diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 642 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1396 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1324 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8930 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27220 |
5 files changed, 19757 insertions, 19755 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 81b080e3..5c151794 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2285499 . 3453610657) +(2285497 . 3453749792) (-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 -2286) +(-32 R -2382) ((|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 -2286 UP UPUP -3750) +(-40 -2382 UP UPUP -4030) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2700 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2700 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2700 (-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)))) (-2700 (|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 -2286) +((|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 -2382) ((|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."))) ((-4417 . T) (-4418 . T)) -((-2700 (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|))))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|))))))) +((-2805 (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|))))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2286) +(-54 |Base| R -2382) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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 -2520) +((-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 -2628) ((|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 -2520) +(-62 -2628) ((|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 -2520) +(-63 -2628) ((|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 -2520) +(-64 -2628) ((|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 -2520) +(-65 -2628) ((|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 -2520) +(-66 -2628) ((|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 -2520) +(-67 -2628) ((|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 -2520) +(-68 -2628) ((|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 -2520) +(-69 -2628) ((|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 -2520) +(-70 -2628) ((|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 -2520) +(-71 -2628) ((|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 -2520) +(-72 -2628) ((|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 -2520) +(-73 -2628) ((|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 -2520) +(-74 -2628) ((|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 -2520) +(-77 -2628) ((|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 -2520) +(-78 -2628) ((|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 -2520) +(-79 -2628) ((|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 -2520) +(-80 -2628) ((|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 -2520) +(-81 -2628) ((|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 -2520) +(-82 -2628) ((|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 -2520) +(-83 -2628) ((|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 -2520) +(-84 -2628) ((|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 -2520) +(-85 -2628) ((|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 -2520) +(-86 -2628) ((|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 -2520) +(-87 -2628) ((|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 -2520) +(-88 -2628) ((|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 -2520) +(-89 -2628) ((|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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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 -2286 UP) +(-115 -2382 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}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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"))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2700 (-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)))) (-2700 (|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)))))) +((-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)))))) (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4419 "*") . T)) NIL -(-135 |minix| -2201 S T$) +(-135 |minix| -2293 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2201 R) +(-136 |minix| -2293 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4417 . T) (-4407 . T) (-4418 . T)) -((-2700 (-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)))))) +((-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)))))) (-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."))) ((-4414 . T)) NIL -(-148 -2286 UP UPUP) +(-148 -2382 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 -2286) +(-158 R -2382) ((|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 -4413)) (|HasAttribute| |#2| (QUOTE -4416)) (|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})"))) -((-4410 -2700 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3611 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4410 -2805 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3654 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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}."))) -((-4410 -2700 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4416 |has| |#1| (-6 -4416)) (-3611 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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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(|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-909)))) (-12 (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-909))))) (-2805 (|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)))) (-2805 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-2805 (|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))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2805 (-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 -4413)) (|HasAttribute| |#1| (QUOTE -4416)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2805 (-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 @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2286) +(-188 R -2382) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2286 UP UPUP R) +(-215 -2382 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 -2286 FP) +(-216 -2382 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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2286) +(-219 R -2382) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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}."))) ((-4414 . T)) NIL -(-224 R -2286) +(-224 R -2382) ((|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}."))) -((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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}"))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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 (-4419 "*"))) (|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))) (-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 (-4419 "*"))) (|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 -2201 R) +(-237 S -2293 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 -4414)) (|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 -2201 R) +(-238 -2293 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"))) ((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) NIL -(-239 -2201 A B) +(-239 -2293 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 -2201 R) +(-240 -2293 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."))) ((-4411 |has| |#2| (-1049)) (-4412 |has| |#2| (-1049)) (-4414 |has| |#2| (-6 -4414)) ((-4419 "*") |has| |#2| (-172)) (-4417 . T)) -((-2700 (-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 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|#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4414)) (|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|))))) (-241) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -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}"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|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'}."))) 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(QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-2805 (-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))))) (-2805 (|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)))) (-2805 (|HasAttribute| |#3| (QUOTE -4414)) (-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"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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 -2286) +(-277 R -2382) ((|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 -2286) +(-278 R -2382) ((|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 @@ -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| -1467 -2806 |exactQuo|) +(-290 S R |Mod| -3550 -3132 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL @@ -1110,21 +1110,21 @@ NIL NIL (-295 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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 -2286 S) +(-298 -2382 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 -2286) +(-299 E -2382) ((|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 -2286) +(-311 -2382) ((|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))}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (|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))) (-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)))))) (-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."))) -((-4414 -2700 (-2336 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2700 (-2336 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 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(|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (|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)))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-1111)))) (-2805 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2805 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2805 (-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 -2382) ((|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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|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 -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-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 -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (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))) (-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 -2512) (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 -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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 -2286) +((-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 -2382) ((|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 -2286) +(-330 -2382) ((|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL @@ -1272,15 +1272,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-336 S -2286 UP UPUP R) +(-336 S -2382 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 -2286 UP UPUP R) +(-337 -2382 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 -2286 UP UPUP R) +(-338 -2382 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 -2286 UP UPUP) +(-343 S -2382 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 -2286 UP UPUP) +(-344 -2382 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."))) ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|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)))) +((-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)))) (-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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL -(-352 R UP -2286) +(-352 R UP -2382) ((|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|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)))) +((-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)))) (-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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|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)))) +((-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)))) (-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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -2286 GF) +((-2805 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +(-358 -2382 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 -2286 FP FPP) +(-360 -2382 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}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2805 (|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}."))) -((-4400 . T) (-4408 . T) (-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-4400 . T) (-4408 . T) (-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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 -2286 UP UPUP R) +(-394 -2382 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 -2520 |returnType| -2143 |symbols|) +(-400 -2628 |returnType| -2763 |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 -2286 UP) +(-401 -2382 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1554,7 +1554,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4400)) (|HasAttribute| |#1| (QUOTE -4408))) (-406) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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."))) ((-4404 -12 (|has| |#1| (-6 -4415)) (|has| |#1| (-454)) (|has| |#1| (-6 -4404))) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2700 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2700 (-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)))) (-2700 (-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))))) (-2700 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2700 (|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 -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|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)))) (-2700 (-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))) (-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 -4415)) (|HasAttribute| |#1| (QUOTE -4404)) (|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))))) (-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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1588,11 +1588,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-415 R -2286 UP A) +(-415 R -2382 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4414 . T)) NIL -(-416 R -2286 UP A |ibasis|) +(-416 R -2382 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."))) ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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))) (-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)))) (-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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4417 . T) (-4407 . T) (-4418 . T)) NIL -(-428 R -2286) +(-428 R -2382) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1648,7 +1648,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4404 -12 (|has| |#1| (-6 -4404)) (|has| |#2| (-6 -4404))) (-4411 . T) (-4412 . T) (-4414 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#2| (QUOTE -4404)))) -(-430 R -2286) +(-430 R -2382) ((|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}."))) -((-4414 -2700 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) +((-4414 -2805 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-558)) (-4409 |has| |#1| (-558))) NIL -(-433 R -2286) +(-433 R -2382) ((|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 -2286) +(-434 R -2382) ((|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 -2286) +(-435 R -2382) ((|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 -2286 UP) +(-437 R -2382 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 -2286) +(-445 R UP -2382) ((|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"))) (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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| -2286 R) +(-473 |lv| -2382 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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|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 -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-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 -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (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))) (-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 -2512) (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 -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-477 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#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 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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 (|:| -2010 |#1|) (|:| -2818 |#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 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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)}"))) ((-4418 . T) (-4417 . 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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . 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(QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-793))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-848))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (|HasCategory| (-566) (QUOTE (-850))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1049)))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2805 (|HasCategory| |#2| (QUOTE (-1049))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4414)) (|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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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 -2286 UP UPUP R) +((-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 -2382 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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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 -2286 UP |AlExt| |AlPol|) +(-496 -2382 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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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 -2286) +(-501 R UP -2382) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1952,7 +1952,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-506 -2286 |Expon| |VarSet| |DPoly|) +(-506 -2382 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((-2700 (|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)))) +((-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)))) (-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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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 (-4419 "*"))) (|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))) (-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 (-4419 "*"))) (|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 -2286 |Par|) +(-534 K -2382 |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 -2286 |Par|) +(-540 K -2382 |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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) -(-553 R -2286) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +(-553 R -2382) ((|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 -2286 UP UPUP R) +(-554 R0 -2382 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."))) -((-3601 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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."))) ((-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL -(-559 R -2286) +(-559 R -2382) ((|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 -2286 L) +(-562 R -2382 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 -2286 UP UPUP R) +(-564 -2382 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 -2286 UP) +(-565 -2382 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 -2286 L) +(-568 R -2382 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 -2286) +(-569 R -2382) ((|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 -2286 UP) +(-570 -2382 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 -2286) +(-572 -2382) ((|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."))) -((-3601 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3645 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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 -2286) +(-575 R -2382) ((|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 -2286 UP) +(-576 -2382 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 -2286) +(-577 R -2382) ((|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 -2286) +(-585 R -2382) ((|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 -2286) +(-586 E -2382) ((|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 -2286) +(-587 -2382) ((|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}."))) ((-4412 . T) (-4411 . 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"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2700 (|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)))) (-2700 (|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)))))) +((-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)))))) (-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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|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 -2409) (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))) (-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 -2512) (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.}"))) ((-4412 |has| |#1| (-558)) (-4411 |has| |#1| (-558)) ((-4419 "*") |has| |#1| (-558)) (-4410 |has| |#1| (-558)) (-4414 . 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 -2286 FG) +(-600 R -2382 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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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)."))) -((-4414 -2700 (-2336 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) -((-2700 (|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|)))) (-2700 (-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|)))) +((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . 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|)))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#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 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#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 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-615 -2286 UP) +(-615 -2382 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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}."))) ((-4411 . T) (-4412 . T) (-4414 . T)) ((|HasCategory| |#1| (QUOTE (-848)))) -(-622 R -2286) +(-622 R -2382) ((|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 -2286) +(-630 R -2382) ((|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| -2286) +(-631 |lv| -2382) ((|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."))) ((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-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 (|:| -1924 (-1157)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 (-52))) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-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 (|:| -2010 (-1157)) (|:| -2818 (-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 (|:| -2010 (-1157)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 (-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)."))) -((-4414 -2700 (-2336 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . T)) -((-2700 (|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|)))) (-2700 (-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|)))) +((-4414 -2805 (-2438 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4412 . T) (-4411 . 