2849 *4)))) + (-12 (-5 *2 (-644 (-2 (|:| -2004 (-1175)) (|:| -3867 *4)))) (-4 *4 (-1099)) (-5 *1 (-889 *3 *4)) (-4 *3 (-1099)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-644 *5)) (-4 *5 (-13 (-1099) (-34))) (-5 *2 (-644 (-1139 *3 *5))) (-5 *1 (-1139 *3 *5)) (-4 *3 (-13 (-1099) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-644 (-2 (|:| |val| *4) (|:| -2327 *5)))) + (-12 (-5 *3 (-644 (-2 (|:| |val| *4) (|:| -3570 *5)))) (-4 *4 (-13 (-1099) (-34))) (-4 *5 (-13 (-1099) (-34))) (-5 *2 (-644 (-1139 *4 *5))) (-5 *1 (-1139 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2327 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -3570 *4))) (-4 *3 (-13 (-1099) (-34))) (-4 *4 (-13 (-1099) (-34))) (-5 *1 (-1139 *3 *4)))) ((*1 *1 *2 *3) @@ -3385,107 +3517,135 @@ (-4 *4 (-13 (-1099) (-34))) (-5 *1 (-1140 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1164 *2 *3)) (-4 *2 (-1099)) (-4 *3 (-1099))))) -(((*1 *2 *2 *1 *3 *4) - (-12 (-5 *2 (-644 *8)) (-5 *3 (-1 *8 *8 *8)) - (-5 *4 (-1 (-112) *8 *8)) (-4 *1 (-1207 *5 *6 *7 *8)) (-4 *5 (-558)) - (-4 *6 (-793)) (-4 *7 (-850)) (-4 *8 (-1064 *5 *6 *7))))) -(((*1 *2 *3) - (-12 (-5 *3 (-644 *5)) (-4 *5 (-432 *4)) (-4 *4 (-558)) - (-5 *2 (-862)) (-5 *1 (-32 *4 *5))))) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-771)) (-4 *1 (-1240 *4)) (-4 *4 (-1049)) - (-5 *2 (-1264 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-644 (-1134))) (-5 *1 (-1089))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) - (|:| |fn| (-1264 (-317 (-225)))) (|:| |yinit| (-644 (-225))) - (|:| |intvals| (-644 (-225))) (|:| |g| (-317 (-225))) - (|:| |abserr| (-225)) (|:| |relerr| (-225)))) - (-5 *2 (-381)) (-5 *1 (-205))))) -(((*1 *1 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(-436)) (|:| -2895 "void"))) (-14 *5 (-644 (-1175))) (-14 *6 (-1179)))) ((*1 *1 *2) (-12 (-5 *2 (-331)) (-5 *1 (-400 *3 *4 *5 *6)) (-14 *3 (-1175)) - (-14 *4 (-3 (|:| |fst| (-436)) (|:| -1616 "void"))) + (-14 *4 (-3 (|:| |fst| (-436)) (|:| -2895 "void"))) (-14 *5 (-644 (-1175))) (-14 *6 (-1179)))) ((*1 *1 *2) (-12 (-5 *2 (-332 *4)) (-4 *4 (-13 (-850) (-21))) @@ -3641,14 +3801,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-436)) (-5 *1 (-439)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3248 (-644 (-331))))) + (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3261 (-644 (-331))))) (-4 *1 (-442)))) ((*1 *1 *2) (-12 (-5 *2 (-331)) (-4 *1 (-442)))) ((*1 *1 *2) (-12 (-5 *2 (-644 (-331))) (-4 *1 (-442)))) ((*1 *1 *2) (-12 (-5 *2 (-1264 (-699))) (-4 *1 (-442)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3248 (-644 (-331))))) + (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3261 (-644 (-331))))) (-4 *1 (-443)))) ((*1 *1 *2) (-12 (-5 *2 (-331)) (-4 *1 (-443)))) ((*1 *1 *2) (-12 (-5 *2 (-644 (-331))) (-4 *1 (-443)))) @@ -3717,7 +3877,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-644 (-2 (|:| -3223 *3) (|:| -2044 *4)))) + (-12 (-5 *2 (-644 (-2 (|:| -1364 *3) (|:| -3319 *4)))) (-4 *3 (-1049)) (-4 *4 (-726)) (-5 *1 (-735 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-566)) (-4 *1 (-763)))) ((*1 *1 *2) @@ -3726,25 +3886,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) - (|:| -2498 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) + (|:| -2446 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-317 (-225))) - (|:| -2498 (-644 (-1093 (-843 (-225))))) + (|:| -2446 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-769)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-317 (-225))) - (|:| -2498 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) + (|:| -2446 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-769)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) - (|:| -2498 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) + (|:| -2446 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-769)))) ((*1 *2 *3) (-12 (-5 *2 (-774)) (-5 *1 (-773 *3)) (-4 *3 (-1214)))) @@ -3762,23 +3922,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-225))) (|:| -3625 (-644 (-225))) + (-2 (|:| |fn| (-317 (-225))) (|:| -1761 (-644 (-225))) (|:| |lb| (-644 (-843 (-225)))) (|:| |cf| (-644 (-317 (-225)))) (|:| |ub| (-644 (-843 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-644 (-317 (-225)))) - (|:| -3625 (-644 (-225))))))) + (|:| -1761 (-644 (-225))))))) (-5 *1 (-841)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -3625 (-644 (-225))))) + (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -1761 (-644 (-225))))) (-5 *1 (-841)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-225))) (|:| -3625 (-644 (-225))) + 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\ No newline at end of file |