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|)))) (-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 -((-2326 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-2426 (|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4414 . T)) @@ -2507,7 +2507,7 @@ NIL (-644 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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 -2286 L) +(-652 R -2382 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}."))) ((-4411 . T) (-4412 . T) (-4414 . T)) NIL -(-657 -2286 UP) +(-657 -2382 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 -2887) +(-658 A -2614) ((|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}}"))) ((-4411 . T) (-4412 . T) (-4414 . 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}."))) ((-4418 . T) (-4417 . T)) NIL -(-667 -2286) +(-667 -2382) ((|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 -2286 |Row| |Col| M) +(-668 -2382 |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."))) ((-4414 . T) (-4417 . T) (-4411 . T) (-4412 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (-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))) (-2700 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|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 (-4419 "*"))) (|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 (-4419 "*"))) (|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 -((-2700 (-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))) (-2700 (-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|))))) +((-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|))))) (-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."))) ((-4417 . T) (-4418 . T)) -((-2700 (-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))) (-2700 (-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 (-4419 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-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 (-4419 "*"))) (|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 -2286 FLAF FLAS) +(-692 S -2382 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"))) -((-4410 . T) (-4415 |has| (-699) (-365)) (-4409 |has| (-699) (-365)) (-3611 . T) (-4416 |has| (-699) (-6 -4416)) (-4413 |has| (-699) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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))) (-2700 (|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))))) (-2700 (|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)))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2700 (-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))) (-2700 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2700 (-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 -4416)) (|HasAttribute| (-699) (QUOTE -4413)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-351))))) +((-4410 . T) (-4415 |has| (-699) (-365)) (-4409 |has| (-699) (-365)) (-3654 . T) (-4416 |has| (-699) (-6 -4416)) (-4413 |has| (-699) (-6 -4413)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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 -4416)) (|HasAttribute| (-699) (QUOTE -4413)) (-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))))) (-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}."))) ((-4418 . 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 -2286 PG) +(-698 OV E -2382 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}"))) -((-3601 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) +((-3645 . T) (-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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 -2739 I) +(-706 S -2840 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| -1467 -2806 |exactQuo|) +(-711 R |Mod| -3550 -3132 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL (-712 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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))))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4412 |has| |#1| (-172)) (-4411 |has| |#1| (-172)) (-4414 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-715 R |Mod| -1467 -2806 |exactQuo|) +(-715 R |Mod| -3550 -3132 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4414 . T)) NIL @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4412 . T) (-4411 . T)) NIL -(-718 -2286) +(-718 -2382) ((|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]]}."))) ((-4414 . 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 -2286 UP) +(-727 -2382 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."))) (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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 -2286) +(-765 -2382) ((|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 -2286) +(-766 P -2382) ((|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 -2286) +(-768 UP -2382) ((|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."))) (((-4419 "*") . T)) NIL -(-772 R -2286) +(-772 R -2382) ((|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 -2286 |ExtF| |SUEx| |ExtP| |n|) +(-777 -2382 |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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3120,23 +3120,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4411 . T) (-4412 . T) (-4414 . T)) NIL -(-798 -2700 R OS S) +(-798 -2805 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-799 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4411 . T) (-4412 . T) (-4414 . 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|))) (-2700 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (|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|))) (-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))))) (-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 -2286 L) +(-801 R -2382 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 -2286) +(-802 R -2382) ((|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 -2286) +(-804 R -2382) ((|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 -2286 UP UPUP R) +(-806 -2382 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 -2286 UP L LQ) +(-807 -2382 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 -2286 UP L LQ) +(-809 -2382 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 -2286 UP) +(-810 -2382 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 -2286 L UP A LO) +(-811 -2382 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 -2286 UP) +(-812 -2382 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 -2286 LO) +(-813 -2382 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-814 -2286 LODO) +(-814 -2382 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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|#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasAttribute| |#2| (QUOTE -4414)) (|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"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-817 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4419 "*") |has| |#2| (-365)) (-4410 |has| |#2| (-365)) (-4415 |has| |#2| (-365)) (-4409 |has| |#2| (-365)) (-4414 . T) (-4412 . T) (-4411 . 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."))) ((-4414 |has| |#1| (-848))) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|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))) (-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)))) (-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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4414 |has| |#1| (-848))) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) +((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2805 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2805 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-844) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-845 -2201 S) +(-845 -2293 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| -1674) +(-854 R |sigma| -2916) ((|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."))) ((-4411 . T) (-4412 . T) (-4414 . 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| -1674) +(-855 |x| R |sigma| -2916) ((|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}."))) ((-4411 . T) (-4412 . T) (-4414 . 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)."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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)}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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)))) (-2700 (-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)))) (-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)))))) (-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 (-2326 (|HasCategory| |#2| (QUOTE (-1049)))) (-2326 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2326 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) +((-12 (-2426 (|HasCategory| |#2| (QUOTE (-1049)))) (-2426 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-2426 (|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 -2739) +(-890 R -2840) ((|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 -2286) +(-896 UP -2382) ((|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))) (-2700 (-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))) (-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))))) (-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."))) ((-4414 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) +((-2805 (|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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-911 R0 -2286 UP UPUP R) +(-911 R0 -2382 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 -2286) +(-918 -2382) ((|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}."))) (((-4419 "*") . T)) NIL -(-922 -2286 P) +(-922 -2382 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-923 |xx| -2286) +(-923 |xx| -2382) ((|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 -2286) +(-929 R -2382) ((|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 -2286) +(-932 S R -2382) ((|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 -2286 -2739) +(-937 R -2382 -2840) ((|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 -2739) +(-938 -2840) ((|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"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) NIL -(-950 E V R P -2286) +(-950 E V R P -2382) ((|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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-953 E V R P -2286) +((|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 -4415)) (|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 -2382) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-454)))) @@ -3763,12 +3763,12 @@ NIL (-958 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2805 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2805 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-959) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -2286) +(-960 -2382) ((|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}"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (|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 -4415))) +((|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 -4415))) (-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"))) ((-4414 -12 (|has| |#2| (-475)) (|has| |#1| (-475)))) -((-2700 (-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)))) (-2700 (-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)))) (-2700 (-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)))) (-2700 (-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)))) (-2700 (-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))))) +((-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))))) (-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 -2286) +(-985 K R UP -2382) ((|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.}"))) ((-4410 |has| |#1| (-291)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (|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)))) (-2700 (|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))) (-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)))) (-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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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 -2286 UP UPUP |radicnd| |n|) +(-1003 -2382 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4410 |has| (-409 |#2|) (-365)) (-4415 |has| (-409 |#2|) (-365)) (-4409 |has| (-409 |#2|) (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2700 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2700 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2700 (-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)))) (-2700 (|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))) (-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))))) (-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."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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)))) (-2700 (-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))) (-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))))) (-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}}"))) ((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) NIL -(-1013 R -2286) +(-1013 R -2382) ((|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 -2286) +(-1014 R -2382) ((|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 -2286 UP) +(-1015 -2382 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 -2286 UP) +(-1016 -2382 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"))) ((-4410 . T) (-4415 . T) (-4409 . T) (-4412 . T) (-4411 . T) ((-4419 "*") . T) (-4414 . T)) -((-2700 (|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 -2286 L) +((-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 -2382 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 -2286 |Expon| |VarSet| |FPol| |LFPol|) +(-1034 -2382 |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"))) (((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . 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.}"))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1036) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4128,7 +4128,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4414 . T)) NIL -(-1050 |xx| -2286) +(-1050 |xx| -2382) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4147,7 +4147,7 @@ NIL (-1054 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4417 . T) (-4412 . T) (-4411 . T)) -((|HasCategory| |#3| (QUOTE (-172))) (-2700 (-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)))) (-2700 (|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))) (-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))))) (-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}"))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2713) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2818) (QUOTE (-52))))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1175)) (|:| -2818 (-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 -2286) +(-1075 |Base| R -2382) ((|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 -2286) +(-1076 |Base| R -2382) ((|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."))) ((-4410 |has| |#1| (-365)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2700 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2700 (-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)))) (-2700 (|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))) (-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))))) (-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"))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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)}}"))) ((-4417 . T) (-4407 . T) (-4418 . T)) -((-2700 (-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|))))) +((-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|))))) (-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))))) (-2805 (|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 -4414)) (|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 -2286) +(-1115 R -2382) ((|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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-909))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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 -4415)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2700 (|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))) (-2805 (|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}"))) ((-4418 . T) (-4417 . T)) NIL -(-1127 UP -2286) +(-1127 UP -2382) ((|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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2700 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2805 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) (-1141 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4414 . T) (-4406 |has| |#2| (-6 (-4419 "*"))) (-4417 . T) (-4411 . T) (-4412 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2700 (-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))) (-2700 (|HasAttribute| |#2| (QUOTE (-4419 "*"))) (|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 (-4419 "*"))) (|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 (-4419 "*"))) (|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}."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-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."))) ((-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#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 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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 (|:| -2010 |#1|) (|:| -2818 |#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 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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."))) ((-4418 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-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))) (-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))))) (-1156) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4418 . T) (-4417 . T)) @@ -4559,11 +4559,11 @@ NIL (-1157) NIL ((-4418 . T) (-4417 . T)) -((-2700 (-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)))))) +((-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)))))) (-1158 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#1|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#1|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (QUOTE (-1099))) (|HasCategory| (-1157) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 (-1157)) (|:| -2818 |#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."))) -(((-4419 "*") -2700 (-2336 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-820))) (|has| |#1| (-172)) (-2336 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-909)))) (-4410 -2700 (-2336 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-820))) (|has| |#1| (-558)) (-2336 (|has| |#1| (-365)) (|has| (-1173 |#1| |#2| |#3|) (-909)))) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . 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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 -4415)) (|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))))) (-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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . 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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))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2700 (|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 -4415))) +((|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 -4415))) (-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}"))) ((-4417 . T) (-4418 . T)) -((-12 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1924) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2713) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2010) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2818) (|devaluate| |#2|)))))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2805 (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2010 |#1|) (|:| -2818 |#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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4418 . T) (-4417 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2805 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1201 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4740,7 +4740,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1203 R -2286) +(-1203 R -2382) ((|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 -2286) +(-1205 R -2382) ((|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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2700 (|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))) (-2805 (|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 -2286) +(-1212 -2382) ((|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)))))) (-2805 (-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)))) (-2805 (-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}"))) (((-4419 "*") |has| |#2| (-172)) (-4410 |has| |#2| (-558)) (-4413 |has| |#2| (-365)) (-4415 |has| |#2| (-6 -4415)) (-4412 . T) (-4411 . T) (-4414 . T)) -((|HasCategory| |#2| (QUOTE (-909))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2700 (|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)))) (-2700 (|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))))) (-2700 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (|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 -4415)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2700 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|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 -4415)) (|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))))) (-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 -2409) (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 -2512) (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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) @@ -4923,21 +4923,21 @@ 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)}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|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 -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-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 -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (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))) (-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 -2512) (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 -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4415 |has| |#1| (-365)) (-4409 |has| |#1| (-365)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2700 (|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))) (-2700 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2700 (|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 -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2700 (-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 -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (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))) (-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 -2512) (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 -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (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))}."))) (((-4419 "*") |has| (-1249 |#2| |#3| |#4|) (-172)) (-4410 |has| (-1249 |#2| |#3| |#4|) (-558)) (-4411 . T) (-4412 . T) (-4414 . 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))) (-2700 (|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))) (-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)))) (-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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) +((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL ((|HasAttribute| |#1| (QUOTE -4418))) (-1252 S) -((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) +((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL (-1253 |Coef1| |Coef2| UTS1 UTS2) @@ -4947,7 +4947,7 @@ NIL (-1254 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3450) (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 -2540) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4117) (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."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . 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}."))) (((-4419 "*") |has| |#1| (-172)) (-4410 |has| |#1| (-558)) (-4411 . T) (-4412 . T) (-4414 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2700 (|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 -2409) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2700 (-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 -3450) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2439) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|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 -2512) (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 -4117) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -2540) (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 -2286 UP L UTS) +(-1258 -2382 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."))) ((-4418 . T) (-4417 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-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)))) (-2700 (|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|))))) +((-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|))))) (-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 -2286) +(-1273 K R UP -2382) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4410 |has| |#2| (-6 -4410)) (-4412 . T) (-4411 . T) (-4414 . T)) NIL -(-1282 S -2286) +(-1282 S -2382) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1283 -2286) +(-1283 -2382) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4409 . T) (-4415 . T) (-4410 . T) ((-4419 "*") . T) (-4411 . T) (-4412 . T) (-4414 . T)) NIL @@ -5116,4 +5116,4 @@ NIL NIL NIL NIL -((-3 NIL 2285479 2285484 2285489 2285494) (-2 NIL 2285459 2285464 2285469 2285474) (-1 NIL 2285439 2285444 2285449 2285454) (0 NIL 2285419 2285424 2285429 2285434) (-1292 "ZMOD.spad" 2285228 2285241 2285357 2285414) (-1291 "ZLINDEP.spad" 2284272 2284283 2285218 2285223) (-1290 "ZDSOLVE.spad" 2274121 2274143 2284262 2284267) (-1289 "YSTREAM.spad" 2273614 2273625 2274111 2274116) (-1288 "XRPOLY.spad" 2272834 2272854 2273470 2273539) (-1287 "XPR.spad" 2270625 2270638 2272552 2272651) (-1286 "XPOLY.spad" 2270180 2270191 2270481 2270550) (-1285 "XPOLYC.spad" 2269497 2269513 2270106 2270175) (-1284 "XPBWPOLY.spad" 2267934 2267954 2269277 2269346) (-1283 "XF.spad" 2266395 2266410 2267836 2267929) (-1282 "XF.spad" 2264836 2264853 2266279 2266284) (-1281 "XFALG.spad" 2261860 2261876 2264762 2264831) (-1280 "XEXPPKG.spad" 2261111 2261137 2261850 2261855) (-1279 "XDPOLY.spad" 2260725 2260741 2260967 2261036) (-1278 "XALG.spad" 2260385 2260396 2260681 2260720) (-1277 "WUTSET.spad" 2256224 2256241 2260031 2260058) (-1276 "WP.spad" 2255423 2255467 2256082 2256149) (-1275 "WHILEAST.spad" 2255221 2255230 2255413 2255418) (-1274 "WHEREAST.spad" 2254892 2254901 2255211 2255216) (-1273 "WFFINTBS.spad" 2252455 2252477 2254882 2254887) (-1272 "WEIER.spad" 2250669 2250680 2252445 2252450) (-1271 "VSPACE.spad" 2250342 2250353 2250637 2250664) (-1270 "VSPACE.spad" 2250035 2250048 2250332 2250337) (-1269 "VOID.spad" 2249712 2249721 2250025 2250030) (-1268 "VIEW.spad" 2247334 2247343 2249702 2249707) (-1267 "VIEWDEF.spad" 2242531 2242540 2247324 2247329) (-1266 "VIEW3D.spad" 2226366 2226375 2242521 2242526) (-1265 "VIEW2D.spad" 2214103 2214112 2226356 2226361) (-1264 "VECTOR.spad" 2212777 2212788 2213028 2213055) (-1263 "VECTOR2.spad" 2211404 2211417 2212767 2212772) (-1262 "VECTCAT.spad" 2209304 2209315 2211372 2211399) (-1261 "VECTCAT.spad" 2207011 2207024 2209081 2209086) (-1260 "VARIABLE.spad" 2206791 2206806 2207001 2207006) (-1259 "UTYPE.spad" 2206435 2206444 2206781 2206786) (-1258 "UTSODETL.spad" 2205728 2205752 2206391 2206396) (-1257 "UTSODE.spad" 2203916 2203936 2205718 2205723) (-1256 "UTS.spad" 2198705 2198733 2202383 2202480) (-1255 "UTSCAT.spad" 2196156 2196172 2198603 2198700) (-1254 "UTSCAT.spad" 2193251 2193269 2195700 2195705) (-1253 "UTS2.spad" 2192844 2192879 2193241 2193246) (-1252 "URAGG.spad" 2187476 2187487 2192834 2192839) (-1251 "URAGG.spad" 2182072 2182085 2187432 2187437) (-1250 "UPXSSING.spad" 2179715 2179741 2181153 2181286) (-1249 "UPXS.spad" 2176863 2176891 2177847 2177996) (-1248 "UPXSCONS.spad" 2174620 2174640 2174995 2175144) (-1247 "UPXSCCA.spad" 2173185 2173205 2174466 2174615) (-1246 "UPXSCCA.spad" 2171892 2171914 2173175 2173180) (-1245 "UPXSCAT.spad" 2170473 2170489 2171738 2171887) (-1244 "UPXS2.spad" 2170014 2170067 2170463 2170468) (-1243 "UPSQFREE.spad" 2168426 2168440 2170004 2170009) (-1242 "UPSCAT.spad" 2166019 2166043 2168324 2168421) (-1241 "UPSCAT.spad" 2163318 2163344 2165625 2165630) (-1240 "UPOLYC.spad" 2158296 2158307 2163160 2163313) (-1239 "UPOLYC.spad" 2153166 2153179 2158032 2158037) (-1238 "UPOLYC2.spad" 2152635 2152654 2153156 2153161) (-1237 "UP.spad" 2149828 2149843 2150221 2150374) (-1236 "UPMP.spad" 2148718 2148731 2149818 2149823) (-1235 "UPDIVP.spad" 2148281 2148295 2148708 2148713) (-1234 "UPDECOMP.spad" 2146518 2146532 2148271 2148276) (-1233 "UPCDEN.spad" 2145725 2145741 2146508 2146513) (-1232 "UP2.spad" 2145087 2145108 2145715 2145720) (-1231 "UNISEG.spad" 2144440 2144451 2145006 2145011) (-1230 "UNISEG2.spad" 2143933 2143946 2144396 2144401) (-1229 "UNIFACT.spad" 2143034 2143046 2143923 2143928) (-1228 "ULS.spad" 2133586 2133614 2134679 2135108) (-1227 "ULSCONS.spad" 2125980 2126000 2126352 2126501) (-1226 "ULSCCAT.spad" 2123709 2123729 2125826 2125975) (-1225 "ULSCCAT.spad" 2121546 2121568 2123665 2123670) (-1224 "ULSCAT.spad" 2119762 2119778 2121392 2121541) (-1223 "ULS2.spad" 2119274 2119327 2119752 2119757) (-1222 "UINT8.spad" 2119151 2119160 2119264 2119269) (-1221 "UINT64.spad" 2119027 2119036 2119141 2119146) (-1220 "UINT32.spad" 2118903 2118912 2119017 2119022) (-1219 "UINT16.spad" 2118779 2118788 2118893 2118898) (-1218 "UFD.spad" 2117844 2117853 2118705 2118774) (-1217 "UFD.spad" 2116971 2116982 2117834 2117839) (-1216 "UDVO.spad" 2115818 2115827 2116961 2116966) (-1215 "UDPO.spad" 2113245 2113256 2115774 2115779) (-1214 "TYPE.spad" 2113177 2113186 2113235 2113240) (-1213 "TYPEAST.spad" 2113096 2113105 2113167 2113172) (-1212 "TWOFACT.spad" 2111746 2111761 2113086 2113091) (-1211 "TUPLE.spad" 2111230 2111241 2111645 2111650) (-1210 "TUBETOOL.spad" 2108067 2108076 2111220 2111225) (-1209 "TUBE.spad" 2106708 2106725 2108057 2108062) (-1208 "TS.spad" 2105297 2105313 2106273 2106370) (-1207 "TSETCAT.spad" 2092424 2092441 2105265 2105292) (-1206 "TSETCAT.spad" 2079537 2079556 2092380 2092385) (-1205 "TRMANIP.spad" 2073903 2073920 2079243 2079248) (-1204 "TRIMAT.spad" 2072862 2072887 2073893 2073898) (-1203 "TRIGMNIP.spad" 2071379 2071396 2072852 2072857) (-1202 "TRIGCAT.spad" 2070891 2070900 2071369 2071374) (-1201 "TRIGCAT.spad" 2070401 2070412 2070881 2070886) (-1200 "TREE.spad" 2068972 2068983 2070008 2070035) (-1199 "TRANFUN.spad" 2068803 2068812 2068962 2068967) (-1198 "TRANFUN.spad" 2068632 2068643 2068793 2068798) (-1197 "TOPSP.spad" 2068306 2068315 2068622 2068627) (-1196 "TOOLSIGN.spad" 2067969 2067980 2068296 2068301) (-1195 "TEXTFILE.spad" 2066526 2066535 2067959 2067964) (-1194 "TEX.spad" 2063658 2063667 2066516 2066521) (-1193 "TEX1.spad" 2063214 2063225 2063648 2063653) (-1192 "TEMUTL.spad" 2062769 2062778 2063204 2063209) (-1191 "TBCMPPK.spad" 2060862 2060885 2062759 2062764) (-1190 "TBAGG.spad" 2059898 2059921 2060842 2060857) (-1189 "TBAGG.spad" 2058942 2058967 2059888 2059893) (-1188 "TANEXP.spad" 2058318 2058329 2058932 2058937) (-1187 "TABLE.spad" 2056729 2056752 2056999 2057026) (-1186 "TABLEAU.spad" 2056210 2056221 2056719 2056724) (-1185 "TABLBUMP.spad" 2052993 2053004 2056200 2056205) (-1184 "SYSTEM.spad" 2052221 2052230 2052983 2052988) (-1183 "SYSSOLP.spad" 2049694 2049705 2052211 2052216) (-1182 "SYSNNI.spad" 2048874 2048885 2049684 2049689) (-1181 "SYSINT.spad" 2048278 2048289 2048864 2048869) (-1180 "SYNTAX.spad" 2044472 2044481 2048268 2048273) (-1179 "SYMTAB.spad" 2042528 2042537 2044462 2044467) (-1178 "SYMS.spad" 2038513 2038522 2042518 2042523) (-1177 "SYMPOLY.spad" 2037520 2037531 2037602 2037729) (-1176 "SYMFUNC.spad" 2036995 2037006 2037510 2037515) (-1175 "SYMBOL.spad" 2034422 2034431 2036985 2036990) (-1174 "SWITCH.spad" 2031179 2031188 2034412 2034417) (-1173 "SUTS.spad" 2028078 2028106 2029646 2029743) (-1172 "SUPXS.spad" 2025213 2025241 2026210 2026359) (-1171 "SUP.spad" 2022018 2022029 2022799 2022952) (-1170 "SUPFRACF.spad" 2021123 2021141 2022008 2022013) (-1169 "SUP2.spad" 2020513 2020526 2021113 2021118) (-1168 "SUMRF.spad" 2019479 2019490 2020503 2020508) (-1167 "SUMFS.spad" 2019112 2019129 2019469 2019474) (-1166 "SULS.spad" 2009651 2009679 2010757 2011186) (-1165 "SUCHTAST.spad" 2009420 2009429 2009641 2009646) (-1164 "SUCH.spad" 2009100 2009115 2009410 2009415) (-1163 "SUBSPACE.spad" 2001107 2001122 2009090 2009095) (-1162 "SUBRESP.spad" 2000267 2000281 2001063 2001068) (-1161 "STTF.spad" 1996366 1996382 2000257 2000262) (-1160 "STTFNC.spad" 1992834 1992850 1996356 1996361) (-1159 "STTAYLOR.spad" 1985232 1985243 1992715 1992720) (-1158 "STRTBL.spad" 1983737 1983754 1983886 1983913) (-1157 "STRING.spad" 1983146 1983155 1983160 1983187) (-1156 "STRICAT.spad" 1982934 1982943 1983114 1983141) (-1155 "STREAM.spad" 1979792 1979803 1982459 1982474) (-1154 "STREAM3.spad" 1979337 1979352 1979782 1979787) (-1153 "STREAM2.spad" 1978405 1978418 1979327 1979332) (-1152 "STREAM1.spad" 1978109 1978120 1978395 1978400) (-1151 "STINPROD.spad" 1977015 1977031 1978099 1978104) (-1150 "STEP.spad" 1976216 1976225 1977005 1977010) (-1149 "STBL.spad" 1974742 1974770 1974909 1974924) (-1148 "STAGG.spad" 1973817 1973828 1974732 1974737) (-1147 "STAGG.spad" 1972890 1972903 1973807 1973812) (-1146 "STACK.spad" 1972241 1972252 1972497 1972524) (-1145 "SREGSET.spad" 1969945 1969962 1971887 1971914) (-1144 "SRDCMPK.spad" 1968490 1968510 1969935 1969940) (-1143 "SRAGG.spad" 1963587 1963596 1968458 1968485) (-1142 "SRAGG.spad" 1958704 1958715 1963577 1963582) (-1141 "SQMATRIX.spad" 1956320 1956338 1957236 1957323) (-1140 "SPLTREE.spad" 1950872 1950885 1955756 1955783) (-1139 "SPLNODE.spad" 1947460 1947473 1950862 1950867) (-1138 "SPFCAT.spad" 1946237 1946246 1947450 1947455) (-1137 "SPECOUT.spad" 1944787 1944796 1946227 1946232) (-1136 "SPADXPT.spad" 1936926 1936935 1944777 1944782) (-1135 "spad-parser.spad" 1936391 1936400 1936916 1936921) (-1134 "SPADAST.spad" 1936092 1936101 1936381 1936386) (-1133 "SPACEC.spad" 1920105 1920116 1936082 1936087) (-1132 "SPACE3.spad" 1919881 1919892 1920095 1920100) (-1131 "SORTPAK.spad" 1919426 1919439 1919837 1919842) (-1130 "SOLVETRA.spad" 1917183 1917194 1919416 1919421) (-1129 "SOLVESER.spad" 1915703 1915714 1917173 1917178) (-1128 "SOLVERAD.spad" 1911713 1911724 1915693 1915698) (-1127 "SOLVEFOR.spad" 1910133 1910151 1911703 1911708) (-1126 "SNTSCAT.spad" 1909733 1909750 1910101 1910128) (-1125 "SMTS.spad" 1907993 1908019 1909298 1909395) (-1124 "SMP.spad" 1905468 1905488 1905858 1905985) (-1123 "SMITH.spad" 1904311 1904336 1905458 1905463) (-1122 "SMATCAT.spad" 1902421 1902451 1904255 1904306) (-1121 "SMATCAT.spad" 1900463 1900495 1902299 1902304) (-1120 "SKAGG.spad" 1899424 1899435 1900431 1900458) (-1119 "SINT.spad" 1898250 1898259 1899290 1899419) (-1118 "SIMPAN.spad" 1897978 1897987 1898240 1898245) (-1117 "SIG.spad" 1897306 1897315 1897968 1897973) (-1116 "SIGNRF.spad" 1896414 1896425 1897296 1897301) (-1115 "SIGNEF.spad" 1895683 1895700 1896404 1896409) (-1114 "SIGAST.spad" 1895064 1895073 1895673 1895678) (-1113 "SHP.spad" 1892982 1892997 1895020 1895025) (-1112 "SHDP.spad" 1882693 1882720 1883202 1883333) (-1111 "SGROUP.spad" 1882301 1882310 1882683 1882688) (-1110 "SGROUP.spad" 1881907 1881918 1882291 1882296) (-1109 "SGCF.spad" 1874788 1874797 1881897 1881902) (-1108 "SFRTCAT.spad" 1873716 1873733 1874756 1874783) (-1107 "SFRGCD.spad" 1872779 1872799 1873706 1873711) (-1106 "SFQCMPK.spad" 1867416 1867436 1872769 1872774) (-1105 "SFORT.spad" 1866851 1866865 1867406 1867411) (-1104 "SEXOF.spad" 1866694 1866734 1866841 1866846) (-1103 "SEX.spad" 1866586 1866595 1866684 1866689) (-1102 "SEXCAT.spad" 1864137 1864177 1866576 1866581) (-1101 "SET.spad" 1862437 1862448 1863558 1863597) (-1100 "SETMN.spad" 1860871 1860888 1862427 1862432) (-1099 "SETCAT.spad" 1860193 1860202 1860861 1860866) (-1098 "SETCAT.spad" 1859513 1859524 1860183 1860188) (-1097 "SETAGG.spad" 1856034 1856045 1859493 1859508) (-1096 "SETAGG.spad" 1852563 1852576 1856024 1856029) (-1095 "SEQAST.spad" 1852266 1852275 1852553 1852558) (-1094 "SEGXCAT.spad" 1851388 1851401 1852256 1852261) (-1093 "SEG.spad" 1851201 1851212 1851307 1851312) (-1092 "SEGCAT.spad" 1850108 1850119 1851191 1851196) (-1091 "SEGBIND.spad" 1849180 1849191 1850063 1850068) (-1090 "SEGBIND2.spad" 1848876 1848889 1849170 1849175) (-1089 "SEGAST.spad" 1848590 1848599 1848866 1848871) (-1088 "SEG2.spad" 1848015 1848028 1848546 1848551) (-1087 "SDVAR.spad" 1847291 1847302 1848005 1848010) (-1086 "SDPOL.spad" 1844717 1844728 1845008 1845135) (-1085 "SCPKG.spad" 1842796 1842807 1844707 1844712) (-1084 "SCOPE.spad" 1841945 1841954 1842786 1842791) (-1083 "SCACHE.spad" 1840627 1840638 1841935 1841940) (-1082 "SASTCAT.spad" 1840536 1840545 1840617 1840622) (-1081 "SAOS.spad" 1840408 1840417 1840526 1840531) (-1080 "SAERFFC.spad" 1840121 1840141 1840398 1840403) (-1079 "SAE.spad" 1838296 1838312 1838907 1839042) (-1078 "SAEFACT.spad" 1837997 1838017 1838286 1838291) (-1077 "RURPK.spad" 1835638 1835654 1837987 1837992) (-1076 "RULESET.spad" 1835079 1835103 1835628 1835633) (-1075 "RULE.spad" 1833283 1833307 1835069 1835074) (-1074 "RULECOLD.spad" 1833135 1833148 1833273 1833278) (-1073 "RTVALUE.spad" 1832868 1832877 1833125 1833130) (-1072 "RSTRCAST.spad" 1832585 1832594 1832858 1832863) (-1071 "RSETGCD.spad" 1828963 1828983 1832575 1832580) (-1070 "RSETCAT.spad" 1818747 1818764 1828931 1828958) (-1069 "RSETCAT.spad" 1808551 1808570 1818737 1818742) (-1068 "RSDCMPK.spad" 1807003 1807023 1808541 1808546) (-1067 "RRCC.spad" 1805387 1805417 1806993 1806998) (-1066 "RRCC.spad" 1803769 1803801 1805377 1805382) (-1065 "RPTAST.spad" 1803471 1803480 1803759 1803764) (-1064 "RPOLCAT.spad" 1782831 1782846 1803339 1803466) (-1063 "RPOLCAT.spad" 1761905 1761922 1782415 1782420) (-1062 "ROUTINE.spad" 1757768 1757777 1760552 1760579) (-1061 "ROMAN.spad" 1757096 1757105 1757634 1757763) (-1060 "ROIRC.spad" 1756176 1756208 1757086 1757091) (-1059 "RNS.spad" 1755079 1755088 1756078 1756171) (-1058 "RNS.spad" 1754068 1754079 1755069 1755074) (-1057 "RNG.spad" 1753803 1753812 1754058 1754063) (-1056 "RMODULE.spad" 1753568 1753579 1753793 1753798) (-1055 "RMCAT2.spad" 1752976 1753033 1753558 1753563) (-1054 "RMATRIX.spad" 1751800 1751819 1752143 1752182) (-1053 "RMATCAT.spad" 1747333 1747364 1751756 1751795) (-1052 "RMATCAT.spad" 1742756 1742789 1747181 1747186) (-1051 "RLINSET.spad" 1742150 1742161 1742746 1742751) (-1050 "RINTERP.spad" 1742038 1742058 1742140 1742145) (-1049 "RING.spad" 1741508 1741517 1742018 1742033) (-1048 "RING.spad" 1740986 1740997 1741498 1741503) (-1047 "RIDIST.spad" 1740370 1740379 1740976 1740981) (-1046 "RGCHAIN.spad" 1738949 1738965 1739855 1739882) (-1045 "RGBCSPC.spad" 1738730 1738742 1738939 1738944) (-1044 "RGBCMDL.spad" 1738260 1738272 1738720 1738725) (-1043 "RF.spad" 1735874 1735885 1738250 1738255) (-1042 "RFFACTOR.spad" 1735336 1735347 1735864 1735869) (-1041 "RFFACT.spad" 1735071 1735083 1735326 1735331) (-1040 "RFDIST.spad" 1734059 1734068 1735061 1735066) (-1039 "RETSOL.spad" 1733476 1733489 1734049 1734054) (-1038 "RETRACT.spad" 1732904 1732915 1733466 1733471) (-1037 "RETRACT.spad" 1732330 1732343 1732894 1732899) (-1036 "RETAST.spad" 1732142 1732151 1732320 1732325) (-1035 "RESULT.spad" 1730202 1730211 1730789 1730816) (-1034 "RESRING.spad" 1729549 1729596 1730140 1730197) (-1033 "RESLATC.spad" 1728873 1728884 1729539 1729544) (-1032 "REPSQ.spad" 1728602 1728613 1728863 1728868) (-1031 "REP.spad" 1726154 1726163 1728592 1728597) (-1030 "REPDB.spad" 1725859 1725870 1726144 1726149) (-1029 "REP2.spad" 1715431 1715442 1725701 1725706) (-1028 "REP1.spad" 1709421 1709432 1715381 1715386) (-1027 "REGSET.spad" 1707218 1707235 1709067 1709094) (-1026 "REF.spad" 1706547 1706558 1707173 1707178) (-1025 "REDORDER.spad" 1705723 1705740 1706537 1706542) (-1024 "RECLOS.spad" 1704506 1704526 1705210 1705303) (-1023 "REALSOLV.spad" 1703638 1703647 1704496 1704501) (-1022 "REAL.spad" 1703510 1703519 1703628 1703633) (-1021 "REAL0Q.spad" 1700792 1700807 1703500 1703505) (-1020 "REAL0.spad" 1697620 1697635 1700782 1700787) (-1019 "RDUCEAST.spad" 1697341 1697350 1697610 1697615) (-1018 "RDIV.spad" 1696992 1697017 1697331 1697336) (-1017 "RDIST.spad" 1696555 1696566 1696982 1696987) (-1016 "RDETRS.spad" 1695351 1695369 1696545 1696550) (-1015 "RDETR.spad" 1693458 1693476 1695341 1695346) (-1014 "RDEEFS.spad" 1692531 1692548 1693448 1693453) (-1013 "RDEEF.spad" 1691527 1691544 1692521 1692526) (-1012 "RCFIELD.spad" 1688713 1688722 1691429 1691522) (-1011 "RCFIELD.spad" 1685985 1685996 1688703 1688708) (-1010 "RCAGG.spad" 1683897 1683908 1685975 1685980) (-1009 "RCAGG.spad" 1681736 1681749 1683816 1683821) (-1008 "RATRET.spad" 1681096 1681107 1681726 1681731) (-1007 "RATFACT.spad" 1680788 1680800 1681086 1681091) (-1006 "RANDSRC.spad" 1680107 1680116 1680778 1680783) (-1005 "RADUTIL.spad" 1679861 1679870 1680097 1680102) (-1004 "RADIX.spad" 1676762 1676776 1678328 1678421) (-1003 "RADFF.spad" 1675175 1675212 1675294 1675450) (-1002 "RADCAT.spad" 1674768 1674777 1675165 1675170) (-1001 "RADCAT.spad" 1674359 1674370 1674758 1674763) (-1000 "QUEUE.spad" 1673701 1673712 1673966 1673993) (-999 "QUAT.spad" 1672283 1672293 1672625 1672690) (-998 "QUATCT2.spad" 1671902 1671920 1672273 1672278) (-997 "QUATCAT.spad" 1670067 1670077 1671832 1671897) (-996 "QUATCAT.spad" 1667983 1667995 1669750 1669755) (-995 "QUAGG.spad" 1666809 1666819 1667951 1667978) (-994 "QQUTAST.spad" 1666578 1666586 1666799 1666804) (-993 "QFORM.spad" 1666041 1666055 1666568 1666573) (-992 "QFCAT.spad" 1664744 1664754 1665943 1666036) (-991 "QFCAT.spad" 1663038 1663050 1664239 1664244) (-990 "QFCAT2.spad" 1662729 1662745 1663028 1663033) (-989 "QEQUAT.spad" 1662286 1662294 1662719 1662724) (-988 "QCMPACK.spad" 1657033 1657052 1662276 1662281) (-987 "QALGSET.spad" 1653108 1653140 1656947 1656952) (-986 "QALGSET2.spad" 1651104 1651122 1653098 1653103) (-985 "PWFFINTB.spad" 1648414 1648435 1651094 1651099) (-984 "PUSHVAR.spad" 1647743 1647762 1648404 1648409) (-983 "PTRANFN.spad" 1643869 1643879 1647733 1647738) (-982 "PTPACK.spad" 1640957 1640967 1643859 1643864) (-981 "PTFUNC2.spad" 1640778 1640792 1640947 1640952) (-980 "PTCAT.spad" 1640027 1640037 1640746 1640773) (-979 "PSQFR.spad" 1639334 1639358 1640017 1640022) (-978 "PSEUDLIN.spad" 1638192 1638202 1639324 1639329) (-977 "PSETPK.spad" 1623625 1623641 1638070 1638075) (-976 "PSETCAT.spad" 1617545 1617568 1623605 1623620) (-975 "PSETCAT.spad" 1611439 1611464 1617501 1617506) (-974 "PSCURVE.spad" 1610422 1610430 1611429 1611434) (-973 "PSCAT.spad" 1609189 1609218 1610320 1610417) (-972 "PSCAT.spad" 1608046 1608077 1609179 1609184) (-971 "PRTITION.spad" 1606991 1606999 1608036 1608041) (-970 "PRTDAST.spad" 1606710 1606718 1606981 1606986) (-969 "PRS.spad" 1596272 1596289 1606666 1606671) (-968 "PRQAGG.spad" 1595703 1595713 1596240 1596267) (-967 "PROPLOG.spad" 1594998 1595006 1595693 1595698) (-966 "PROPFRML.spad" 1593806 1593817 1594988 1594993) (-965 "PROPERTY.spad" 1593292 1593300 1593796 1593801) (-964 "PRODUCT.spad" 1590972 1590984 1591258 1591313) (-963 "PR.spad" 1589358 1589370 1590063 1590190) (-962 "PRINT.spad" 1589110 1589118 1589348 1589353) (-961 "PRIMES.spad" 1587361 1587371 1589100 1589105) (-960 "PRIMELT.spad" 1585342 1585356 1587351 1587356) (-959 "PRIMCAT.spad" 1584965 1584973 1585332 1585337) (-958 "PRIMARR.spad" 1583970 1583980 1584148 1584175) (-957 "PRIMARR2.spad" 1582693 1582705 1583960 1583965) (-956 "PREASSOC.spad" 1582065 1582077 1582683 1582688) (-955 "PPCURVE.spad" 1581202 1581210 1582055 1582060) (-954 "PORTNUM.spad" 1580977 1580985 1581192 1581197) (-953 "POLYROOT.spad" 1579806 1579828 1580933 1580938) (-952 "POLY.spad" 1577139 1577149 1577656 1577783) (-951 "POLYLIFT.spad" 1576400 1576423 1577129 1577134) (-950 "POLYCATQ.spad" 1574502 1574524 1576390 1576395) (-949 "POLYCAT.spad" 1567908 1567929 1574370 1574497) (-948 "POLYCAT.spad" 1560652 1560675 1567116 1567121) (-947 "POLY2UP.spad" 1560100 1560114 1560642 1560647) (-946 "POLY2.spad" 1559695 1559707 1560090 1560095) (-945 "POLUTIL.spad" 1558636 1558665 1559651 1559656) (-944 "POLTOPOL.spad" 1557384 1557399 1558626 1558631) (-943 "POINT.spad" 1556222 1556232 1556309 1556336) (-942 "PNTHEORY.spad" 1552888 1552896 1556212 1556217) (-941 "PMTOOLS.spad" 1551645 1551659 1552878 1552883) (-940 "PMSYM.spad" 1551190 1551200 1551635 1551640) (-939 "PMQFCAT.spad" 1550777 1550791 1551180 1551185) (-938 "PMPRED.spad" 1550246 1550260 1550767 1550772) (-937 "PMPREDFS.spad" 1549690 1549712 1550236 1550241) (-936 "PMPLCAT.spad" 1548760 1548778 1549622 1549627) (-935 "PMLSAGG.spad" 1548341 1548355 1548750 1548755) (-934 "PMKERNEL.spad" 1547908 1547920 1548331 1548336) (-933 "PMINS.spad" 1547484 1547494 1547898 1547903) (-932 "PMFS.spad" 1547057 1547075 1547474 1547479) (-931 "PMDOWN.spad" 1546343 1546357 1547047 1547052) (-930 "PMASS.spad" 1545351 1545359 1546333 1546338) (-929 "PMASSFS.spad" 1544316 1544332 1545341 1545346) (-928 "PLOTTOOL.spad" 1544096 1544104 1544306 1544311) (-927 "PLOT.spad" 1538927 1538935 1544086 1544091) (-926 "PLOT3D.spad" 1535347 1535355 1538917 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1455345 1455350) (-887 "PATMATCH.spad" 1453174 1453205 1454725 1454730) (-886 "PATMAB.spad" 1452599 1452609 1453164 1453169) (-885 "PATLRES.spad" 1451683 1451697 1452589 1452594) (-884 "PATAB.spad" 1451447 1451457 1451673 1451678) (-883 "PARTPERM.spad" 1448809 1448817 1451437 1451442) (-882 "PARSURF.spad" 1448237 1448265 1448799 1448804) (-881 "PARSU2.spad" 1448032 1448048 1448227 1448232) (-880 "script-parser.spad" 1447552 1447560 1448022 1448027) (-879 "PARSCURV.spad" 1446980 1447008 1447542 1447547) (-878 "PARSC2.spad" 1446769 1446785 1446970 1446975) (-877 "PARPCURV.spad" 1446227 1446255 1446759 1446764) (-876 "PARPC2.spad" 1446016 1446032 1446217 1446222) (-875 "PAN2EXPR.spad" 1445428 1445436 1446006 1446011) (-874 "PALETTE.spad" 1444398 1444406 1445418 1445423) (-873 "PAIR.spad" 1443381 1443394 1443986 1443991) (-872 "PADICRC.spad" 1440711 1440729 1441886 1441979) (-871 "PADICRAT.spad" 1438726 1438738 1438947 1439040) (-870 "PADIC.spad" 1438421 1438433 1438652 1438721) (-869 "PADICCT.spad" 1436962 1436974 1438347 1438416) (-868 "PADEPAC.spad" 1435641 1435660 1436952 1436957) (-867 "PADE.spad" 1434381 1434397 1435631 1435636) (-866 "OWP.spad" 1433621 1433651 1434239 1434306) (-865 "OVERSET.spad" 1433194 1433202 1433611 1433616) (-864 "OVAR.spad" 1432975 1432998 1433184 1433189) (-863 "OUT.spad" 1432059 1432067 1432965 1432970) (-862 "OUTFORM.spad" 1421355 1421363 1432049 1432054) (-861 "OUTBFILE.spad" 1420773 1420781 1421345 1421350) (-860 "OUTBCON.spad" 1419771 1419779 1420763 1420768) (-859 "OUTBCON.spad" 1418767 1418777 1419761 1419766) (-858 "OSI.spad" 1418242 1418250 1418757 1418762) (-857 "OSGROUP.spad" 1418160 1418168 1418232 1418237) (-856 "ORTHPOL.spad" 1416621 1416631 1418077 1418082) (-855 "OREUP.spad" 1416074 1416102 1416301 1416340) (-854 "ORESUP.spad" 1415373 1415397 1415754 1415793) (-853 "OREPCTO.spad" 1413192 1413204 1415293 1415298) (-852 "OREPCAT.spad" 1407249 1407259 1413148 1413187) (-851 "OREPCAT.spad" 1401196 1401208 1407097 1407102) (-850 "ORDSET.spad" 1400362 1400370 1401186 1401191) (-849 "ORDSET.spad" 1399526 1399536 1400352 1400357) (-848 "ORDRING.spad" 1398916 1398924 1399506 1399521) (-847 "ORDRING.spad" 1398314 1398324 1398906 1398911) (-846 "ORDMON.spad" 1398169 1398177 1398304 1398309) (-845 "ORDFUNS.spad" 1397295 1397311 1398159 1398164) (-844 "ORDFIN.spad" 1397115 1397123 1397285 1397290) (-843 "ORDCOMP.spad" 1395580 1395590 1396662 1396691) (-842 "ORDCOMP2.spad" 1394865 1394877 1395570 1395575) (-841 "OPTPROB.spad" 1393503 1393511 1394855 1394860) (-840 "OPTPACK.spad" 1385888 1385896 1393493 1393498) (-839 "OPTCAT.spad" 1383563 1383571 1385878 1385883) (-838 "OPSIG.spad" 1383215 1383223 1383553 1383558) (-837 "OPQUERY.spad" 1382764 1382772 1383205 1383210) (-836 "OP.spad" 1382506 1382516 1382586 1382653) (-835 "OPERCAT.spad" 1381970 1381980 1382496 1382501) (-834 "OPERCAT.spad" 1381432 1381444 1381960 1381965) (-833 "ONECOMP.spad" 1380177 1380187 1380979 1381008) (-832 "ONECOMP2.spad" 1379595 1379607 1380167 1380172) (-831 "OMSERVER.spad" 1378597 1378605 1379585 1379590) (-830 "OMSAGG.spad" 1378385 1378395 1378553 1378592) (-829 "OMPKG.spad" 1376997 1377005 1378375 1378380) (-828 "OM.spad" 1375962 1375970 1376987 1376992) (-827 "OMLO.spad" 1375387 1375399 1375848 1375887) (-826 "OMEXPR.spad" 1375221 1375231 1375377 1375382) (-825 "OMERR.spad" 1374764 1374772 1375211 1375216) (-824 "OMERRK.spad" 1373798 1373806 1374754 1374759) (-823 "OMENC.spad" 1373142 1373150 1373788 1373793) (-822 "OMDEV.spad" 1367431 1367439 1373132 1373137) (-821 "OMCONN.spad" 1366840 1366848 1367421 1367426) (-820 "OINTDOM.spad" 1366603 1366611 1366766 1366835) (-819 "OFMONOID.spad" 1362790 1362800 1366593 1366598) (-818 "ODVAR.spad" 1362051 1362061 1362780 1362785) (-817 "ODR.spad" 1361695 1361721 1361863 1362012) (-816 "ODPOL.spad" 1359077 1359087 1359417 1359544) (-815 "ODP.spad" 1348924 1348944 1349297 1349428) (-814 "ODETOOLS.spad" 1347507 1347526 1348914 1348919) (-813 "ODESYS.spad" 1345157 1345174 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1300470 1300637 1300642) (-793 "OAMONS.spad" 1299982 1299990 1300452 1300457) (-792 "OAMON.spad" 1299843 1299851 1299972 1299977) (-791 "OAGROUP.spad" 1299705 1299713 1299833 1299838) (-790 "NUMTUBE.spad" 1299292 1299308 1299695 1299700) (-789 "NUMQUAD.spad" 1287154 1287162 1299282 1299287) (-788 "NUMODE.spad" 1278290 1278298 1287144 1287149) (-787 "NUMINT.spad" 1275848 1275856 1278280 1278285) (-786 "NUMFMT.spad" 1274688 1274696 1275838 1275843) (-785 "NUMERIC.spad" 1266760 1266770 1274493 1274498) (-784 "NTSCAT.spad" 1265262 1265278 1266728 1266755) (-783 "NTPOLFN.spad" 1264807 1264817 1265179 1265184) (-782 "NSUP.spad" 1257853 1257863 1262393 1262546) (-781 "NSUP2.spad" 1257245 1257257 1257843 1257848) (-780 "NSMP.spad" 1253476 1253495 1253784 1253911) (-779 "NREP.spad" 1251848 1251862 1253466 1253471) (-778 "NPCOEF.spad" 1251094 1251114 1251838 1251843) (-777 "NORMRETR.spad" 1250692 1250731 1251084 1251089) (-776 "NORMPK.spad" 1248594 1248613 1250682 1250687) (-775 "NORMMA.spad" 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"MSET.spad" 1153422 1153432 1155186 1155225) (-736 "MSETAGG.spad" 1153267 1153277 1153390 1153417) (-735 "MRING.spad" 1150238 1150250 1152975 1153042) (-734 "MRF2.spad" 1149806 1149820 1150228 1150233) (-733 "MRATFAC.spad" 1149352 1149369 1149796 1149801) (-732 "MPRFF.spad" 1147382 1147401 1149342 1149347) (-731 "MPOLY.spad" 1144853 1144868 1145212 1145339) (-730 "MPCPF.spad" 1144117 1144136 1144843 1144848) (-729 "MPC3.spad" 1143932 1143972 1144107 1144112) (-728 "MPC2.spad" 1143574 1143607 1143922 1143927) (-727 "MONOTOOL.spad" 1141909 1141926 1143564 1143569) (-726 "MONOID.spad" 1141228 1141236 1141899 1141904) (-725 "MONOID.spad" 1140545 1140555 1141218 1141223) (-724 "MONOGEN.spad" 1139291 1139304 1140405 1140540) (-723 "MONOGEN.spad" 1138059 1138074 1139175 1139180) (-722 "MONADWU.spad" 1136073 1136081 1138049 1138054) (-721 "MONADWU.spad" 1134085 1134095 1136063 1136068) (-720 "MONAD.spad" 1133229 1133237 1134075 1134080) (-719 "MONAD.spad" 1132371 1132381 1133219 1133224) (-718 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1116679) (-699 "MFLOAT.spad" 1113701 1113709 1115075 1115180) (-698 "MFINFACT.spad" 1113101 1113123 1113691 1113696) (-697 "MESH.spad" 1110833 1110841 1113091 1113096) (-696 "MDDFACT.spad" 1109026 1109036 1110823 1110828) (-695 "MDAGG.spad" 1108313 1108323 1109006 1109021) (-694 "MCMPLX.spad" 1104324 1104332 1104938 1105139) (-693 "MCDEN.spad" 1103532 1103544 1104314 1104319) (-692 "MCALCFN.spad" 1100634 1100660 1103522 1103527) (-691 "MAYBE.spad" 1099918 1099929 1100624 1100629) (-690 "MATSTOR.spad" 1097194 1097204 1099908 1099913) (-689 "MATRIX.spad" 1095898 1095908 1096382 1096409) (-688 "MATLIN.spad" 1093224 1093248 1095782 1095787) (-687 "MATCAT.spad" 1084809 1084831 1093192 1093219) (-686 "MATCAT.spad" 1076266 1076290 1084651 1084656) (-685 "MATCAT2.spad" 1075534 1075582 1076256 1076261) (-684 "MAPPKG3.spad" 1074433 1074447 1075524 1075529) (-683 "MAPPKG2.spad" 1073767 1073779 1074423 1074428) (-682 "MAPPKG1.spad" 1072585 1072595 1073757 1073762) (-681 "MAPPAST.spad" 1071898 1071906 1072575 1072580) (-680 "MAPHACK3.spad" 1071706 1071720 1071888 1071893) (-679 "MAPHACK2.spad" 1071471 1071483 1071696 1071701) (-678 "MAPHACK1.spad" 1071101 1071111 1071461 1071466) (-677 "MAGMA.spad" 1068891 1068908 1071091 1071096) (-676 "MACROAST.spad" 1068470 1068478 1068881 1068886) (-675 "M3D.spad" 1066166 1066176 1067848 1067853) (-674 "LZSTAGG.spad" 1063394 1063404 1066156 1066161) (-673 "LZSTAGG.spad" 1060620 1060632 1063384 1063389) (-672 "LWORD.spad" 1057325 1057342 1060610 1060615) (-671 "LSTAST.spad" 1057109 1057117 1057315 1057320) (-670 "LSQM.spad" 1055335 1055349 1055733 1055784) (-669 "LSPP.spad" 1054868 1054885 1055325 1055330) (-668 "LSMP.spad" 1053708 1053736 1054858 1054863) (-667 "LSMP1.spad" 1051512 1051526 1053698 1053703) (-666 "LSAGG.spad" 1051181 1051191 1051480 1051507) (-665 "LSAGG.spad" 1050870 1050882 1051171 1051176) (-664 "LPOLY.spad" 1049824 1049843 1050726 1050795) (-663 "LPEFRAC.spad" 1049081 1049091 1049814 1049819) (-662 "LO.spad" 1048482 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523207) (-337 "FDIVCAT.spad" 520696 520720 522644 522649) (-336 "FDIVCAT.spad" 518736 518762 520686 520691) (-335 "FDIV2.spad" 518390 518430 518726 518731) (-334 "FCTRDATA.spad" 517422 517430 518380 518385) (-333 "FCPAK1.spad" 515975 515983 517412 517417) (-332 "FCOMP.spad" 515354 515364 515965 515970) (-331 "FC.spad" 505269 505277 515344 515349) (-330 "FAXF.spad" 498204 498218 505171 505264) (-329 "FAXF.spad" 491191 491207 498160 498165) (-328 "FARRAY.spad" 489337 489347 490374 490401) (-327 "FAMR.spad" 487457 487469 489235 489332) (-326 "FAMR.spad" 485561 485575 487341 487346) (-325 "FAMONOID.spad" 485211 485221 485515 485520) (-324 "FAMONC.spad" 483433 483445 485201 485206) (-323 "FAGROUP.spad" 483039 483049 483329 483356) (-322 "FACUTIL.spad" 481235 481252 483029 483034) (-321 "FACTFUNC.spad" 480411 480421 481225 481230) (-320 "EXPUPXS.spad" 477244 477267 478543 478692) (-319 "EXPRTUBE.spad" 474472 474480 477234 477239) (-318 "EXPRODE.spad" 471344 471360 474462 474467) (-317 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424188 424193) (-296 "EQTBL.spad" 419991 420013 420200 420227) (-295 "EQ.spad" 414784 414794 417583 417695) (-294 "EQ2.spad" 414500 414512 414774 414779) (-293 "EP.spad" 410814 410824 414490 414495) (-292 "ENV.spad" 409466 409474 410804 410809) (-291 "ENTIRER.spad" 409134 409142 409410 409461) (-290 "EMR.spad" 408335 408376 409060 409129) (-289 "ELTAGG.spad" 406575 406594 408325 408330) (-288 "ELTAGG.spad" 404779 404800 406531 406536) (-287 "ELTAB.spad" 404226 404244 404769 404774) (-286 "ELFUTS.spad" 403605 403624 404216 404221) (-285 "ELEMFUN.spad" 403294 403302 403595 403600) (-284 "ELEMFUN.spad" 402981 402991 403284 403289) (-283 "ELAGG.spad" 400924 400934 402961 402976) (-282 "ELAGG.spad" 398804 398816 400843 400848) (-281 "ELABEXPR.spad" 397727 397735 398794 398799) (-280 "EFUPXS.spad" 394503 394533 397683 397688) (-279 "EFULS.spad" 391339 391362 394459 394464) (-278 "EFSTRUC.spad" 389294 389310 391329 391334) (-277 "EF.spad" 384060 384076 389284 389289) (-276 "EAB.spad" 382336 382344 384050 384055) (-275 "E04UCFA.spad" 381872 381880 382326 382331) (-274 "E04NAFA.spad" 381449 381457 381862 381867) (-273 "E04MBFA.spad" 381029 381037 381439 381444) (-272 "E04JAFA.spad" 380565 380573 381019 381024) (-271 "E04GCFA.spad" 380101 380109 380555 380560) (-270 "E04FDFA.spad" 379637 379645 380091 380096) (-269 "E04DGFA.spad" 379173 379181 379627 379632) (-268 "E04AGNT.spad" 375015 375023 379163 379168) (-267 "DVARCAT.spad" 371700 371710 375005 375010) (-266 "DVARCAT.spad" 368383 368395 371690 371695) (-265 "DSMP.spad" 365850 365864 366155 366282) (-264 "DROPT.spad" 359795 359803 365840 365845) (-263 "DROPT1.spad" 359458 359468 359785 359790) (-262 "DROPT0.spad" 354285 354293 359448 359453) (-261 "DRAWPT.spad" 352440 352448 354275 354280) (-260 "DRAW.spad" 345040 345053 352430 352435) (-259 "DRAWHACK.spad" 344348 344358 345030 345035) (-258 "DRAWCX.spad" 341790 341798 344338 344343) (-257 "DRAWCURV.spad" 341327 341342 341780 341785) (-256 "DRAWCFUN.spad" 330499 330507 341317 341322) (-255 "DQAGG.spad" 328667 328677 330467 330494) (-254 "DPOLCAT.spad" 324008 324024 328535 328662) (-253 "DPOLCAT.spad" 319435 319453 323964 323969) (-252 "DPMO.spad" 311661 311677 311799 312100) (-251 "DPMM.spad" 303900 303918 304025 304326) (-250 "DOMTMPLT.spad" 303560 303568 303890 303895) (-249 "DOMCTOR.spad" 303315 303323 303550 303555) (-248 "DOMAIN.spad" 302446 302454 303305 303310) (-247 "DMP.spad" 299704 299719 300276 300403) (-246 "DLP.spad" 299052 299062 299694 299699) (-245 "DLIST.spad" 297631 297641 298235 298262) (-244 "DLAGG.spad" 296042 296052 297621 297626) (-243 "DIVRING.spad" 295584 295592 295986 296037) (-242 "DIVRING.spad" 295170 295180 295574 295579) (-241 "DISPLAY.spad" 293350 293358 295160 295165) (-240 "DIRPROD.spad" 282930 282946 283570 283701) (-239 "DIRPROD2.spad" 281738 281756 282920 282925) (-238 "DIRPCAT.spad" 280680 280696 281602 281733) (-237 "DIRPCAT.spad" 279351 279369 280275 280280) (-236 "DIOSP.spad" 278176 278184 279341 279346) (-235 "DIOPS.spad" 277160 277170 278156 278171) (-234 "DIOPS.spad" 276118 276130 277116 277121) (-233 "DIFRING.spad" 275410 275418 276098 276113) (-232 "DIFRING.spad" 274710 274720 275400 275405) (-231 "DIFEXT.spad" 273869 273879 274690 274705) (-230 "DIFEXT.spad" 272945 272957 273768 273773) (-229 "DIAGG.spad" 272575 272585 272925 272940) (-228 "DIAGG.spad" 272213 272225 272565 272570) (-227 "DHMATRIX.spad" 270517 270527 271670 271697) (-226 "DFSFUN.spad" 263925 263933 270507 270512) (-225 "DFLOAT.spad" 260646 260654 263815 263920) (-224 "DFINTTLS.spad" 258855 258871 260636 260641) (-223 "DERHAM.spad" 256765 256797 258835 258850) (-222 "DEQUEUE.spad" 256083 256093 256372 256399) (-221 "DEGRED.spad" 255698 255712 256073 256078) (-220 "DEFINTRF.spad" 253223 253233 255688 255693) (-219 "DEFINTEF.spad" 251719 251735 253213 253218) (-218 "DEFAST.spad" 251087 251095 251709 251714) (-217 "DECIMAL.spad" 249193 249201 249554 249647) (-216 "DDFACT.spad" 246992 247009 249183 249188) (-215 "DBLRESP.spad" 246590 246614 246982 246987) (-214 "DBASE.spad" 245244 245254 246580 246585) (-213 "DATAARY.spad" 244706 244719 245234 245239) (-212 "D03FAFA.spad" 244534 244542 244696 244701) (-211 "D03EEFA.spad" 244354 244362 244524 244529) (-210 "D03AGNT.spad" 243434 243442 244344 244349) (-209 "D02EJFA.spad" 242896 242904 243424 243429) (-208 "D02CJFA.spad" 242374 242382 242886 242891) (-207 "D02BHFA.spad" 241864 241872 242364 242369) (-206 "D02BBFA.spad" 241354 241362 241854 241859) (-205 "D02AGNT.spad" 236158 236166 241344 241349) (-204 "D01WGTS.spad" 234477 234485 236148 236153) (-203 "D01TRNS.spad" 234454 234462 234467 234472) (-202 "D01GBFA.spad" 233976 233984 234444 234449) (-201 "D01FCFA.spad" 233498 233506 233966 233971) (-200 "D01ASFA.spad" 232966 232974 233488 233493) (-199 "D01AQFA.spad" 232412 232420 232956 232961) (-198 "D01APFA.spad" 231836 231844 232402 232407) (-197 "D01ANFA.spad" 231330 231338 231826 231831) (-196 "D01AMFA.spad" 230840 230848 231320 231325) (-195 "D01ALFA.spad" 230380 230388 230830 230835) (-194 "D01AKFA.spad" 229906 229914 230370 230375) (-193 "D01AJFA.spad" 229429 229437 229896 229901) (-192 "D01AGNT.spad" 225488 225496 229419 229424) (-191 "CYCLOTOM.spad" 224994 225002 225478 225483) (-190 "CYCLES.spad" 221826 221834 224984 224989) (-189 "CVMP.spad" 221243 221253 221816 221821) (-188 "CTRIGMNP.spad" 219733 219749 221233 221238) (-187 "CTOR.spad" 219424 219432 219723 219728) (-186 "CTORKIND.spad" 219027 219035 219414 219419) (-185 "CTORCAT.spad" 218276 218284 219017 219022) (-184 "CTORCAT.spad" 217523 217533 218266 218271) (-183 "CTORCALL.spad" 217103 217111 217513 217518) (-182 "CSTTOOLS.spad" 216346 216359 217093 217098) (-181 "CRFP.spad" 210050 210063 216336 216341) (-180 "CRCEAST.spad" 209770 209778 210040 210045) (-179 "CRAPACK.spad" 208813 208823 209760 209765) (-178 "CPMATCH.spad" 208313 208328 208738 208743) (-177 "CPIMA.spad" 208018 208037 208303 208308) (-176 "COORDSYS.spad" 202911 202921 208008 208013) (-175 "CONTOUR.spad" 202318 202326 202901 202906) (-174 "CONTFRAC.spad" 197930 197940 202220 202313) (-173 "CONDUIT.spad" 197688 197696 197920 197925) (-172 "COMRING.spad" 197362 197370 197626 197683) (-171 "COMPPROP.spad" 196876 196884 197352 197357) (-170 "COMPLPAT.spad" 196643 196658 196866 196871) (-169 "COMPLEX.spad" 190780 190790 191024 191285) (-168 "COMPLEX2.spad" 190493 190505 190770 190775) (-167 "COMPFACT.spad" 190095 190109 190483 190488) (-166 "COMPCAT.spad" 188163 188173 189829 190090) (-165 "COMPCAT.spad" 185959 185971 187627 187632) (-164 "COMMUPC.spad" 185705 185723 185949 185954) (-163 "COMMONOP.spad" 185238 185246 185695 185700) (-162 "COMM.spad" 185047 185055 185228 185233) (-161 "COMMAAST.spad" 184810 184818 185037 185042) (-160 "COMBOPC.spad" 183715 183723 184800 184805) (-159 "COMBINAT.spad" 182460 182470 183705 183710) (-158 "COMBF.spad" 179828 179844 182450 182455) (-157 "COLOR.spad" 178665 178673 179818 179823) (-156 "COLONAST.spad" 178331 178339 178655 178660) (-155 "CMPLXRT.spad" 178040 178057 178321 178326) (-154 "CLLCTAST.spad" 177702 177710 178030 178035) (-153 "CLIP.spad" 173794 173802 177692 177697) (-152 "CLIF.spad" 172433 172449 173750 173789) (-151 "CLAGG.spad" 168918 168928 172423 172428) (-150 "CLAGG.spad" 165274 165286 168781 168786) (-149 "CINTSLPE.spad" 164599 164612 165264 165269) (-148 "CHVAR.spad" 162677 162699 164589 164594) (-147 "CHARZ.spad" 162592 162600 162657 162672) (-146 "CHARPOL.spad" 162100 162110 162582 162587) (-145 "CHARNZ.spad" 161853 161861 162080 162095) (-144 "CHAR.spad" 159721 159729 161843 161848) (-143 "CFCAT.spad" 159037 159045 159711 159716) (-142 "CDEN.spad" 158195 158209 159027 159032) (-141 "CCLASS.spad" 156344 156352 157606 157645) (-140 "CATEGORY.spad" 155434 155442 156334 156339) (-139 "CATCTOR.spad" 155325 155333 155424 155429) (-138 "CATAST.spad" 154943 154951 155315 155320) (-137 "CASEAST.spad" 154657 154665 154933 154938) (-136 "CARTEN.spad" 149760 149784 154647 154652) (-135 "CARTEN2.spad" 149146 149173 149750 149755) (-134 "CARD.spad" 146435 146443 149120 149141) (-133 "CAPSLAST.spad" 146209 146217 146425 146430) (-132 "CACHSET.spad" 145831 145839 146199 146204) (-131 "CABMON.spad" 145384 145392 145821 145826) (-130 "BYTEORD.spad" 145059 145067 145374 145379) (-129 "BYTE.spad" 144484 144492 145049 145054) (-128 "BYTEBUF.spad" 142341 142349 143653 143680) (-127 "BTREE.spad" 141410 141420 141948 141975) (-126 "BTOURN.spad" 140413 140423 141017 141044) (-125 "BTCAT.spad" 139801 139811 140381 140408) (-124 "BTCAT.spad" 139209 139221 139791 139796) (-123 "BTAGG.spad" 138331 138339 139177 139204) (-122 "BTAGG.spad" 137473 137483 138321 138326) (-121 "BSTREE.spad" 136208 136218 137080 137107) (-120 "BRILL.spad" 134403 134414 136198 136203) (-119 "BRAGG.spad" 133327 133337 134393 134398) (-118 "BRAGG.spad" 132215 132227 133283 133288) (-117 "BPADICRT.spad" 130196 130208 130451 130544) (-116 "BPADIC.spad" 129860 129872 130122 130191) (-115 "BOUNDZRO.spad" 129516 129533 129850 129855) (-114 "BOP.spad" 124640 124648 129506 129511) (-113 "BOP1.spad" 122060 122070 124630 124635) (-112 "BOOLEAN.spad" 121492 121500 122050 122055) (-111 "BMODULE.spad" 121204 121216 121460 121487) (-110 "BITS.spad" 120623 120631 120840 120867) (-109 "BINDING.spad" 120034 120042 120613 120618) (-108 "BINARY.spad" 118145 118153 118501 118594) (-107 "BGAGG.spad" 117342 117352 118125 118140) (-106 "BGAGG.spad" 116547 116559 117332 117337) (-105 "BFUNCT.spad" 116111 116119 116527 116542) (-104 "BEZOUT.spad" 115245 115272 116061 116066) (-103 "BBTREE.spad" 112064 112074 114852 114879) (-102 "BASTYPE.spad" 111736 111744 112054 112059) (-101 "BASTYPE.spad" 111406 111416 111726 111731) (-100 "BALFACT.spad" 110845 110858 111396 111401) (-99 "AUTOMOR.spad" 110292 110301 110825 110840) (-98 "ATTREG.spad" 107011 107018 110044 110287) (-97 "ATTRBUT.spad" 103034 103041 106991 107006) (-96 "ATTRAST.spad" 102751 102758 103024 103029) (-95 "ATRIG.spad" 102221 102228 102741 102746) (-94 "ATRIG.spad" 101689 101698 102211 102216) (-93 "ASTCAT.spad" 101593 101600 101679 101684) (-92 "ASTCAT.spad" 101495 101504 101583 101588) (-91 "ASTACK.spad" 100828 100837 101102 101129) (-90 "ASSOCEQ.spad" 99628 99639 100784 100789) (-89 "ASP9.spad" 98709 98722 99618 99623) (-88 "ASP8.spad" 97752 97765 98699 98704) (-87 "ASP80.spad" 97074 97087 97742 97747) (-86 "ASP7.spad" 96234 96247 97064 97069) (-85 "ASP78.spad" 95685 95698 96224 96229) (-84 "ASP77.spad" 95054 95067 95675 95680) (-83 "ASP74.spad" 94146 94159 95044 95049) (-82 "ASP73.spad" 93417 93430 94136 94141) (-81 "ASP6.spad" 92284 92297 93407 93412) (-80 "ASP55.spad" 90793 90806 92274 92279) (-79 "ASP50.spad" 88610 88623 90783 90788) (-78 "ASP4.spad" 87905 87918 88600 88605) (-77 "ASP49.spad" 86904 86917 87895 87900) (-76 "ASP42.spad" 85311 85350 86894 86899) (-75 "ASP41.spad" 83890 83929 85301 85306) (-74 "ASP35.spad" 82878 82891 83880 83885) (-73 "ASP34.spad" 82179 82192 82868 82873) (-72 "ASP33.spad" 81739 81752 82169 82174) (-71 "ASP31.spad" 80879 80892 81729 81734) (-70 "ASP30.spad" 79771 79784 80869 80874) (-69 "ASP29.spad" 79237 79250 79761 79766) (-68 "ASP28.spad" 70510 70523 79227 79232) (-67 "ASP27.spad" 69407 69420 70500 70505) (-66 "ASP24.spad" 68494 68507 69397 69402) (-65 "ASP20.spad" 67958 67971 68484 68489) (-64 "ASP1.spad" 67339 67352 67948 67953) (-63 "ASP19.spad" 62025 62038 67329 67334) (-62 "ASP12.spad" 61439 61452 62015 62020) (-61 "ASP10.spad" 60710 60723 61429 61434) (-60 "ARRAY2.spad" 60070 60079 60317 60344) (-59 "ARRAY1.spad" 58905 58914 59253 59280) (-58 "ARRAY12.spad" 57574 57585 58895 58900) (-57 "ARR2CAT.spad" 53236 53257 57542 57569) (-56 "ARR2CAT.spad" 48918 48941 53226 53231) (-55 "ARITY.spad" 48290 48297 48908 48913) (-54 "APPRULE.spad" 47534 47556 48280 48285) (-53 "APPLYORE.spad" 47149 47162 47524 47529) (-52 "ANY.spad" 45491 45498 47139 47144) (-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 2285477 2285482 2285487 2285492) (-2 NIL 2285457 2285462 2285467 2285472) (-1 NIL 2285437 2285442 2285447 2285452) (0 NIL 2285417 2285422 2285427 2285432) (-1292 "ZMOD.spad" 2285226 2285239 2285355 2285412) (-1291 "ZLINDEP.spad" 2284270 2284281 2285216 2285221) (-1290 "ZDSOLVE.spad" 2274119 2274141 2284260 2284265) (-1289 "YSTREAM.spad" 2273612 2273623 2274109 2274114) (-1288 "XRPOLY.spad" 2272832 2272852 2273468 2273537) (-1287 "XPR.spad" 2270623 2270636 2272550 2272649) (-1286 "XPOLY.spad" 2270178 2270189 2270479 2270548) (-1285 "XPOLYC.spad" 2269495 2269511 2270104 2270173) (-1284 "XPBWPOLY.spad" 2267932 2267952 2269275 2269344) (-1283 "XF.spad" 2266393 2266408 2267834 2267927) (-1282 "XF.spad" 2264834 2264851 2266277 2266282) (-1281 "XFALG.spad" 2261858 2261874 2264760 2264829) (-1280 "XEXPPKG.spad" 2261109 2261135 2261848 2261853) (-1279 "XDPOLY.spad" 2260723 2260739 2260965 2261034) (-1278 "XALG.spad" 2260383 2260394 2260679 2260718) (-1277 "WUTSET.spad" 2256222 2256239 2260029 2260056) (-1276 "WP.spad" 2255421 2255465 2256080 2256147) (-1275 "WHILEAST.spad" 2255219 2255228 2255411 2255416) (-1274 "WHEREAST.spad" 2254890 2254899 2255209 2255214) (-1273 "WFFINTBS.spad" 2252453 2252475 2254880 2254885) (-1272 "WEIER.spad" 2250667 2250678 2252443 2252448) (-1271 "VSPACE.spad" 2250340 2250351 2250635 2250662) (-1270 "VSPACE.spad" 2250033 2250046 2250330 2250335) (-1269 "VOID.spad" 2249710 2249719 2250023 2250028) (-1268 "VIEW.spad" 2247332 2247341 2249700 2249705) (-1267 "VIEWDEF.spad" 2242529 2242538 2247322 2247327) (-1266 "VIEW3D.spad" 2226364 2226373 2242519 2242524) (-1265 "VIEW2D.spad" 2214101 2214110 2226354 2226359) (-1264 "VECTOR.spad" 2212775 2212786 2213026 2213053) (-1263 "VECTOR2.spad" 2211402 2211415 2212765 2212770) (-1262 "VECTCAT.spad" 2209302 2209313 2211370 2211397) (-1261 "VECTCAT.spad" 2207009 2207022 2209079 2209084) (-1260 "VARIABLE.spad" 2206789 2206804 2206999 2207004) (-1259 "UTYPE.spad" 2206433 2206442 2206779 2206784) (-1258 "UTSODETL.spad" 2205726 2205750 2206389 2206394) (-1257 "UTSODE.spad" 2203914 2203934 2205716 2205721) (-1256 "UTS.spad" 2198703 2198731 2202381 2202478) (-1255 "UTSCAT.spad" 2196154 2196170 2198601 2198698) (-1254 "UTSCAT.spad" 2193249 2193267 2195698 2195703) (-1253 "UTS2.spad" 2192842 2192877 2193239 2193244) (-1252 "URAGG.spad" 2187475 2187486 2192832 2192837) (-1251 "URAGG.spad" 2182072 2182085 2187431 2187436) (-1250 "UPXSSING.spad" 2179715 2179741 2181153 2181286) (-1249 "UPXS.spad" 2176863 2176891 2177847 2177996) (-1248 "UPXSCONS.spad" 2174620 2174640 2174995 2175144) (-1247 "UPXSCCA.spad" 2173185 2173205 2174466 2174615) (-1246 "UPXSCCA.spad" 2171892 2171914 2173175 2173180) (-1245 "UPXSCAT.spad" 2170473 2170489 2171738 2171887) (-1244 "UPXS2.spad" 2170014 2170067 2170463 2170468) (-1243 "UPSQFREE.spad" 2168426 2168440 2170004 2170009) (-1242 "UPSCAT.spad" 2166019 2166043 2168324 2168421) (-1241 "UPSCAT.spad" 2163318 2163344 2165625 2165630) (-1240 "UPOLYC.spad" 2158296 2158307 2163160 2163313) (-1239 "UPOLYC.spad" 2153166 2153179 2158032 2158037) (-1238 "UPOLYC2.spad" 2152635 2152654 2153156 2153161) (-1237 "UP.spad" 2149828 2149843 2150221 2150374) (-1236 "UPMP.spad" 2148718 2148731 2149818 2149823) (-1235 "UPDIVP.spad" 2148281 2148295 2148708 2148713) (-1234 "UPDECOMP.spad" 2146518 2146532 2148271 2148276) (-1233 "UPCDEN.spad" 2145725 2145741 2146508 2146513) (-1232 "UP2.spad" 2145087 2145108 2145715 2145720) (-1231 "UNISEG.spad" 2144440 2144451 2145006 2145011) (-1230 "UNISEG2.spad" 2143933 2143946 2144396 2144401) (-1229 "UNIFACT.spad" 2143034 2143046 2143923 2143928) (-1228 "ULS.spad" 2133586 2133614 2134679 2135108) (-1227 "ULSCONS.spad" 2125980 2126000 2126352 2126501) (-1226 "ULSCCAT.spad" 2123709 2123729 2125826 2125975) (-1225 "ULSCCAT.spad" 2121546 2121568 2123665 2123670) (-1224 "ULSCAT.spad" 2119762 2119778 2121392 2121541) (-1223 "ULS2.spad" 2119274 2119327 2119752 2119757) (-1222 "UINT8.spad" 2119151 2119160 2119264 2119269) (-1221 "UINT64.spad" 2119027 2119036 2119141 2119146) (-1220 "UINT32.spad" 2118903 2118912 2119017 2119022) (-1219 "UINT16.spad" 2118779 2118788 2118893 2118898) (-1218 "UFD.spad" 2117844 2117853 2118705 2118774) (-1217 "UFD.spad" 2116971 2116982 2117834 2117839) (-1216 "UDVO.spad" 2115818 2115827 2116961 2116966) (-1215 "UDPO.spad" 2113245 2113256 2115774 2115779) (-1214 "TYPE.spad" 2113177 2113186 2113235 2113240) (-1213 "TYPEAST.spad" 2113096 2113105 2113167 2113172) (-1212 "TWOFACT.spad" 2111746 2111761 2113086 2113091) (-1211 "TUPLE.spad" 2111230 2111241 2111645 2111650) (-1210 "TUBETOOL.spad" 2108067 2108076 2111220 2111225) (-1209 "TUBE.spad" 2106708 2106725 2108057 2108062) (-1208 "TS.spad" 2105297 2105313 2106273 2106370) (-1207 "TSETCAT.spad" 2092424 2092441 2105265 2105292) (-1206 "TSETCAT.spad" 2079537 2079556 2092380 2092385) (-1205 "TRMANIP.spad" 2073903 2073920 2079243 2079248) (-1204 "TRIMAT.spad" 2072862 2072887 2073893 2073898) (-1203 "TRIGMNIP.spad" 2071379 2071396 2072852 2072857) (-1202 "TRIGCAT.spad" 2070891 2070900 2071369 2071374) (-1201 "TRIGCAT.spad" 2070401 2070412 2070881 2070886) (-1200 "TREE.spad" 2068972 2068983 2070008 2070035) (-1199 "TRANFUN.spad" 2068803 2068812 2068962 2068967) (-1198 "TRANFUN.spad" 2068632 2068643 2068793 2068798) (-1197 "TOPSP.spad" 2068306 2068315 2068622 2068627) (-1196 "TOOLSIGN.spad" 2067969 2067980 2068296 2068301) (-1195 "TEXTFILE.spad" 2066526 2066535 2067959 2067964) (-1194 "TEX.spad" 2063658 2063667 2066516 2066521) (-1193 "TEX1.spad" 2063214 2063225 2063648 2063653) (-1192 "TEMUTL.spad" 2062769 2062778 2063204 2063209) (-1191 "TBCMPPK.spad" 2060862 2060885 2062759 2062764) (-1190 "TBAGG.spad" 2059898 2059921 2060842 2060857) (-1189 "TBAGG.spad" 2058942 2058967 2059888 2059893) (-1188 "TANEXP.spad" 2058318 2058329 2058932 2058937) (-1187 "TABLE.spad" 2056729 2056752 2056999 2057026) (-1186 "TABLEAU.spad" 2056210 2056221 2056719 2056724) (-1185 "TABLBUMP.spad" 2052993 2053004 2056200 2056205) (-1184 "SYSTEM.spad" 2052221 2052230 2052983 2052988) (-1183 "SYSSOLP.spad" 2049694 2049705 2052211 2052216) (-1182 "SYSNNI.spad" 2048874 2048885 2049684 2049689) (-1181 "SYSINT.spad" 2048278 2048289 2048864 2048869) (-1180 "SYNTAX.spad" 2044472 2044481 2048268 2048273) (-1179 "SYMTAB.spad" 2042528 2042537 2044462 2044467) (-1178 "SYMS.spad" 2038513 2038522 2042518 2042523) (-1177 "SYMPOLY.spad" 2037520 2037531 2037602 2037729) (-1176 "SYMFUNC.spad" 2036995 2037006 2037510 2037515) (-1175 "SYMBOL.spad" 2034422 2034431 2036985 2036990) (-1174 "SWITCH.spad" 2031179 2031188 2034412 2034417) (-1173 "SUTS.spad" 2028078 2028106 2029646 2029743) (-1172 "SUPXS.spad" 2025213 2025241 2026210 2026359) (-1171 "SUP.spad" 2022018 2022029 2022799 2022952) (-1170 "SUPFRACF.spad" 2021123 2021141 2022008 2022013) (-1169 "SUP2.spad" 2020513 2020526 2021113 2021118) (-1168 "SUMRF.spad" 2019479 2019490 2020503 2020508) (-1167 "SUMFS.spad" 2019112 2019129 2019469 2019474) (-1166 "SULS.spad" 2009651 2009679 2010757 2011186) (-1165 "SUCHTAST.spad" 2009420 2009429 2009641 2009646) (-1164 "SUCH.spad" 2009100 2009115 2009410 2009415) (-1163 "SUBSPACE.spad" 2001107 2001122 2009090 2009095) (-1162 "SUBRESP.spad" 2000267 2000281 2001063 2001068) (-1161 "STTF.spad" 1996366 1996382 2000257 2000262) (-1160 "STTFNC.spad" 1992834 1992850 1996356 1996361) (-1159 "STTAYLOR.spad" 1985232 1985243 1992715 1992720) (-1158 "STRTBL.spad" 1983737 1983754 1983886 1983913) (-1157 "STRING.spad" 1983146 1983155 1983160 1983187) (-1156 "STRICAT.spad" 1982934 1982943 1983114 1983141) (-1155 "STREAM.spad" 1979792 1979803 1982459 1982474) (-1154 "STREAM3.spad" 1979337 1979352 1979782 1979787) (-1153 "STREAM2.spad" 1978405 1978418 1979327 1979332) (-1152 "STREAM1.spad" 1978109 1978120 1978395 1978400) (-1151 "STINPROD.spad" 1977015 1977031 1978099 1978104) (-1150 "STEP.spad" 1976216 1976225 1977005 1977010) (-1149 "STBL.spad" 1974742 1974770 1974909 1974924) (-1148 "STAGG.spad" 1973817 1973828 1974732 1974737) (-1147 "STAGG.spad" 1972890 1972903 1973807 1973812) (-1146 "STACK.spad" 1972241 1972252 1972497 1972524) (-1145 "SREGSET.spad" 1969945 1969962 1971887 1971914) (-1144 "SRDCMPK.spad" 1968490 1968510 1969935 1969940) (-1143 "SRAGG.spad" 1963587 1963596 1968458 1968485) (-1142 "SRAGG.spad" 1958704 1958715 1963577 1963582) (-1141 "SQMATRIX.spad" 1956320 1956338 1957236 1957323) (-1140 "SPLTREE.spad" 1950872 1950885 1955756 1955783) (-1139 "SPLNODE.spad" 1947460 1947473 1950862 1950867) (-1138 "SPFCAT.spad" 1946237 1946246 1947450 1947455) (-1137 "SPECOUT.spad" 1944787 1944796 1946227 1946232) (-1136 "SPADXPT.spad" 1936926 1936935 1944777 1944782) (-1135 "spad-parser.spad" 1936391 1936400 1936916 1936921) (-1134 "SPADAST.spad" 1936092 1936101 1936381 1936386) (-1133 "SPACEC.spad" 1920105 1920116 1936082 1936087) (-1132 "SPACE3.spad" 1919881 1919892 1920095 1920100) (-1131 "SORTPAK.spad" 1919426 1919439 1919837 1919842) (-1130 "SOLVETRA.spad" 1917183 1917194 1919416 1919421) (-1129 "SOLVESER.spad" 1915703 1915714 1917173 1917178) (-1128 "SOLVERAD.spad" 1911713 1911724 1915693 1915698) (-1127 "SOLVEFOR.spad" 1910133 1910151 1911703 1911708) (-1126 "SNTSCAT.spad" 1909733 1909750 1910101 1910128) (-1125 "SMTS.spad" 1907993 1908019 1909298 1909395) (-1124 "SMP.spad" 1905468 1905488 1905858 1905985) (-1123 "SMITH.spad" 1904311 1904336 1905458 1905463) (-1122 "SMATCAT.spad" 1902421 1902451 1904255 1904306) (-1121 "SMATCAT.spad" 1900463 1900495 1902299 1902304) (-1120 "SKAGG.spad" 1899424 1899435 1900431 1900458) (-1119 "SINT.spad" 1898250 1898259 1899290 1899419) (-1118 "SIMPAN.spad" 1897978 1897987 1898240 1898245) (-1117 "SIG.spad" 1897306 1897315 1897968 1897973) (-1116 "SIGNRF.spad" 1896414 1896425 1897296 1897301) (-1115 "SIGNEF.spad" 1895683 1895700 1896404 1896409) (-1114 "SIGAST.spad" 1895064 1895073 1895673 1895678) (-1113 "SHP.spad" 1892982 1892997 1895020 1895025) (-1112 "SHDP.spad" 1882693 1882720 1883202 1883333) (-1111 "SGROUP.spad" 1882301 1882310 1882683 1882688) (-1110 "SGROUP.spad" 1881907 1881918 1882291 1882296) (-1109 "SGCF.spad" 1874788 1874797 1881897 1881902) (-1108 "SFRTCAT.spad" 1873716 1873733 1874756 1874783) (-1107 "SFRGCD.spad" 1872779 1872799 1873706 1873711) (-1106 "SFQCMPK.spad" 1867416 1867436 1872769 1872774) (-1105 "SFORT.spad" 1866851 1866865 1867406 1867411) (-1104 "SEXOF.spad" 1866694 1866734 1866841 1866846) (-1103 "SEX.spad" 1866586 1866595 1866684 1866689) (-1102 "SEXCAT.spad" 1864137 1864177 1866576 1866581) (-1101 "SET.spad" 1862437 1862448 1863558 1863597) (-1100 "SETMN.spad" 1860871 1860888 1862427 1862432) (-1099 "SETCAT.spad" 1860193 1860202 1860861 1860866) (-1098 "SETCAT.spad" 1859513 1859524 1860183 1860188) (-1097 "SETAGG.spad" 1856034 1856045 1859493 1859508) (-1096 "SETAGG.spad" 1852563 1852576 1856024 1856029) (-1095 "SEQAST.spad" 1852266 1852275 1852553 1852558) (-1094 "SEGXCAT.spad" 1851388 1851401 1852256 1852261) (-1093 "SEG.spad" 1851201 1851212 1851307 1851312) (-1092 "SEGCAT.spad" 1850108 1850119 1851191 1851196) (-1091 "SEGBIND.spad" 1849180 1849191 1850063 1850068) (-1090 "SEGBIND2.spad" 1848876 1848889 1849170 1849175) (-1089 "SEGAST.spad" 1848590 1848599 1848866 1848871) (-1088 "SEG2.spad" 1848015 1848028 1848546 1848551) (-1087 "SDVAR.spad" 1847291 1847302 1848005 1848010) (-1086 "SDPOL.spad" 1844717 1844728 1845008 1845135) (-1085 "SCPKG.spad" 1842796 1842807 1844707 1844712) (-1084 "SCOPE.spad" 1841945 1841954 1842786 1842791) (-1083 "SCACHE.spad" 1840627 1840638 1841935 1841940) (-1082 "SASTCAT.spad" 1840536 1840545 1840617 1840622) (-1081 "SAOS.spad" 1840408 1840417 1840526 1840531) (-1080 "SAERFFC.spad" 1840121 1840141 1840398 1840403) (-1079 "SAE.spad" 1838296 1838312 1838907 1839042) (-1078 "SAEFACT.spad" 1837997 1838017 1838286 1838291) (-1077 "RURPK.spad" 1835638 1835654 1837987 1837992) (-1076 "RULESET.spad" 1835079 1835103 1835628 1835633) (-1075 "RULE.spad" 1833283 1833307 1835069 1835074) (-1074 "RULECOLD.spad" 1833135 1833148 1833273 1833278) (-1073 "RTVALUE.spad" 1832868 1832877 1833125 1833130) (-1072 "RSTRCAST.spad" 1832585 1832594 1832858 1832863) (-1071 "RSETGCD.spad" 1828963 1828983 1832575 1832580) (-1070 "RSETCAT.spad" 1818747 1818764 1828931 1828958) (-1069 "RSETCAT.spad" 1808551 1808570 1818737 1818742) (-1068 "RSDCMPK.spad" 1807003 1807023 1808541 1808546) (-1067 "RRCC.spad" 1805387 1805417 1806993 1806998) (-1066 "RRCC.spad" 1803769 1803801 1805377 1805382) (-1065 "RPTAST.spad" 1803471 1803480 1803759 1803764) (-1064 "RPOLCAT.spad" 1782831 1782846 1803339 1803466) (-1063 "RPOLCAT.spad" 1761905 1761922 1782415 1782420) (-1062 "ROUTINE.spad" 1757768 1757777 1760552 1760579) (-1061 "ROMAN.spad" 1757096 1757105 1757634 1757763) (-1060 "ROIRC.spad" 1756176 1756208 1757086 1757091) (-1059 "RNS.spad" 1755079 1755088 1756078 1756171) (-1058 "RNS.spad" 1754068 1754079 1755069 1755074) (-1057 "RNG.spad" 1753803 1753812 1754058 1754063) (-1056 "RMODULE.spad" 1753568 1753579 1753793 1753798) (-1055 "RMCAT2.spad" 1752976 1753033 1753558 1753563) (-1054 "RMATRIX.spad" 1751800 1751819 1752143 1752182) (-1053 "RMATCAT.spad" 1747333 1747364 1751756 1751795) (-1052 "RMATCAT.spad" 1742756 1742789 1747181 1747186) (-1051 "RLINSET.spad" 1742150 1742161 1742746 1742751) (-1050 "RINTERP.spad" 1742038 1742058 1742140 1742145) (-1049 "RING.spad" 1741508 1741517 1742018 1742033) (-1048 "RING.spad" 1740986 1740997 1741498 1741503) (-1047 "RIDIST.spad" 1740370 1740379 1740976 1740981) (-1046 "RGCHAIN.spad" 1738949 1738965 1739855 1739882) (-1045 "RGBCSPC.spad" 1738730 1738742 1738939 1738944) (-1044 "RGBCMDL.spad" 1738260 1738272 1738720 1738725) (-1043 "RF.spad" 1735874 1735885 1738250 1738255) (-1042 "RFFACTOR.spad" 1735336 1735347 1735864 1735869) (-1041 "RFFACT.spad" 1735071 1735083 1735326 1735331) (-1040 "RFDIST.spad" 1734059 1734068 1735061 1735066) (-1039 "RETSOL.spad" 1733476 1733489 1734049 1734054) (-1038 "RETRACT.spad" 1732904 1732915 1733466 1733471) (-1037 "RETRACT.spad" 1732330 1732343 1732894 1732899) (-1036 "RETAST.spad" 1732142 1732151 1732320 1732325) (-1035 "RESULT.spad" 1730202 1730211 1730789 1730816) (-1034 "RESRING.spad" 1729549 1729596 1730140 1730197) (-1033 "RESLATC.spad" 1728873 1728884 1729539 1729544) (-1032 "REPSQ.spad" 1728602 1728613 1728863 1728868) (-1031 "REP.spad" 1726154 1726163 1728592 1728597) (-1030 "REPDB.spad" 1725859 1725870 1726144 1726149) (-1029 "REP2.spad" 1715431 1715442 1725701 1725706) (-1028 "REP1.spad" 1709421 1709432 1715381 1715386) (-1027 "REGSET.spad" 1707218 1707235 1709067 1709094) (-1026 "REF.spad" 1706547 1706558 1707173 1707178) (-1025 "REDORDER.spad" 1705723 1705740 1706537 1706542) (-1024 "RECLOS.spad" 1704506 1704526 1705210 1705303) (-1023 "REALSOLV.spad" 1703638 1703647 1704496 1704501) (-1022 "REAL.spad" 1703510 1703519 1703628 1703633) (-1021 "REAL0Q.spad" 1700792 1700807 1703500 1703505) (-1020 "REAL0.spad" 1697620 1697635 1700782 1700787) (-1019 "RDUCEAST.spad" 1697341 1697350 1697610 1697615) (-1018 "RDIV.spad" 1696992 1697017 1697331 1697336) (-1017 "RDIST.spad" 1696555 1696566 1696982 1696987) (-1016 "RDETRS.spad" 1695351 1695369 1696545 1696550) (-1015 "RDETR.spad" 1693458 1693476 1695341 1695346) (-1014 "RDEEFS.spad" 1692531 1692548 1693448 1693453) (-1013 "RDEEF.spad" 1691527 1691544 1692521 1692526) (-1012 "RCFIELD.spad" 1688713 1688722 1691429 1691522) (-1011 "RCFIELD.spad" 1685985 1685996 1688703 1688708) (-1010 "RCAGG.spad" 1683897 1683908 1685975 1685980) (-1009 "RCAGG.spad" 1681736 1681749 1683816 1683821) (-1008 "RATRET.spad" 1681096 1681107 1681726 1681731) (-1007 "RATFACT.spad" 1680788 1680800 1681086 1681091) (-1006 "RANDSRC.spad" 1680107 1680116 1680778 1680783) (-1005 "RADUTIL.spad" 1679861 1679870 1680097 1680102) (-1004 "RADIX.spad" 1676762 1676776 1678328 1678421) (-1003 "RADFF.spad" 1675175 1675212 1675294 1675450) (-1002 "RADCAT.spad" 1674768 1674777 1675165 1675170) (-1001 "RADCAT.spad" 1674359 1674370 1674758 1674763) (-1000 "QUEUE.spad" 1673701 1673712 1673966 1673993) (-999 "QUAT.spad" 1672283 1672293 1672625 1672690) (-998 "QUATCT2.spad" 1671902 1671920 1672273 1672278) (-997 "QUATCAT.spad" 1670067 1670077 1671832 1671897) (-996 "QUATCAT.spad" 1667983 1667995 1669750 1669755) (-995 "QUAGG.spad" 1666809 1666819 1667951 1667978) (-994 "QQUTAST.spad" 1666578 1666586 1666799 1666804) (-993 "QFORM.spad" 1666041 1666055 1666568 1666573) (-992 "QFCAT.spad" 1664744 1664754 1665943 1666036) (-991 "QFCAT.spad" 1663038 1663050 1664239 1664244) (-990 "QFCAT2.spad" 1662729 1662745 1663028 1663033) (-989 "QEQUAT.spad" 1662286 1662294 1662719 1662724) (-988 "QCMPACK.spad" 1657033 1657052 1662276 1662281) (-987 "QALGSET.spad" 1653108 1653140 1656947 1656952) (-986 "QALGSET2.spad" 1651104 1651122 1653098 1653103) (-985 "PWFFINTB.spad" 1648414 1648435 1651094 1651099) (-984 "PUSHVAR.spad" 1647743 1647762 1648404 1648409) (-983 "PTRANFN.spad" 1643869 1643879 1647733 1647738) (-982 "PTPACK.spad" 1640957 1640967 1643859 1643864) (-981 "PTFUNC2.spad" 1640778 1640792 1640947 1640952) (-980 "PTCAT.spad" 1640027 1640037 1640746 1640773) (-979 "PSQFR.spad" 1639334 1639358 1640017 1640022) (-978 "PSEUDLIN.spad" 1638192 1638202 1639324 1639329) (-977 "PSETPK.spad" 1623625 1623641 1638070 1638075) (-976 "PSETCAT.spad" 1617545 1617568 1623605 1623620) (-975 "PSETCAT.spad" 1611439 1611464 1617501 1617506) (-974 "PSCURVE.spad" 1610422 1610430 1611429 1611434) (-973 "PSCAT.spad" 1609189 1609218 1610320 1610417) (-972 "PSCAT.spad" 1608046 1608077 1609179 1609184) (-971 "PRTITION.spad" 1606991 1606999 1608036 1608041) (-970 "PRTDAST.spad" 1606710 1606718 1606981 1606986) (-969 "PRS.spad" 1596272 1596289 1606666 1606671) (-968 "PRQAGG.spad" 1595703 1595713 1596240 1596267) (-967 "PROPLOG.spad" 1594998 1595006 1595693 1595698) (-966 "PROPFRML.spad" 1593806 1593817 1594988 1594993) (-965 "PROPERTY.spad" 1593292 1593300 1593796 1593801) (-964 "PRODUCT.spad" 1590972 1590984 1591258 1591313) (-963 "PR.spad" 1589358 1589370 1590063 1590190) (-962 "PRINT.spad" 1589110 1589118 1589348 1589353) (-961 "PRIMES.spad" 1587361 1587371 1589100 1589105) (-960 "PRIMELT.spad" 1585342 1585356 1587351 1587356) (-959 "PRIMCAT.spad" 1584965 1584973 1585332 1585337) (-958 "PRIMARR.spad" 1583970 1583980 1584148 1584175) (-957 "PRIMARR2.spad" 1582693 1582705 1583960 1583965) (-956 "PREASSOC.spad" 1582065 1582077 1582683 1582688) (-955 "PPCURVE.spad" 1581202 1581210 1582055 1582060) (-954 "PORTNUM.spad" 1580977 1580985 1581192 1581197) (-953 "POLYROOT.spad" 1579806 1579828 1580933 1580938) (-952 "POLY.spad" 1577139 1577149 1577656 1577783) (-951 "POLYLIFT.spad" 1576400 1576423 1577129 1577134) (-950 "POLYCATQ.spad" 1574502 1574524 1576390 1576395) (-949 "POLYCAT.spad" 1567908 1567929 1574370 1574497) (-948 "POLYCAT.spad" 1560652 1560675 1567116 1567121) (-947 "POLY2UP.spad" 1560100 1560114 1560642 1560647) (-946 "POLY2.spad" 1559695 1559707 1560090 1560095) (-945 "POLUTIL.spad" 1558636 1558665 1559651 1559656) (-944 "POLTOPOL.spad" 1557384 1557399 1558626 1558631) (-943 "POINT.spad" 1556222 1556232 1556309 1556336) (-942 "PNTHEORY.spad" 1552888 1552896 1556212 1556217) (-941 "PMTOOLS.spad" 1551645 1551659 1552878 1552883) (-940 "PMSYM.spad" 1551190 1551200 1551635 1551640) (-939 "PMQFCAT.spad" 1550777 1550791 1551180 1551185) (-938 "PMPRED.spad" 1550246 1550260 1550767 1550772) (-937 "PMPREDFS.spad" 1549690 1549712 1550236 1550241) (-936 "PMPLCAT.spad" 1548760 1548778 1549622 1549627) (-935 "PMLSAGG.spad" 1548341 1548355 1548750 1548755) (-934 "PMKERNEL.spad" 1547908 1547920 1548331 1548336) (-933 "PMINS.spad" 1547484 1547494 1547898 1547903) (-932 "PMFS.spad" 1547057 1547075 1547474 1547479) (-931 "PMDOWN.spad" 1546343 1546357 1547047 1547052) (-930 "PMASS.spad" 1545351 1545359 1546333 1546338) (-929 "PMASSFS.spad" 1544316 1544332 1545341 1545346) (-928 "PLOTTOOL.spad" 1544096 1544104 1544306 1544311) (-927 "PLOT.spad" 1538927 1538935 1544086 1544091) (-926 "PLOT3D.spad" 1535347 1535355 1538917 1538922) (-925 "PLOT1.spad" 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1492266 1494695 1494700) (-905 "PERM.spad" 1487924 1487934 1492073 1492088) (-904 "PERMGRP.spad" 1482660 1482670 1487914 1487919) (-903 "PERMCAT.spad" 1481212 1481222 1482640 1482655) (-902 "PERMAN.spad" 1479744 1479758 1481202 1481207) (-901 "PENDTREE.spad" 1479083 1479093 1479373 1479378) (-900 "PDRING.spad" 1477574 1477584 1479063 1479078) (-899 "PDRING.spad" 1476073 1476085 1477564 1477569) (-898 "PDEPROB.spad" 1475088 1475096 1476063 1476068) (-897 "PDEPACK.spad" 1469090 1469098 1475078 1475083) (-896 "PDECOMP.spad" 1468552 1468569 1469080 1469085) (-895 "PDECAT.spad" 1466906 1466914 1468542 1468547) (-894 "PCOMP.spad" 1466757 1466770 1466896 1466901) (-893 "PBWLB.spad" 1465339 1465356 1466747 1466752) (-892 "PATTERN.spad" 1459770 1459780 1465329 1465334) (-891 "PATTERN2.spad" 1459506 1459518 1459760 1459765) (-890 "PATTERN1.spad" 1457808 1457824 1459496 1459501) (-889 "PATRES.spad" 1455355 1455367 1457798 1457803) (-888 "PATRES2.spad" 1455017 1455031 1455345 1455350) (-887 "PATMATCH.spad" 1453174 1453205 1454725 1454730) (-886 "PATMAB.spad" 1452599 1452609 1453164 1453169) (-885 "PATLRES.spad" 1451683 1451697 1452589 1452594) (-884 "PATAB.spad" 1451447 1451457 1451673 1451678) (-883 "PARTPERM.spad" 1448809 1448817 1451437 1451442) (-882 "PARSURF.spad" 1448237 1448265 1448799 1448804) (-881 "PARSU2.spad" 1448032 1448048 1448227 1448232) (-880 "script-parser.spad" 1447552 1447560 1448022 1448027) (-879 "PARSCURV.spad" 1446980 1447008 1447542 1447547) (-878 "PARSC2.spad" 1446769 1446785 1446970 1446975) (-877 "PARPCURV.spad" 1446227 1446255 1446759 1446764) (-876 "PARPC2.spad" 1446016 1446032 1446217 1446222) (-875 "PAN2EXPR.spad" 1445428 1445436 1446006 1446011) (-874 "PALETTE.spad" 1444398 1444406 1445418 1445423) (-873 "PAIR.spad" 1443381 1443394 1443986 1443991) (-872 "PADICRC.spad" 1440711 1440729 1441886 1441979) (-871 "PADICRAT.spad" 1438726 1438738 1438947 1439040) (-870 "PADIC.spad" 1438421 1438433 1438652 1438721) (-869 "PADICCT.spad" 1436962 1436974 1438347 1438416) (-868 "PADEPAC.spad" 1435641 1435660 1436952 1436957) (-867 "PADE.spad" 1434381 1434397 1435631 1435636) (-866 "OWP.spad" 1433621 1433651 1434239 1434306) (-865 "OVERSET.spad" 1433194 1433202 1433611 1433616) (-864 "OVAR.spad" 1432975 1432998 1433184 1433189) (-863 "OUT.spad" 1432059 1432067 1432965 1432970) (-862 "OUTFORM.spad" 1421355 1421363 1432049 1432054) (-861 "OUTBFILE.spad" 1420773 1420781 1421345 1421350) (-860 "OUTBCON.spad" 1419771 1419779 1420763 1420768) (-859 "OUTBCON.spad" 1418767 1418777 1419761 1419766) (-858 "OSI.spad" 1418242 1418250 1418757 1418762) (-857 "OSGROUP.spad" 1418160 1418168 1418232 1418237) (-856 "ORTHPOL.spad" 1416621 1416631 1418077 1418082) (-855 "OREUP.spad" 1416074 1416102 1416301 1416340) (-854 "ORESUP.spad" 1415373 1415397 1415754 1415793) (-853 "OREPCTO.spad" 1413192 1413204 1415293 1415298) (-852 "OREPCAT.spad" 1407249 1407259 1413148 1413187) (-851 "OREPCAT.spad" 1401196 1401208 1407097 1407102) (-850 "ORDSET.spad" 1400362 1400370 1401186 1401191) (-849 "ORDSET.spad" 1399526 1399536 1400352 1400357) (-848 "ORDRING.spad" 1398916 1398924 1399506 1399521) (-847 "ORDRING.spad" 1398314 1398324 1398906 1398911) (-846 "ORDMON.spad" 1398169 1398177 1398304 1398309) (-845 "ORDFUNS.spad" 1397295 1397311 1398159 1398164) (-844 "ORDFIN.spad" 1397115 1397123 1397285 1397290) (-843 "ORDCOMP.spad" 1395580 1395590 1396662 1396691) (-842 "ORDCOMP2.spad" 1394865 1394877 1395570 1395575) (-841 "OPTPROB.spad" 1393503 1393511 1394855 1394860) (-840 "OPTPACK.spad" 1385888 1385896 1393493 1393498) (-839 "OPTCAT.spad" 1383563 1383571 1385878 1385883) (-838 "OPSIG.spad" 1383215 1383223 1383553 1383558) (-837 "OPQUERY.spad" 1382764 1382772 1383205 1383210) (-836 "OP.spad" 1382506 1382516 1382586 1382653) (-835 "OPERCAT.spad" 1381970 1381980 1382496 1382501) (-834 "OPERCAT.spad" 1381432 1381444 1381960 1381965) (-833 "ONECOMP.spad" 1380177 1380187 1380979 1381008) (-832 "ONECOMP2.spad" 1379595 1379607 1380167 1380172) (-831 "OMSERVER.spad" 1378597 1378605 1379585 1379590) (-830 "OMSAGG.spad" 1378385 1378395 1378553 1378592) (-829 "OMPKG.spad" 1376997 1377005 1378375 1378380) (-828 "OM.spad" 1375962 1375970 1376987 1376992) (-827 "OMLO.spad" 1375387 1375399 1375848 1375887) (-826 "OMEXPR.spad" 1375221 1375231 1375377 1375382) (-825 "OMERR.spad" 1374764 1374772 1375211 1375216) (-824 "OMERRK.spad" 1373798 1373806 1374754 1374759) (-823 "OMENC.spad" 1373142 1373150 1373788 1373793) (-822 "OMDEV.spad" 1367431 1367439 1373132 1373137) (-821 "OMCONN.spad" 1366840 1366848 1367421 1367426) (-820 "OINTDOM.spad" 1366603 1366611 1366766 1366835) (-819 "OFMONOID.spad" 1362790 1362800 1366593 1366598) (-818 "ODVAR.spad" 1362051 1362061 1362780 1362785) (-817 "ODR.spad" 1361695 1361721 1361863 1362012) (-816 "ODPOL.spad" 1359077 1359087 1359417 1359544) (-815 "ODP.spad" 1348924 1348944 1349297 1349428) (-814 "ODETOOLS.spad" 1347507 1347526 1348914 1348919) (-813 "ODESYS.spad" 1345157 1345174 1347497 1347502) (-812 "ODERTRIC.spad" 1341098 1341115 1345114 1345119) (-811 "ODERED.spad" 1340485 1340509 1341088 1341093) (-810 "ODERAT.spad" 1338036 1338053 1340475 1340480) (-809 "ODEPRRIC.spad" 1334927 1334949 1338026 1338031) (-808 "ODEPROB.spad" 1334184 1334192 1334917 1334922) (-807 "ODEPRIM.spad" 1331458 1331480 1334174 1334179) (-806 "ODEPAL.spad" 1330834 1330858 1331448 1331453) (-805 "ODEPACK.spad" 1317436 1317444 1330824 1330829) (-804 "ODEINT.spad" 1316867 1316883 1317426 1317431) (-803 "ODEIFTBL.spad" 1314262 1314270 1316857 1316862) (-802 "ODEEF.spad" 1309629 1309645 1314252 1314257) (-801 "ODECONST.spad" 1309148 1309166 1309619 1309624) (-800 "ODECAT.spad" 1307744 1307752 1309138 1309143) (-799 "OCT.spad" 1305882 1305892 1306598 1306637) (-798 "OCTCT2.spad" 1305526 1305547 1305872 1305877) (-797 "OC.spad" 1303300 1303310 1305482 1305521) (-796 "OC.spad" 1300799 1300811 1302983 1302988) (-795 "OCAMON.spad" 1300647 1300655 1300789 1300794) (-794 "OASGP.spad" 1300462 1300470 1300637 1300642) (-793 "OAMONS.spad" 1299982 1299990 1300452 1300457) (-792 "OAMON.spad" 1299843 1299851 1299972 1299977) (-791 "OAGROUP.spad" 1299705 1299713 1299833 1299838) (-790 "NUMTUBE.spad" 1299292 1299308 1299695 1299700) (-789 "NUMQUAD.spad" 1287154 1287162 1299282 1299287) (-788 "NUMODE.spad" 1278290 1278298 1287144 1287149) (-787 "NUMINT.spad" 1275848 1275856 1278280 1278285) (-786 "NUMFMT.spad" 1274688 1274696 1275838 1275843) (-785 "NUMERIC.spad" 1266760 1266770 1274493 1274498) (-784 "NTSCAT.spad" 1265262 1265278 1266728 1266755) (-783 "NTPOLFN.spad" 1264807 1264817 1265179 1265184) (-782 "NSUP.spad" 1257853 1257863 1262393 1262546) (-781 "NSUP2.spad" 1257245 1257257 1257843 1257848) (-780 "NSMP.spad" 1253476 1253495 1253784 1253911) (-779 "NREP.spad" 1251848 1251862 1253466 1253471) (-778 "NPCOEF.spad" 1251094 1251114 1251838 1251843) (-777 "NORMRETR.spad" 1250692 1250731 1251084 1251089) (-776 "NORMPK.spad" 1248594 1248613 1250682 1250687) (-775 "NORMMA.spad" 1248282 1248308 1248584 1248589) (-774 "NONE.spad" 1248023 1248031 1248272 1248277) (-773 "NONE1.spad" 1247699 1247709 1248013 1248018) (-772 "NODE1.spad" 1247168 1247184 1247689 1247694) (-771 "NNI.spad" 1246055 1246063 1247142 1247163) (-770 "NLINSOL.spad" 1244677 1244687 1246045 1246050) (-769 "NIPROB.spad" 1243218 1243226 1244667 1244672) (-768 "NFINTBAS.spad" 1240678 1240695 1243208 1243213) (-767 "NETCLT.spad" 1240652 1240663 1240668 1240673) (-766 "NCODIV.spad" 1238850 1238866 1240642 1240647) (-765 "NCNTFRAC.spad" 1238492 1238506 1238840 1238845) (-764 "NCEP.spad" 1236652 1236666 1238482 1238487) (-763 "NASRING.spad" 1236248 1236256 1236642 1236647) (-762 "NASRING.spad" 1235842 1235852 1236238 1236243) (-761 "NARNG.spad" 1235186 1235194 1235832 1235837) (-760 "NARNG.spad" 1234528 1234538 1235176 1235181) (-759 "NAGSP.spad" 1233601 1233609 1234518 1234523) (-758 "NAGS.spad" 1223126 1223134 1233591 1233596) (-757 "NAGF07.spad" 1221519 1221527 1223116 1223121) (-756 "NAGF04.spad" 1215751 1215759 1221509 1221514) (-755 "NAGF02.spad" 1209560 1209568 1215741 1215746) (-754 "NAGF01.spad" 1205163 1205171 1209550 1209555) (-753 "NAGE04.spad" 1198623 1198631 1205153 1205158) (-752 "NAGE02.spad" 1188965 1188973 1198613 1198618) (-751 "NAGE01.spad" 1184849 1184857 1188955 1188960) (-750 "NAGD03.spad" 1182769 1182777 1184839 1184844) (-749 "NAGD02.spad" 1175300 1175308 1182759 1182764) (-748 "NAGD01.spad" 1169413 1169421 1175290 1175295) (-747 "NAGC06.spad" 1165200 1165208 1169403 1169408) (-746 "NAGC05.spad" 1163669 1163677 1165190 1165195) (-745 "NAGC02.spad" 1162924 1162932 1163659 1163664) (-744 "NAALG.spad" 1162459 1162469 1162892 1162919) (-743 "NAALG.spad" 1162014 1162026 1162449 1162454) (-742 "MULTSQFR.spad" 1158972 1158989 1162004 1162009) (-741 "MULTFACT.spad" 1158355 1158372 1158962 1158967) (-740 "MTSCAT.spad" 1156389 1156410 1158253 1158350) (-739 "MTHING.spad" 1156046 1156056 1156379 1156384) (-738 "MSYSCMD.spad" 1155480 1155488 1156036 1156041) (-737 "MSET.spad" 1153422 1153432 1155186 1155225) (-736 "MSETAGG.spad" 1153267 1153277 1153390 1153417) (-735 "MRING.spad" 1150238 1150250 1152975 1153042) (-734 "MRF2.spad" 1149806 1149820 1150228 1150233) (-733 "MRATFAC.spad" 1149352 1149369 1149796 1149801) (-732 "MPRFF.spad" 1147382 1147401 1149342 1149347) (-731 "MPOLY.spad" 1144853 1144868 1145212 1145339) (-730 "MPCPF.spad" 1144117 1144136 1144843 1144848) (-729 "MPC3.spad" 1143932 1143972 1144107 1144112) (-728 "MPC2.spad" 1143574 1143607 1143922 1143927) (-727 "MONOTOOL.spad" 1141909 1141926 1143564 1143569) (-726 "MONOID.spad" 1141228 1141236 1141899 1141904) (-725 "MONOID.spad" 1140545 1140555 1141218 1141223) (-724 "MONOGEN.spad" 1139291 1139304 1140405 1140540) (-723 "MONOGEN.spad" 1138059 1138074 1139175 1139180) (-722 "MONADWU.spad" 1136073 1136081 1138049 1138054) (-721 "MONADWU.spad" 1134085 1134095 1136063 1136068) (-720 "MONAD.spad" 1133229 1133237 1134075 1134080) (-719 "MONAD.spad" 1132371 1132381 1133219 1133224) (-718 "MOEBIUS.spad" 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"MFLOAT.spad" 1113701 1113709 1115075 1115180) (-698 "MFINFACT.spad" 1113101 1113123 1113691 1113696) (-697 "MESH.spad" 1110833 1110841 1113091 1113096) (-696 "MDDFACT.spad" 1109026 1109036 1110823 1110828) (-695 "MDAGG.spad" 1108313 1108323 1109006 1109021) (-694 "MCMPLX.spad" 1104324 1104332 1104938 1105139) (-693 "MCDEN.spad" 1103532 1103544 1104314 1104319) (-692 "MCALCFN.spad" 1100634 1100660 1103522 1103527) (-691 "MAYBE.spad" 1099918 1099929 1100624 1100629) (-690 "MATSTOR.spad" 1097194 1097204 1099908 1099913) (-689 "MATRIX.spad" 1095898 1095908 1096382 1096409) (-688 "MATLIN.spad" 1093224 1093248 1095782 1095787) (-687 "MATCAT.spad" 1084809 1084831 1093192 1093219) (-686 "MATCAT.spad" 1076266 1076290 1084651 1084656) (-685 "MATCAT2.spad" 1075534 1075582 1076256 1076261) (-684 "MAPPKG3.spad" 1074433 1074447 1075524 1075529) (-683 "MAPPKG2.spad" 1073767 1073779 1074423 1074428) (-682 "MAPPKG1.spad" 1072585 1072595 1073757 1073762) (-681 "MAPPAST.spad" 1071898 1071906 1072575 1072580) (-680 "MAPHACK3.spad" 1071706 1071720 1071888 1071893) (-679 "MAPHACK2.spad" 1071471 1071483 1071696 1071701) (-678 "MAPHACK1.spad" 1071101 1071111 1071461 1071466) (-677 "MAGMA.spad" 1068891 1068908 1071091 1071096) (-676 "MACROAST.spad" 1068470 1068478 1068881 1068886) (-675 "M3D.spad" 1066166 1066176 1067848 1067853) (-674 "LZSTAGG.spad" 1063394 1063404 1066156 1066161) (-673 "LZSTAGG.spad" 1060620 1060632 1063384 1063389) (-672 "LWORD.spad" 1057325 1057342 1060610 1060615) (-671 "LSTAST.spad" 1057109 1057117 1057315 1057320) (-670 "LSQM.spad" 1055335 1055349 1055733 1055784) (-669 "LSPP.spad" 1054868 1054885 1055325 1055330) (-668 "LSMP.spad" 1053708 1053736 1054858 1054863) (-667 "LSMP1.spad" 1051512 1051526 1053698 1053703) (-666 "LSAGG.spad" 1051181 1051191 1051480 1051507) (-665 "LSAGG.spad" 1050870 1050882 1051171 1051176) (-664 "LPOLY.spad" 1049824 1049843 1050726 1050795) (-663 "LPEFRAC.spad" 1049081 1049091 1049814 1049819) (-662 "LO.spad" 1048482 1048496 1049015 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"DIOPS.spad" 276118 276130 277116 277121) (-233 "DIFRING.spad" 275410 275418 276098 276113) (-232 "DIFRING.spad" 274710 274720 275400 275405) (-231 "DIFEXT.spad" 273869 273879 274690 274705) (-230 "DIFEXT.spad" 272945 272957 273768 273773) (-229 "DIAGG.spad" 272575 272585 272925 272940) (-228 "DIAGG.spad" 272213 272225 272565 272570) (-227 "DHMATRIX.spad" 270517 270527 271670 271697) (-226 "DFSFUN.spad" 263925 263933 270507 270512) (-225 "DFLOAT.spad" 260646 260654 263815 263920) (-224 "DFINTTLS.spad" 258855 258871 260636 260641) (-223 "DERHAM.spad" 256765 256797 258835 258850) (-222 "DEQUEUE.spad" 256083 256093 256372 256399) (-221 "DEGRED.spad" 255698 255712 256073 256078) (-220 "DEFINTRF.spad" 253223 253233 255688 255693) (-219 "DEFINTEF.spad" 251719 251735 253213 253218) (-218 "DEFAST.spad" 251087 251095 251709 251714) (-217 "DECIMAL.spad" 249193 249201 249554 249647) (-216 "DDFACT.spad" 246992 247009 249183 249188) (-215 "DBLRESP.spad" 246590 246614 246982 246987) (-214 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(-154 "CLLCTAST.spad" 177702 177710 178030 178035) (-153 "CLIP.spad" 173794 173802 177692 177697) (-152 "CLIF.spad" 172433 172449 173750 173789) (-151 "CLAGG.spad" 168918 168928 172423 172428) (-150 "CLAGG.spad" 165274 165286 168781 168786) (-149 "CINTSLPE.spad" 164599 164612 165264 165269) (-148 "CHVAR.spad" 162677 162699 164589 164594) (-147 "CHARZ.spad" 162592 162600 162657 162672) (-146 "CHARPOL.spad" 162100 162110 162582 162587) (-145 "CHARNZ.spad" 161853 161861 162080 162095) (-144 "CHAR.spad" 159721 159729 161843 161848) (-143 "CFCAT.spad" 159037 159045 159711 159716) (-142 "CDEN.spad" 158195 158209 159027 159032) (-141 "CCLASS.spad" 156344 156352 157606 157645) (-140 "CATEGORY.spad" 155434 155442 156334 156339) (-139 "CATCTOR.spad" 155325 155333 155424 155429) (-138 "CATAST.spad" 154943 154951 155315 155320) (-137 "CASEAST.spad" 154657 154665 154933 154938) (-136 "CARTEN.spad" 149760 149784 154647 154652) (-135 "CARTEN2.spad" 149146 149173 149750 149755) (-134 "CARD.spad" 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(-70 "ASP30.spad" 79771 79784 80869 80874) (-69 "ASP29.spad" 79237 79250 79761 79766) (-68 "ASP28.spad" 70510 70523 79227 79232) (-67 "ASP27.spad" 69407 69420 70500 70505) (-66 "ASP24.spad" 68494 68507 69397 69402) (-65 "ASP20.spad" 67958 67971 68484 68489) (-64 "ASP1.spad" 67339 67352 67948 67953) (-63 "ASP19.spad" 62025 62038 67329 67334) (-62 "ASP12.spad" 61439 61452 62015 62020) (-61 "ASP10.spad" 60710 60723 61429 61434) (-60 "ARRAY2.spad" 60070 60079 60317 60344) (-59 "ARRAY1.spad" 58905 58914 59253 59280) (-58 "ARRAY12.spad" 57574 57585 58895 58900) (-57 "ARR2CAT.spad" 53236 53257 57542 57569) (-56 "ARR2CAT.spad" 48918 48941 53226 53231) (-55 "ARITY.spad" 48290 48297 48908 48913) (-54 "APPRULE.spad" 47534 47556 48280 48285) (-53 "APPLYORE.spad" 47149 47162 47524 47529) (-52 "ANY.spad" 45491 45498 47139 47144) (-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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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 99508e4b..dba73988 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188029 . 3453610663) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) #0#) |has| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (-310 (-2 (|:| -1924 |#1|) (|:| -2713 |#2|))))) -((((-566)) . T) (($) -2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-1038 (-409 (-566))))) ((|#1|) . T)) +(188029 . 3453749799) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +((((-566)) . 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T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566))))) +((($) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566))))) (|has| |#1| (-909)) ((((-862)) . T)) ((((-862)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-862)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) -((($ $) . T) ((#0=(-409 (-566)) #0#) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) -(-2700 (|has| |#1| (-820)) (|has| |#1| (-850))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-848))) +((($ $) . T) ((#0=(-409 (-566)) #0#) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) +(-2805 (|has| |#1| (-820)) (|has| |#1| (-850))) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) ((((-862)) . T)) ((((-862)) . 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T)) (|has| |#1| (-558)) (|has| |#1| (-558)) @@ -288,21 +288,21 @@ ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) (-12 (|has| |#1| (-1099)) (|has| |#2| (-1099))) ((($) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) . T)) +((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) (($) . 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T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-538)) |has| |#1| (-614 (-538)))) ((((-862)) . T) (((-1180)) . T)) -((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) ((((-1180)) . 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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 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 |#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) (($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . T)) +((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-818 (-1175))) . T) (($) -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)) . 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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|) -2700 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2805 (|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 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) ((((-862)) . T)) -((((-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) -((((-390) (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) +((((-390) (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#2| (-1150)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|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|) . 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T)) ((((-144)) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2805 (|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)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -((($) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#2|) |has| |#1| (-365)) ((|#1|) . T)) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#2|) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) . 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T)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-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))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-1264 |#1|) (-1264 |#1|)) . T)) ((((-566) (-144)) . T)) ((($) . T)) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2805 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2805 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-1180)) . T) (((-862)) . T)) ((((-1180)) . T)) ((((-862)) . T)) @@ -979,20 +979,20 @@ (((|#1| (-971)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((($) . T) (((-566)) . T) (((-870 |#1|)) . T) (((-409 (-566))) . T)) (((|#1|) . T)) (|has| |#2| (-793)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#2| (-848)) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) -(-2700 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) +(-2805 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-172)) ((|#4|) . T) (((-566)) . T)) (((|#2|) |has| |#2| (-172))) @@ -1004,7 +1004,7 @@ (((|#1|) . T)) ((((-409 (-566))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-409 (-566))) . T)) -((($) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) (|has| |#1| (-828)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) (|has| |#1| (-1099)) @@ -1015,13 +1015,13 @@ (((|#4|) |has| |#4| (-1099))) (((|#3|) |has| |#3| (-1099))) (|has| |#3| (-370)) -((($) |has| |#1| (-558)) ((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +((($) |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))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) ((((-862)) . T)) ((((-862)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558)))) +(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |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)) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) -((($ $) -2700 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) +((($ $) -2805 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) ((($) . T) (((-566)) . 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T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2805 (|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)))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-475)) (|has| |#1| (-558)) (|has| |#1| (-1049)) (|has| |#1| (-1111))) +(-2805 (|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)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|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 (-2903 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-240 (-2997 |#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)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2700 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2805 (|has| |#1| (-351)) (|has| |#1| (-370))) ((((-1141 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1049))) -(((|#2|) . T) (((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-699)) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|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 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) -((((-566)) -2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049))) ((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-1099))) (((-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-566)) -2805 (|has| |#2| (-172)) (|has| |#2| (-848)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049))) ((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-1099))) (((-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) @@ -1134,8 +1134,8 @@ ((((-862)) . T)) ((((-862)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) |has| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (-310 (-2 (|:| -1924 |#1|) (|:| -2713 |#2|))))) -(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) |has| (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|)) (-310 (-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) +(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) |has| (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|)) (-310 (-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))))) ((((-862)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1149,10 +1149,10 @@ ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) ((((-566)) . T) (($) . 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T)) -((($) -2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) -2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) ((((-566) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -1209,41 +1209,41 @@ (-12 (|has| |#1| (-370)) (|has| |#2| (-370))) ((((-862)) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) (((|#1|) . 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T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#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 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-862)) -2805 (|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 (|:| -1924 |#1|) (|:| -2713 |#2|)) #0#) |has| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (-310 (-2 (|:| -1924 |#1|) (|:| -2713 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#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)) (($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) -((($) -2700 (|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)) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1157) (-52)) . T)) (((|#1|) . T)) -((((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T) (($) -2700 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) -((($) -2700 (|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) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -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))))) (((|#2|) |has| |#2| (-172))) -((($) -2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((-566)) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) +((($) -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)))) ((((-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 (|:| -1924 |#1|) (|:| -2713 |#2|)) #0#) |has| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (-310 (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (|has| |#1| (-850)) (((|#2| (-771) (-1081)) . T)) (((|#1| |#2|) . T)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-172)) (|has| |#1| (-558))) (|has| |#1| (-791)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2700 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) -(-2700 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) +(-2805 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) +(-2805 (|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))) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-566)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-566)) . T) (($) . T)) +((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (((-566)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-566)) . T) (($) . T)) ((((-862)) . T)) -(-2700 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) (((|#1|) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) (((-566)) . T) (($) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099))) (((-958 |#1|)) . T)) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2805 (|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|) -2700 (|has| |#4| (-172)) (|has| |#4| (-365)))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#4|) -2805 (|has| |#4| (-172)) (|has| |#4| (-365)))) +(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)))) (|has| |#2| (-365)) (((|#1|) |has| |#1| (-172))) -(((|#4|) -2700 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049))) (($) |has| |#4| (-172))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049))) (($) |has| |#3| (-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))) (((|#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)) -2700 (|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 (|:| -1924 (-1157)) (|:| -2713 #0#))) . T)) +((((-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 (|:| -2010 (-1157)) (|:| -2818 #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)) -(-2700 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2805 (|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))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1256 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558)))) +((((-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)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2|) . T) (((-566)) . T) (((-819 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1672,7 +1672,7 @@ ((((-862)) . T)) ((((-862)) . T)) (|has| |#1| (-1099)) -(((|#2| (-484 (-2903 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-484 (-2997 |#1|) (-771)) (-864 |#1|)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#)) (((|#1| (-533 (-1175)) (-1175)) . T)) (((|#1|) . T)) @@ -1693,17 +1693,17 @@ (((|#2|) |has| |#2| (-172))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1924 (-1175)) (|:| -2713 (-52)))) . T)) +((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) ((((-1175) (-52)) . T)) ((($ $) . T)) (((|#1| (-566)) . T)) ((((-910 |#1|)) . T)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2700 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2805 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) (|has| |#1| (-850)) (|has| |#1| (-850)) @@ -1721,13 +1721,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)))) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -(-2700 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-909))) -((($) -2700 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((|#3|) -2805 (|has| |#3| (-172)) (|has| |#3| (-365)))) +((($) -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))) +((($) -2805 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) ((((-566) |#2|) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) (|has| |#1| (-351)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) (((|#2|) . T) (((-566)) . T)) @@ -1736,7 +1736,7 @@ (|has| |#1| (-820)) (|has| |#1| (-820)) (((|#1|) . T)) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-848)) (|has| |#1| (-848)) (|has| |#1| (-848)) @@ -1745,14 +1745,14 @@ ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) ((((-1175)) |has| |#1| (-900 (-1175))) (((-1081)) . T)) (((|#1|) . 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T)) @@ -2464,10 +2464,10 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . 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))) -((($) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#2|) . T)) ((((-409 (-566))) . T) (((-699)) . T) (($) . T)) -((($) . T) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((#0=(-780 |#1| (-864 |#2|)) #0#) |has| (-780 |#1| (-864 |#2|)) (-310 (-780 |#1| (-864 |#2|))))) ((((-566)) . T) (($) . T)) @@ -2499,13 +2499,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111)) (|has| |#1| (-1099))) (|has| |#1| (-558)) (((|#2|) . T)) ((((-566)) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-583 |#1|)) . T)) ((($) . 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)) -2700 (|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))) -2700 (|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)) -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)) ((((-409 (-566))) |has| |#2| (-1038 (-409 (-566)))) (((-566)) |has| |#2| (-1038 (-566))) ((|#2|) . T) (((-864 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-409 (-566))) . T)) ((((-1124 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) @@ -2538,22 +2538,22 @@ (((|#1| |#2|) . T)) ((((-1175) |#1|) . T)) (((|#4|) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1175) (-52)) . T)) ((((-1249 |#2| |#3| |#4|) (-320 |#2| |#3| |#4|)) . T)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) ((((-862)) . 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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)) (($) |has| |#1| (-558))) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) +((((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) (|has| |#1| (-365)) -((($) |has| |#1| (-848)) (((-566)) -2700 (|has| |#1| (-21)) (|has| |#1| (-848)))) +((($) |has| |#1| (-848)) (((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-848)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) @@ -2566,17 +2566,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (((|#2| |#3|) . T)) -(-2700 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2805 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((|#1| (-533 |#2|)) . T)) (((|#1| (-771)) . T)) (((|#1| (-533 (-1087 (-1175)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-909)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-862)) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)))) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2805 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2805 (|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)) ((($) . T)) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-365)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1249 |#2| |#3| |#4|)) . T) (((-409 (-566))) |has| #0# (-38 (-409 (-566))))) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(-2700 (-12 (|has| |#1| (-308)) (|has| |#1| (-909))) (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2700 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2805 (-12 (|has| |#1| (-308)) (|has| |#1| (-909))) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|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|) -2700 (|has| |#2| (-6 (-4419 "*"))) (|has| |#2| (-172)))) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(((|#2|) -2805 (|has| |#2| (-6 (-4419 "*"))) (|has| |#2| (-172)))) +(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#2| (-909)) (|has| |#1| (-909)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#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)) ((($) . T) (((-566)) . T)) -((((-2 (|:| -1924 (-1157)) (|:| -2713 (-52)))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) (((|#1|) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) ((((-862)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) (((|#1| (-409 (-566))) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-291)) (|has| |#1| (-365))) +(-2805 (|has| |#1| (-291)) (|has| |#1| (-365))) ((((-144)) . T)) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) (|has| |#1| (-848)) @@ -2673,7 +2673,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-187)) . T) (((-862)) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -2686,7 +2686,7 @@ ((((-862)) . T)) ((((-1157)) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -((((-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) (|has| |#1| (-850)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) @@ -2698,16 +2698,16 @@ (((|#2|) . T)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) . T) (((-612 $)) . T)) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2805 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2805 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-1175) (-52)) . T)) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2700 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (|has| |#1| (-909)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . 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)))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#1| (-820)) (((#0=(-910 |#1|) #0#) . T) (($ $) . T) ((#1=(-409 (-566)) #1#) . T)) ((((-409 |#2|)) . T)) (|has| |#1| (-848)) -((((-1200 |#1|)) . T) (((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-1200 |#1|)) . T) (((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) . T) ((#1=(-566) #1#) . T) (($ $) . T)) ((((-910 |#1|)) . T) (($) . 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)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) -((((-2 (|:| -1924 (-1175)) (|:| -2713 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1924 (-1175)) (|:| -2713 #0#))) . T)) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) +((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2010 (-1175)) (|:| -2818 #0#))) . T)) (|has| |#1| (-351)) ((((-566)) . T)) ((((-862)) . T)) (((|#1|) . T)) (((#0=(-1250 |#1| |#2| |#3| |#4|) $) |has| #0# (-287 #0# #0#))) (|has| |#1| (-365)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2700 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((-566)) -2700 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +(((|#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)))) (((#0=(-1081) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) (((#0=(-409 (-566)) #0#) . T) ((#1=(-699) #1#) . T) (($ $) . T)) ((((-317 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-365))) ((((-862)) . T)) (|has| |#1| (-1099)) (((|#1|) . T)) -(((|#1|) -2700 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) -(((|#1|) -2700 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2805 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2805 (|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)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|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))) (((|#2|) . T) (((-566)) |has| |#2| (-639 (-566)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2835,7 +2835,7 @@ (|has| |#2| (-1022)) ((($) . T)) (|has| |#1| (-909)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#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)) -((($) -2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) -((($) |has| |#1| (-848)) (((-566)) -2700 (|has| |#1| (-21)) (|has| |#1| (-848)))) +((($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) |has| |#1| (-848)) (((-566)) -2805 (|has| |#1| (-21)) (|has| |#1| (-848)))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) -(-2700 (|has| |#1| (-370)) (|has| |#1| (-850))) +(-2805 (|has| |#1| (-370)) (|has| |#1| (-850))) (((|#1|) . T)) ((((-771)) . T)) ((((-862)) . T)) @@ -2858,17 +2858,17 @@ ((((-566)) . T) (($) . T)) ((((-566)) . T) (($) . T)) ((((-771) |#1|) . T)) -(((|#2| (-240 (-2903 |#1|) (-771))) . T)) +(((|#2| (-240 (-2997 |#1|) (-771))) . T)) (((|#1| (-533 |#3|)) . T)) ((((-409 (-566))) . T)) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-1157)) . T) (((-862)) . T)) -(((#0=(-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) #0#) |has| (-2 (|:| -1924 (-1175)) (|:| -2713 (-52))) (-310 (-2 (|:| -1924 (-1175)) (|:| -2713 (-52)))))) +(((#0=(-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) #0#) |has| (-2 (|:| -2010 (-1175)) (|:| -2818 (-52))) (-310 (-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))))) ((((-1157)) . T)) (|has| |#1| (-909)) (|has| |#2| (-365)) (((|#1|) . T) (($) . T) (((-566)) . T)) -(-2700 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|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)))) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (-12 (|has| |#1| (-547)) (|has| |#1| (-828))) ((((-862)) . T)) -((((-1175)) -2700 (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))) (-12 (|has| |#1| (-365)) (|has| |#2| (-900 (-1175)))))) +((((-1175)) -2805 (-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) (($) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2931,11 +2931,11 @@ (((|#2|) |has| |#1| (-365))) ((((-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-381)))) (((-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-566))))) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (((|#1|) . T)) ((($) . T) (((-566)) . T) ((|#2|) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|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) (($) . T) (((-566)) . T)) -(-2700 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((|#2|) . T)) (((|#2|) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) -((((-2 (|:| -1924 (-1157)) (|:| -2713 |#1|))) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 |#1|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-409 (-566)))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) ((((-1157) |#1|) . T)) (|has| |#1| (-147)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) (|has| |#1| (-147)) ((((-583 |#1|)) . T)) @@ -2973,7 +2973,7 @@ ((((-409 (-566))) |has| |#2| (-1038 (-566))) (((-566)) |has| |#2| (-1038 (-566))) (((-1175)) |has| |#2| (-1038 (-1175))) ((|#2|) . T)) (((#0=(-409 |#2|) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-351))) (|has| |#1| (-147)) ((((-862)) . T)) ((($) . T)) @@ -2998,7 +2998,7 @@ ((((-862)) . T)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3020,7 +3020,7 @@ ((((-566)) . T)) ((((-862)) . T)) ((((-566)) . T)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2805 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -3032,9 +3032,9 @@ (((|#1|) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) -(-2700 (|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)) -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))) (|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|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2805 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049)))) +(((|#1|) -2805 (|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)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-381)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|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|))))) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2805 (|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 (|:| -1924 (-1157)) (|:| -2713 (-52)))) . T)) +((((-2 (|:| -2010 (-1157)) (|:| -2818 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-566)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-862)) . T)) ((((-862)) . T)) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2805 (|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)) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) -((((-566)) . T) (((-409 (-566))) -2700 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566))))) ((|#2|) . T) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-864 |#1|)) . T)) -((((-1124 |#1| |#2|)) . T) ((|#2|) . T) (($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) -((((-1171 |#1|)) . T) (((-566)) . T) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((-1081)) . T) ((|#1|) . 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T)) +((((-1171 |#1|)) . T) (((-566)) . T) (($) -2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (((-1081)) . T) ((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566)))))) +(-2805 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-1087 (-1175))) . T) (($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2805 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . T)) (((#0=(-583 |#1|) #0#) . T) (($ $) . T) ((#1=(-409 (-566)) #1#) . T)) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -3121,7 +3121,7 @@ (((|#1|) . T)) ((((-862)) . T)) ((((-295 |#3|)) . T)) -(((#0=(-409 (-566)) #0#) |has| |#2| (-38 (-409 (-566)))) ((|#2| |#2|) . T) (($ $) -2700 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +(((#0=(-409 (-566)) #0#) |has| |#2| (-38 (-409 (-566)))) ((|#2| |#2|) . T) (($ $) -2805 (|has| |#2| (-172)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . 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) (($) . T)) -((($ $) -2700 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) -((($ $) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1| |#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-409 (-566)) #0#) . T) (($ $) . T)) ((((-566)) . T)) @@ -3608,17 +3608,17 @@ ((($) . 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)) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2805 (|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)) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1103)) . T)) ((((-862)) . T)) -((($) -2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2805 (|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)) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2805 (|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)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2805 (|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)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1180)) . T)) ((((-1180)) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2805 (|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)) -(-2700 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -(-2700 (-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)))) +(-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)))) ((((-566)) . T)) ((((-566)) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2805 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((((-1175)) -12 (|has| |#2| (-900 (-1175))) (|has| |#2| (-1049)))) -(-2700 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) +(-2805 (-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)) -(-2700 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2805 (|has| |#1| (-351)) (|has| |#1| (-370))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-409 (-566))) . T) (($) . T) (((-566)) . T)) @@ -3720,7 +3720,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((($) . 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)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-848))) (((|#2|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2805 (|has| |#1| (-21)) (|has| |#1| (-848))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-862)) -2700 (-12 (|has| |#1| (-613 (-862))) (|has| |#2| (-613 (-862)))) (-12 (|has| |#1| (-1099)) (|has| |#2| (-1099))))) +((((-862)) -2805 (-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)) ((($) . T) (((-409 (-566))) . T)) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2805 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2805 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-862)) . T) (((-1180)) . T)) (|has| |#4| (-793)) -(-2700 (|has| |#4| (-793)) (|has| |#4| (-848))) +(-2805 (|has| |#4| (-793)) (|has| |#4| (-848))) (|has| |#4| (-848)) (|has| |#3| (-793)) ((((-1180)) . T)) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2805 (|has| |#3| (-793)) (|has| |#3| (-848))) (|has| |#3| (-848)) ((((-566)) . T)) (((|#2|) . T)) -((((-1175)) -2700 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) +((((-1175)) -2805 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-409 (-566)) |#1|))) (|has| |#1| (-900 (-1175))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-771) |#1|))) (|has| |#1| (-900 (-1175))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3779,11 +3779,11 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1139 |#1| |#2|)) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2|) . T) (((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) -((((-2 (|:| -1924 (-1175)) (|:| -2713 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) +((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1022)) -(((|#2|) . T) (((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2010 |#1|) (|:| -2818 |#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)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2805 (|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) (($) -2700 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) ((|#4|) -2700 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049)))) -(((|#2|) . T) (($) -2700 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) +(((|#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)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) @@ -3823,7 +3823,7 @@ ((((-187)) . T) (((-862)) . T)) ((((-862)) . T)) (((|#1|) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-129)) . T) (((-862)) . T)) ((((-566) |#1|) . T)) ((((-129)) . T)) @@ -3832,13 +3832,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) -(-2700 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) +(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-533 |#2|)) . T)) -((((-2 (|:| -1924 (-1175)) (|:| -2713 (-52)))) . T)) +((((-2 (|:| -2010 (-1175)) (|:| -2818 (-52)))) . T)) ((((-566) (-129)) . T)) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) @@ -3853,8 +3853,8 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2805 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2805 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((($) . T)) (((|#2| (-533 (-864 |#1|))) . T)) ((((-1180)) . T)) @@ -3869,13 +3869,13 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-1180)) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2805 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1|) . T)) (((|#2| (-771)) . T)) (((|#1| |#2|) . T)) ((((-1157) |#1|) . T)) ((((-409 |#2|)) . T)) -((((-2 (|:| -1924 |#1|) (|:| -2713 |#2|))) . T)) +((((-2 (|:| -2010 |#1|) (|:| -2818 |#2|))) . T)) (|has| |#1| (-558)) (|has| |#1| (-558)) ((($) . T) ((|#2|) . T)) @@ -3886,14 +3886,14 @@ ((((-566)) . T) (($) . T)) (((|#2| $) |has| |#2| (-287 |#2| |#2|))) (((|#1| (-644 |#1|)) |has| |#1| (-848))) -(-2700 (|has| |#1| (-233)) (|has| |#1| (-351))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-233)) (|has| |#1| (-351))) +(-2805 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1260 |#1|)) . T) (((-566)) . T) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-1038 (-409 (-566))))) (|has| |#1| (-1099)) (((|#1|) . T)) -((((-1260 |#1|)) . T) (((-566)) . T) (($) -2700 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-1081)) . T) ((|#2|) . T) (((-409 (-566))) -2700 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566)))))) +((((-1260 |#1|)) . T) (((-566)) . T) (($) -2805 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-1081)) . T) ((|#2|) . T) (((-409 (-566))) -2805 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566)))))) ((((-409 (-566))) . T) (($) . T)) -((((-999 |#1|)) . T) ((|#1|) . T) (((-566)) -2700 (|has| (-999 |#1|) (-1038 (-566))) (|has| |#1| (-1038 (-566)))) (((-409 (-566))) -2700 (|has| (-999 |#1|) (-1038 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566)))))) +((((-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)))))) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) @@ -3909,10 +3909,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1139 |#1| |#2|) #0#) |has| (-1139 |#1| |#2|) (-310 (-1139 |#1| |#2|)))) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) #0#) |has| (-2 (|:| -1924 |#1|) (|:| -2713 |#2|)) (-310 (-2 (|:| -1924 |#1|) (|:| -2713 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) #0#) |has| (-2 (|:| -2010 |#1|) (|:| -2818 |#2|)) (-310 (-2 (|:| -2010 |#1|) (|:| -2818 |#2|))))) (((#0=(-116 |#1|)) |has| #0# (-310 #0#))) ((($ $) . T)) -(-2700 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2805 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((($ $) . T) ((#0=(-864 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-233)) ((|#2| |#1|) |has| |#1| (-233)) ((|#3| |#1|) . T) ((|#3| $) . 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. -613) 184086) ((-390 . -102) T) ((-1119 . -143) T) ((-126 . -613) 184018) ((-874 . -1099) T) ((-658 . -413) 184002) ((-714 . -613) 183984) ((-249 . -613) 183951) ((-187 . -613) 183933) ((-162 . -613) 183915) ((-157 . -613) 183897) ((-1279 . -726) T) ((-1101 . -34) T) ((-871 . -795) NIL) ((-871 . -792) NIL) ((-858 . -850) T) ((-731 . -886) NIL) ((-1288 . -131) T) ((-383 . -131) T) ((-892 . -616) 183865) ((-904 . -102) T) ((-731 . -1038) 183741) ((-533 . -131) T) ((-1086 . -413) 183725) ((-1000 . -491) 183709) ((-117 . -402) 183686) ((-1166 . -1214) 183665) ((-782 . -413) 183649) ((-780 . -413) 183633) ((-943 . -34) T) ((-694 . -1150) NIL) ((-252 . -648) 183468) ((-251 . -648) 183290) ((-817 . -920) 183269) ((-456 . -413) 183253) ((-602 . -19) 183237) ((-1145 . -1207) 183206) ((-1166 . -886) NIL) ((-1166 . -884) 183158) ((-602 . -604) 183135) ((-1200 . -613) 183067) ((-1174 . -613) 183049) ((-62 . -397) T) ((-1172 . -1038) 182984) ((-1166 . -1038) 182950) ((-694 . -38) 182900) ((-40 . 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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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-616) 77142) ((-128 . -151) 77124) ((-1141 . -900) 77083) ((-44 . -111) 77062) ((-1219 . -1099) T) ((-1180 . -1259) T) ((-1165 . -492) 77043) ((-1165 . -613) 77009) ((-670 . -1049) T) ((-1157 . -614) NIL) ((-1157 . -613) 76991) ((-1062 . -610) 76966) ((-1062 . -1099) T) ((-994 . -492) 76947) ((-74 . -443) T) ((-74 . -397) T) ((-994 . -613) 76913) ((-152 . -1056) 76897) ((-670 . -233) 76876) ((-573 . -556) 76860) ((-357 . -147) 76839) ((-357 . -145) 76790) ((-354 . -147) 76769) ((-354 . -145) 76720) ((-346 . -147) 76699) ((-346 . -145) 76650) ((-265 . -145) 76629) ((-265 . -147) 76608) ((-252 . -38) 76578) ((-247 . -147) 76557) ((-117 . -365) T) ((-247 . -145) 76536) ((-251 . -38) 76506) ((-152 . -111) 76485) ((-1003 . -1038) 76373) ((-1166 . -848) NIL) ((-694 . -1218) T) ((-799 . -1057) T) ((-699 . -1111) T) ((-1284 . -1049) T) ((-1155 . -1214) T) ((-1003 . -379) 76350) ((-910 . -145) T) ((-910 . -147) 76332) ((-870 . -131) T) ((-815 . -1056) 76229) ((-699 . -23) T) ((-694 . -558) T) 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-1038) 1576) ((-596 . -726) T) ((-409 . -850) 1527) ((-169 . -111) 1423) ((-833 . -131) 1375) ((-737 . -151) 1359) ((-1264 . -310) 1297) ((-489 . -308) T) ((-381 . -613) 1264) ((-522 . -1010) 1248) ((-381 . -614) 1162) ((-217 . -308) T) ((-141 . -151) 1144) ((-714 . -287) 1123) ((-489 . -1022) T) ((-582 . -38) 1110) ((-566 . -38) 1097) ((-497 . -38) 1062) ((-217 . -1022) T) ((-871 . -1049) T) ((-836 . -613) 1044) ((-827 . -613) 1026) ((-825 . -613) 1008) ((-816 . -909) 987) ((-1288 . -1111) T) ((-1237 . -1056) 810) ((-855 . -1056) 794) ((-871 . -243) T) ((-871 . -233) NIL) ((-689 . -1214) T) ((-1288 . -23) T) ((-816 . -648) 719) ((-552 . -1214) T) ((-420 . -340) 703) ((-573 . -1056) 690) ((-1237 . -111) 499) ((-701 . -639) 481) ((-855 . -111) 460) ((-383 . -23) T) ((-169 . -616) 238) ((-1187 . -516) 30) ((-681 . -1099) T) ((-676 . -1099) T) ((-662 . -1099) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 82fd46a9..3d47dfeb 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3453610655) +(30 . 3453749791) (4420 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -478,663 +478,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |frobenius| |generators| |createGenericMatrix| - |numberOfChildren| |weierstrass| |e04gcf| |removeDuplicates!| - |extendedResultant| |fmecg| |LagrangeInterpolation| |complexLimit| - |pastel| |dflist| |fractRagits| |power!| |e04mbf| |swap!| |adjoint| - |expr| |polar| |OMParseError?| |extendIfCan| |iibinom| - |noncommutativeJordanAlgebra?| |nextIrreduciblePoly| - |irreducibleFactors| |euclideanNormalForm| |leftRemainder| - |atrapezoidal| |elseBranch| |even?| |iisec| |printInfo| - |palgintegrate| |pade| |badNum| |clipPointsDefault| |getBadValues| - |fortranLiteral| |imagi| |compose| |OMgetInteger| |nextsousResultant2| - |deleteProperty!| |e02zaf| |merge!| |divideExponents| - |modifyPointData| |coerceP| |linearDependenceOverZ| |domainTemplate| - |solveLinearlyOverQ| |style| |OMputAttr| |variable| |powerSum| - |normalizeAtInfinity| |unitVector| |algebraicSort| |rootSplit| - |palgextint| |taylorQuoByVar| |symbol| |iiacos| |singularitiesOf| - |iterators| |cPower| |pomopo!| |realEigenvalues| |clearTable!| - |mulmod| |OMgetType| |dimension| |expression| |d01alf| |f01qcf| - |selectfirst| |addPoint2| |quatern| |bracket| |cycleTail| |integer| - |listConjugateBases| |e02daf| |float?| |basisOfCentroid| |f01ref| - |printHeader| |measure| |script| |makeCrit| |sinh2csch| |rischDE| - |curve| |localIntegralBasis| |genericRightMinimalPolynomial| - |numFunEvals3D| |revert| |setleaves!| |iCompose| |mainCoefficients| - |complexNumericIfCan| |outputAsTex| |closedCurve| - |removeIrreducibleRedundantFactors| |normalForm| |eulerPhi| - |rootPower| |lazyPremWithDefault| |edf2df| |startTable!| |infRittWu?| - |surface| |setValue!| |modTree| |rk4qc| |tex| ** |algebraicOf| - |makeViewport3D| |tubeRadius| |s21baf| - |generalizedContinuumHypothesisAssumed?| |iiexp| |rroot| |f04mcf| - |blue| |pdf2df| |s17agf| |super| |quadraticNorm| |f04maf| |e01bgf| - |port| |elements| |s19adf| |SturmHabichtCoefficients| |block| |s19abf| - |mainPrimitivePart| |conditionP| |isExpt| |identity| |removeSinSq| - |extractTop!| |external?| |parent| |normalizeIfCan| |elliptic?| - |boundOfCauchy| |rotatey| |log2| |outputMeasure| |t| |label| - |degreePartition| |infieldIntegrate| |listLoops| |error| |moebiusMu| - |logIfCan| |pop!| |split| |splitConstant| |closed?| - |univariatePolynomial| |d03faf| |unmakeSUP| |assert| - |standardBasisOfCyclicSubmodule| |reduction| |cyclotomicFactorization| - |octon| |twist| |f02axf| |outlineRender| |elliptic| |OMgetVariable| - |e01saf| |d01ajf| |sncndn| |prepareDecompose| |doublyTransitive?| - |prem| |substring?| |nonLinearPart| |OMsupportsSymbol?| - |incrementKthElement| |showTheIFTable| |UnVectorise| |elRow2!| - |univariateSolve| |clip| |monomRDE| |lieAdmissible?| |OMputEndError| - |newSubProgram| |nullary| |rootKerSimp| |curry| |besselJ| |extract!| - |removeZero| |suffix?| |imagj| |cSec| |lazyPquo| |rightExactQuotient| - |coerceImages| |OMreadFile| |deepestTail| |more?| |product| - |lowerPolynomial| |setref| |leaf?| |optAttributes| |iiperm| - |constructor| |basisOfCommutingElements| |integralDerivationMatrix| - |leftDiscriminant| |phiCoord| |prefix?| |mapExpon| |cAtanh| - |currentCategoryFrame| |odd?| |Ci| |sizeMultiplication| |d01amf| - |lazyResidueClass| |sec2cos| |option| |startTableGcd!| |minimize| - |lifting| |readInt8!| |groebgen| |resetAttributeButtons| |leftMult| - |exportedOperators| |rightLcm| |createMultiplicationMatrix| - |rowEchelon| |endOfFile?| |mainVariables| |e02baf| |iiasec| |real?| - |member?| |extend| |littleEndian| |perfectSquare?| |e01bef| - |OMgetSymbol| |basis| |biRank| |hcrf| |OMputEndBind| |goodPoint| - |imagE| |iisqrt2| |FormatRoman| |constantOperator| - |leadingCoefficientRicDE| |symmetric?| |var2Steps| |janko2| - |completeHermite| |rightTrim| |recoverAfterFail| |expandLog| - |multiplyCoefficients| |corrPoly| |is?| - |purelyAlgebraicLeadingMonomial?| |iisin| |fortranLiteralLine| - |leftTrim| |cycleSplit!| |argument| |overlabel| |infix?| - |rowEchelonLocal| |getOperands| |shiftLeft| |explicitlyEmpty?| - |belong?| |iflist2Result| |rightTraceMatrix| |lazy?| |solveRetract| - |mask| |squareFreeFactors| |basisOfMiddleNucleus| |sorted?| - |subHeight| |cfirst| |doubleComplex?| |cyclePartition| - |numericalOptimization| |hitherPlane| |approxSqrt| |OMserve| - |acoshIfCan| |condition| |lastSubResultantElseSplit| |getCurve| - |notelem| |myDegree| |morphism| |setStatus!| |lists| |minordet| - |tubePoints| |numberOfComputedEntries| |basisOfLeftAnnihilator| - |constant| |taylorIfCan| |predicates| |squareMatrix| |ord| - |nextPrimitivePoly| |findConstructor| |expenseOfEvaluation| - |cothIfCan| |lprop| |expenseOfEvaluationIF| |symmetricProduct| - |s17akf| |makeFR| |principalIdeal| |close| |lowerCase| |errorInfo| - |coth2tanh| |subscript| |createPrimitivePoly| |copy!| |rk4| - |pleskenSplit| |OMgetBVar| |rombergo| |e02bef| |bubbleSort!| - |curveColorPalette| |qelt| |hexDigit?| |numberOfPrimitivePoly| |iipow| - |kind| |d02ejf| |orthonormalBasis| |display| |changeVar| |packageCall| - |karatsuba| |enqueue!| |rotatez| |upperCase| |space| |palgRDE| - |genericRightTrace| |op| |pattern| |paraboloidal| |adaptive| - |quadratic| |clipSurface| |flagFactor| |cSin| |varList| |truncate| - |testDim| |cycleEntry| |atanIfCan| |delta| |toroidal| |appendPoint| - |pmComplexintegrate| |exprToGenUPS| |makeEq| |mantissa| |over| - |rootsOf| |basisOfLeftNucleus| |linearAssociatedLog| |normalize| - |high| |cyclicParents| |scanOneDimSubspaces| |isImplies| - |makeYoungTableau| |sizePascalTriangle| |structuralConstants| |point?| - |functorData| |rightRemainder| |vconcat| |iiacoth| |push| |algint| - |showScalarValues| |makingStats?| |retract| |input| |message| - |square?| |rectangularMatrix| |tube| |setCondition!| - |oneDimensionalArray| |OMopenFile| |factorPolynomial| |isEquiv| |ode1| - |library| |e02gaf| |schwerpunkt| |position!| |quasiAlgebraicSet| - |OMUnknownCD?| |Aleph| |computePowers| |identification| |OMgetApp| - |setAdaptive| |union| |tubePlot| |qroot| |composite| - |selectFiniteRoutines| |comment| |var2StepsDefault| |UpTriBddDenomInv| - |LowTriBddDenomInv| |head| |coth2trigh| |semiResultantEuclideannaif| - |chvar| |graphState| |numberOfNormalPoly| |mr| |setprevious!| - |constDsolve| |OMgetEndObject| |mathieu23| |pushup| |factorial| - |lambda| |allRootsOf| |compile| |unparse| |pushdterm| F2FG |ef2edf| - |setTopPredicate| |zag| |fractRadix| |set| |discreteLog| |fracPart| - |lex| |legendreP| |getConstant| |cons| |testModulus| |recur| - |primitive?| |e04dgf| |unitNormalize| |gethi| |e02agf| |infLex?| - |HermiteIntegrate| |cSech| |buildSyntax| |iidsum| |d02cjf| |kovacic| - |ratDenom| |select!| |fortranLinkerArgs| |rightMult| |dimensionsOf| - |chiSquare| |generalizedEigenvector| |lfextendedint| |rename| - |innerSolve1| |compactFraction| |tan2cot| |inc| |readLineIfCan!| - |coordinate| |zCoord| |OMunhandledSymbol| |semiResultantEuclidean2| - |coleman| |normal?| |OMgetString| |eq?| |critMonD1| |plus| - |selectOptimizationRoutines| |bombieriNorm| |quadraticForm| |prime?| - |linearDependence| |vertConcat| |withPredicates| |gramschmidt| - |associatedSystem| |removeSquaresIfCan| |cAsec| |makeSeries| LODO2FUN - |s17ahf| |triangular?| |exprToXXP| |quotient| |coordinates| |crest| - |useEisensteinCriterion| |diophantineSystem| |exptMod| - |antiCommutator| |setfirst!| |thetaCoord| |intChoose| |iidprod| - |cardinality| |list?| |stFunc2| |binding| |f2st| |sumSquares| - |setProperty| |times| |rarrow| |empty| |binaryTree| |maxint| - |shufflein| |cyclotomicDecomposition| |mainDefiningPolynomial| - |repeating?| |rationalPoint?| |clipParametric| |extractProperty| - |aQuadratic| |Gamma| |optimize| |bat| |mathieu22| |sinhIfCan| FG2F - |reducedDiscriminant| |supDimElseRittWu?| |shallowCopy| |arity| - |polygon| |clearTheFTable| |central?| |makeTerm| |uniform01| - |vectorise| |region| |zoom| |node| |factorAndSplit| |max| |initial| - |normalElement| |zeroSetSplitIntoTriangularSystems| |iiacsc| - |arrayStack| |antisymmetric?| |isMult| |s18adf| |monom| |extension| - |genericLeftNorm| |d02gbf| |stopMusserTrials| |OMputError| |imagI| - |pseudoQuotient| |bfEntry| |OMconnectTCP| |partialQuotients| - |rightPower| |rewriteIdealWithHeadRemainder| |collectQuasiMonic| |mix| - |rightUnit| |meshFun2Var| |OMencodingUnknown| |polynomialZeros| |dec| - |iisinh| |iiabs| |symmetricSquare| |degreeSubResultant| - |prolateSpheroidal| |mainMonomial| |triangSolve| |queue| |dihedral| - |perspective| |host| |rewriteIdealWithQuasiMonicGenerators| |common| - |groebnerFactorize| |distFact| |box| |stirling2| |mapDown!| |back| - |explogs2trigs| |RittWuCompare| |computeInt| |connectTo| - |limitedIntegrate| |constantLeft| |fractionFreeGauss!| |key| |copies| - |nthExponent| |errorKind| |certainlySubVariety?| |primlimintfrac| - |iteratedInitials| |dmp2rfi| |split!| |equality| |quadratic?| - |cyclicSubmodule| |dot| |innerEigenvectors| |integral?| - |semiDiscriminantEuclidean| |subst| |filename| |quasiMonic?| - |pushdown| |primitivePart!| |linearPart| |complexZeros| |palgLODE0| - |viewSizeDefault| |c06frf| |determinant| |permutations| |nthRootIfCan| - |OMputVariable| |superscript| |symmetricRemainder| |removeZeroes| - |genericRightDiscriminant| |drawToScale| |intPatternMatch| |cCsc| - |OMputBind| |badValues| |parse| |setButtonValue| - |fortranCarriageReturn| |numericalIntegration| |digit?| |checkForZero| - |ODESolve| |rightExtendedGcd| |constantToUnaryFunction| |backOldPos| - |isPlus| |fortranCharacter| |var1StepsDefault| |exponential| - |setFormula!| |iterationVar| |indices| |continuedFraction| |cup| - |submod| |s01eaf| |leftLcm| |eval| |makeSUP| |meatAxe| |argumentList!| - |permutation| |leftAlternative?| |representationType| |equation| - |kroneckerDelta| |schema| |rootDirectory| |complex?| |readable?| - |primaryDecomp| |expandPower| |henselFact| |objects| |summation| - |pointColorPalette| |overset?| |xn| |pole?| |singularAtInfinity?| - |ratDsolve| |exprToUPS| |genericLeftDiscriminant| |base| |UP2ifCan| EQ - |basisOfRightNucleus| |replace| |repeating| |edf2efi| |inRadical?| - |internalZeroSetSplit| |totalDifferential| |subResultantsChain| |rk4a| - |edf2fi| |factorByRecursion| |c05pbf| |setleft!| |inverseColeman| - |normalized?| |swapRows!| |leftGcd| |setrest!| |messagePrint| |nlde| - |branchIfCan| |hMonic| |inHallBasis?| |listexp| |bezoutMatrix| - |cyclicGroup| |singleFactorBound| |LyndonWordsList1| |laurentIfCan| - |f02bjf| |nand| |unprotectedRemoveRedundantFactors| |palgRDE0| - |resetBadValues| |stoseInvertible?| |zero| |getProperty| |bag| - |cAcsch| |subResultantChain| |symbolTable| |sech| |rename!| - |algintegrate| |monomRDEsys| |iisech| |quotientByP| |lfunc| - |distdfact| |transcendent?| |any?| |csch| |pascalTriangle| |aLinear| - |strongGenerators| |nthFractionalTerm| |positiveSolve| |And| - |properties| |parts| |index| |s19aaf| |pushucoef| |LiePolyIfCan| - |iiasech| |pushFortranOutputStack| |asinh| |computeCycleLength| - |s17acf| |associator| |aCubic| |newTypeLists| |Or| |getlo| - |popFortranOutputStack| |headAst| |c06fpf| |translate| |lcm| - |genericRightTraceForm| |acosh| |setLength!| |directSum| - |OMencodingBinary| |asechIfCan| |leftQuotient| |Not| |varselect| - |f04axf| |untab| |f01qef| |outputAsFortran| |atanh| |critT| |interval| - |normalizedDivide| |fixPredicate| |delete| |characteristicSet| |pair| - |univariate?| |associatedEquations| |bsolve| |append| - |removeSuperfluousCases| |acoth| |e01baf| |invertible?| |value| - |viewPosDefault| |completeEval| |monomialIntegrate| |po| |integral| - |maxrow| |alternative?| |gcd| |asech| |asinhIfCan| |interactiveEnv| - |order| |spherical| |reverse!| |previous| |linearPolynomials| - |setAttributeButtonStep| |rangeIsFinite| |primintfldpoly| |false| - |arguments| |padicallyExpand| |removeRoughlyRedundantFactorsInPols| - |sign| |radPoly| |radicalRoots| |consnewpol| |pdf2ef| |squareFreePart| - |maxdeg| |multiple| |tower| |parametric?| |s20acf| |lighting| - |infinite?| |sh| |normInvertible?| |repeatUntilLoop| |expintfldpoly| - |rowEchLocal| |applyQuote| |moduleSum| |e02adf| |tan2trig| - |OMputEndObject| |wholeRagits| |stop| |root?| |numberOfDivisors| - |unrankImproperPartitions1| |s14baf| |squareFreePrim| |fi2df| - |denomLODE| |Ei| |autoReduced?| |clearFortranOutputStack| |atanhIfCan| - |interpret| |s17dlf| |stack| |content| |totolex| |just| - |initializeGroupForWordProblem| |pmintegrate| |rCoord| |objectOf| - |FormatArabic| |SturmHabichtMultiple| |pointLists| |ruleset| - |leftUnit| |lyndonIfCan| |e02bdf| |createThreeSpace| |fixedDivisor| - |dim| |compBound| |getDatabase| |mapExponents| |areEquivalent?| - |unit?| |precision| |reflect| |eulerE| |beauzamyBound| |imports| - |complexNumeric| |magnitude| |fixedPoints| |setsubMatrix!| - |cosSinInfo| |totalGroebner| |iiasinh| |edf2ef| |readByte!| - |squareFreeLexTriangular| |leftRecip| |printingInfo?| |recolor| - |postfix| |cCoth| |suchThat| |top!| |normalise| |s17dcf| - |discriminant| |kernels| |selectPolynomials| |move| |separateDegrees| - |groebnerIdeal| |OMencodingSGML| |vector| |setPosition| - |univariatePolynomialsGcds| |exprHasWeightCosWXorSinWX| |pseudoDivide| - |increasePrecision| |operator| |read!| |iicosh| |setMinPoints| - |graphImage| |differentiate| |ellipticCylindrical| |exactQuotient| - |f04mbf| |laurentRep| |log10| |abs| |s17dgf| |halfExtendedResultant2| - |reduceLODE| |coefChoose| |exprHasAlgebraicWeight| |iicot| |e04ycf| - |delete!| |cAcot| |univariate| |bitand| |preprocess| - |chineseRemainder| |selectsecond| |s17aff| |sylvesterMatrix| - |mainContent| |radicalEigenvalues| |terms| |hspace| |bitior| - |palglimint0| |polarCoordinates| |negative?| |pToDmp| |s14abf| - |thenBranch| |stopTableInvSet!| |rangePascalTriangle| |constantIfCan| - F |mpsode| |changeNameToObjf| |initiallyReduce| |minPoints| |ignore?| - |mightHaveRoots| |laplacian| |digamma| |linSolve| |factor| |s18aef| - |finiteBound| |horizConcat| |df2fi| |Nul| |startTableInvSet!| |s13acf| - |sqrt| |numberOfImproperPartitions| |mindeg| |randnum| |qPot| - |minColIndex| |bit?| |nonSingularModel| |createIrreduciblePoly| - |binary| |null| |search| |mdeg| |hostByteOrder| |real| |freeOf?| - |center| |OMlistCDs| |commaSeparate| |coefficients| - |generalizedContinuumHypothesisAssumed| |screenResolution| |not| - |write!| |element?| |whatInfinity| |imag| |minimalPolynomial| - |createPrimitiveNormalPoly| |mapMatrixIfCan| |string?| |directProduct| - |and| |contractSolve| |f02aef| |viewWriteAvailable| |f02aaf| - |tubePointsDefault| |removeRoughlyRedundantFactorsInPol| - |monicRightDivide| |hasPredicate?| |coerceListOfPairs| |any| |iisqrt3| - |or| |extractPoint| |mapGen| |setPredicates| |genus| - |extractSplittingLeaf| |iiatanh| |outputFloating| |B1solve| |conical| - |iExquo| |GospersMethod| |physicalLength!| |e02ajf| |xor| - |toseInvertibleSet| |closeComponent| |brace| |generalSqFr| |omError| - |leadingIndex| |cosh2sech| GF2FG |zeroMatrix| |f01maf| - |doubleFloatFormat| |case| |paren| |OMputApp| |retractable?| - |destruct| |s13aaf| |f02bbf| |OMgetAttr| |f02aff| |monicLeftDivide| - |Zero| |internalDecompose| |monicCompleteDecompose| |lazyVariations| - |mainExpression| |leaves| |complexIntegrate| |s17dhf| - |changeThreshhold| |OMputBVar| |fillPascalTriangle| |One| |yellow| - |measure2Result| |s17adf| |rational| |nary?| |s18def| |OMreceive| - |denominator| |rootNormalize| |sequences| |infinityNorm| - |viewWriteDefault| |minimumExponent| |coerce| |cycles| |supRittWu?| Y - |cTan| |iitan| |factor1| |viewZoomDefault| |monomial| |asecIfCan| - |pack!| |construct| |critpOrder| |RemainderList| |OMgetAtp| |mapUp!| - |rischNormalize| |updatD| |insertRoot!| |multivariate| |meshPar2Var| - |status| |frst| |multiEuclidean| |component| |dimensions| - |stiffnessAndStabilityFactor| |createNormalPrimitivePoly| |curryLeft| - |sup| |variables| |complementaryBasis| |critMTonD1| |hostPlatform| - |exprex| |satisfy?| |bothWays| |rightQuotient| |basisOfRightNucloid| - |getOrder| |transpose| |quasiComponent| |expressIdealMember| |critM| - |coerceL| |mainValue| |internalInfRittWu?| |number?| |isTimes| - 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|optpair| |getZechTable| |neglist| |OMgetFloat| |f02ajf| |inf| |new| - |hi| |stoseInternalLastSubResultant| |composites| |setLabelValue| - |stopTableGcd!| |mathieu11| |pquo| |cAsinh| |OMwrite| |cAcos| |insert| - |stoseIntegralLastSubResultant| |s19acf| |npcoef| |rk4f| |implies| - |decomposeFunc| |graeffe| |leadingExponent| |splitSquarefree| - |zeroVector| |rootProduct| |palgint0| |intcompBasis| |character?| - |csubst| |solve| |rischDEsys| |clearCache| |f02akf| |members| - |indiceSubResultant| |options| |generalTwoFactor| |splitNodeOf!| - |csc2sin| |putColorInfo| |bitLength| |leftFactor| |abelianGroup| - |fullDisplay| |fTable| |eigenvectors| |inputBinaryFile| |hessian| - |second| |nextSublist| |positiveRemainder| |palglimint| - |LazardQuotient2| |primlimitedint| |s17aef| |writeLine!| |rightOne| - |fixedPointExquo| |third| |nthFactor| |primintegrate| |duplicates?| - |insertTop!| |showIntensityFunctions| |check| |atoms| |string| - |torsionIfCan| |heapSort| |rightRegularRepresentation| |reorder| - 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|halfExtendedResultant2| |algebraicDecompose| |algebraic?| + |squareFree| |certainlySubVariety?| |point| |eigenMatrix| |expression| + |nextPrimitivePoly| |reduceLODE| |resize| |someBasis| + |setScreenResolution3D| |mat| |primlimintfrac| |acsch| |integer| + |option?| |acotIfCan| |findConstructor| |coefChoose| |lquo| |dark| + |semiIndiceSubResultantEuclidean| |readInt16!| |iteratedInitials| + |reverseLex| |hasTopPredicate?| |int| |expenseOfEvaluation| + |exprHasAlgebraicWeight| |collectUnder| |cylindrical| |wrregime| + |series| |dmp2rfi| |csch2sinh| |reindex| |acscIfCan| |cothIfCan| + |iicot| |stoseInvertibleSetsqfreg| |basisOfRightAnnihilator| |split!| + |OMputEndAttr| |outputBinaryFile| |lprop| |balancedFactorisation| + |e04ycf| |iiasin| |extendedint| ** |equality| |resultantEuclidean| + |doubleResultant| |radicalSimplify| |expenseOfEvaluationIF| |delete!| + |changeBase| |cCsch| |algebraicVariables| |clipWithRanges| + |quadratic?| |complexSolve| |problemPoints| |port| |symmetricProduct| + |cAcot| |orbits| |failed?| |KrullNumber| |padecf| |min| + |cyclicSubmodule| |fmecg| |distance| |commonDenominator| |s17akf| + |chebyshevT| |preprocess| |aQuartic| |children| |colorFunction| + |realRoots| |LagrangeInterpolation| |dot| |gcdcofactprim| |t| + |torsionIfCan| |label| |error| |makeFR| |close!| |chineseRemainder| + |Lazard| |particularSolution| |innerEigenvectors| |complexLimit| + |interpretString| |f02xef| |triangularSystems| |heapSort| + |setProperties| |principalIdeal| |selectsecond| + |semiResultantEuclidean1| |s18acf| |assert| |showTypeInOutput| + |generators| |integral?| |pastel| |removeCosSq| |connect| + |rightRegularRepresentation| |lowerCase| |s17aff| |numberOfCycles| + |makeResult| |stoseLastSubResultant| |dflist| + |semiDiscriminantEuclidean| |nativeModuleExtension| |numberOfHues| + |attributeData| |reorder| |substring?| |errorInfo| |sylvesterMatrix| + |differentialVariables| |karatsubaDivide| |concat!| |psolve| + |fractRagits| |quasiMonic?| |mkcomm| |rightUnits| |tubeRadiusDefault| + |coth2tanh| |mainContent| |noKaratsuba| |sayLength| |vark| |power!| + |optional?| |pushdown| |swap| |credPol| |zerosOf| |suffix?| + |subscript| |bringDown| |radicalEigenvalues| |sumOfSquares| + |ListOfTerms| |e04mbf| |binomial| |primitivePart!| |listBranches| + |idealSimplify| |OMclose| |iiacos| |createPrimitivePoly| |terms| + |drawCurves| |makeSketch| |mainSquareFreePart| |constructor| + |linearPart| |createPrimitiveElement| |swap!| |cLog| |fractionPart| + |prefix?| |graphCurves| |singularitiesOf| |copy!| |maxIndex| |hspace| + |antiCommutative?| |represents| |complexZeros| |s21bcf| |adjoint| + |normDeriv2| |resultant| |sub| |option| |rk4| |palglimint0| + |laguerreL| |explimitedint| |norm| |polar| |sizeLess?| |palgLODE0| + |iomode| |solveInField| |complexExpand| |pleskenSplit| + |polarCoordinates| |s15adf| |outputGeneral| |createRandomElement| + |nthExpon| |OMParseError?| |viewSizeDefault| |absolutelyIrreducible?| + |solveLinear| |roughEqualIdeals?| |OMgetBVar| |negative?| |recip| + |subMatrix| |setMaxPoints| |c06frf| |extendIfCan| |lagrange| + |checkRur| |supersub| |setlast!| |rombergo| |pToDmp| |seed| |d01asf| + |lazyGintegrate| |iibinom| |mvar| |determinant| |rightTrim| |addiag| + |clearTheSymbolTable| |setPoly| |e02bef| |s14abf| |purelyAlgebraic?| + |quote| |ceiling| |noncommutativeJordanAlgebra?| |permutations| + |outputAsScript| |leftTrim| |curveColor| |sortConstraints| |infix?| + |atom?| |bubbleSort!| |thenBranch| |f02abf| |setFieldInfo| |increment| + |nextIrreduciblePoly| |nthRootIfCan| |karatsubaOnce| |cCosh| + |countRealRootsMultiple| |mask| |lastSubResultant| |curveColorPalette| + |ridHack1| |stopTableInvSet!| |reducedSystem| |pointSizeDefault| + |readInt32!| |OMputVariable| |irreducibleFactors| |sparsityIF| + |associates?| |generic?| |cycleTail| |hexDigit?| |rangePascalTriangle| + |univariatePolynomials| |condition| |integralBasisAtInfinity| + |jordanAdmissible?| |euclideanNormalForm| |remainder| |superscript| + |compiledFunction| |factorSquareFreePolynomial| |hue| + |numberOfPrimitivePoly| |constantIfCan| |OMsetEncoding| |randomLC| + |create3Space| |comment| |constant| |multMonom| |symmetricRemainder| + |leftRemainder| |doubleDisc| + |rewriteSetByReducingWithParticularGenerators| |cAsin| |iipow| + |wordInStrongGenerators| |mpsode| |extendedEuclidean| |makeSin| + |atrapezoidal| |firstDenom| |removeZeroes| |iiacsch| RF2UTS |lifting1| + |close| |d02ejf| |changeNameToObjf| |eisensteinIrreducible?| + |expandTrigProducts| |linearlyDependentOverZ?| |printCode| + |genericRightDiscriminant| |elseBranch| |bindings| |lepol| |positive?| + |orthonormalBasis| |subPolSet?| |initiallyReduce| + |genericLeftTraceForm| |primPartElseUnitCanonical!| |kind| + |drawToScale| |c06eaf| |even?| |cExp| |legendre| |f02awf| |display| + |changeVar| |s17ajf| |minPoints| |ranges| |f02agf| |iisec| + |intPatternMatch| |getGoodPrime| |op| |makeprod| + |isAbsolutelyIrreducible?| |setchildren!| |pattern| |packageCall| + |ignore?| |complexEigenvectors| |fixedPoint| |simplifyExp| + |palgintegrate| |cCsc| |e02ddf| |varList| |fill!| |simplifyLog| + |presub| |karatsuba| |mightHaveRoots| |zeroSetSplit| |isobaric?| + |d01bbf| |mantissa| |f07fdf| |OMputBind| |pade| |df2mf| + |wordInGenerators| |writeInt8!| |enqueue!| |laplacian| + |algebraicCoefficients?| |dmpToP| |symbol?| |badValues| |badNum| + |modifyPoint| |splitLinear| |OMgetEndBind| |cschIfCan| |rotatez| + |eigenvalues| |digamma| |iiatan| |maxPoints| |setButtonValue| + |printStatement| |clipPointsDefault| |increase| |resultantnaif| + |retract| |symmetricDifference| |input| |message| |upperCase| + |linSolve| |resultantReduitEuclidean| |c06fqf| |middle| + |fortranCarriageReturn| |getBadValues| |showArrayValues| |deepExpand| + |lllp| |cos2sec| |library| |space| |s18aef| |push!| |crushedSet| + |integer?| |anfactor| |fortranLiteral| |redPol| |numericalIntegration| + |union| UTS2UP |separateFactors| |palgRDE| |finiteBound| + |useNagFunctions| |tanQ| |unrankImproperPartitions0| |checkForZero| + |imagi| |nil?| |adaptive?| |tanh2coth| |inconsistent?| |universe| + |genericRightTrace| |horizConcat| |initials| |mappingAst| |mr| + |skewSFunction| |ODESolve| |compose| |LiePoly| |c06gqf| |cartesian| + |paraboloidal| |df2fi| |compile| |palginfieldint| |gcdPrimitive| + |power| |euclideanSize| |OMgetInteger| |rightExtendedGcd| + |wordsForStrongGenerators| |trigs| |se2rfi| |set| |adaptive| |rank| + |Nul| |e02akf| |partialNumerators| + |removeRoughlyRedundantFactorsInContents| |constantToUnaryFunction| + |cons| |nextsousResultant2| |shade| |wreath| |rotate| |algSplitSimple| + |quadratic| |startTableInvSet!| |symFunc| |elRow1!| |maximumExponent| + |deleteProperty!| |mulmod| |backOldPos| |oddlambert| + |subResultantGcdEuclidean| |componentUpperBound| |trunc| |clipSurface| + |leftCharacteristicPolynomial| |s13acf| |augment| |userOrdered?| + |constantOpIfCan| |OMgetType| |e02zaf| |isPlus| |moebius| |chebyshevU| + |sinIfCan| |flagFactor| |rdHack1| |numberOfImproperPartitions| + |nthCoef| |SturmHabicht| |fortranCharacter| |inc| + |solveLinearPolynomialEquationByRecursion| |merge!| |OMputFloat| + |mirror| |pureLex| |cSin| |decreasePrecision| |mindeg| + |trailingCoefficient| |ode2| |bipolar| |plus| |divideExponents| + |var1StepsDefault| |setRow!| |assign| |compdegd| |truncate| + |leftScalarTimes!| |randnum| |topFortranOutputStack| + |lineColorDefault| |laguerre| |exponential| |modifyPointData| + |perfectNthRoot| |deref| |froot| |testDim| |qPot| |maxrank| + |divergence| |trim| |coerceP| |toScale| |setFormula!| + |linearAssociatedExp| |possiblyInfinite?| |acosIfCan| |lists| + |cycleEntry| |minColIndex| |diagonal| |linearAssociatedOrder| + |polyPart| |dimension| |applyRules| |iterationVar| |monic?| + |sumOfKthPowerDivisors| |printInfo| |parabolicCylindrical| |bit?| + |points| |coord| |splitDenominator| |d01alf| |brillhartTrials| + |indices| |times| |relativeApprox| |integralBasis| |trapezoidalo| + |member?| |nonSingularModel| |regularRepresentation| |bernoulliB| + |leftDivide| |continuedFraction| |permanent| + |exprHasLogarithmicWeights| |specialTrigs| |optimize| + |internalAugment| |extend| |createIrreduciblePoly| |plus!| + |drawComplexVectorField| |expt| |digit?| |cup| |collectUpper| + |symmetricPower| |firstNumer| |halfExtendedSubResultantGcd1| + |littleEndian| |inrootof| |binary| |mkPrim| |symbolIfCan| + |uncouplingMatrices| |superHeight| |returnType!| |node| + |perfectSquare?| |balancedBinaryTree| |initial| |mdeg| + |createLowComplexityNormalBasis| |characteristicPolynomial| + |listConjugateBases| |arity| |monom| |f01mcf| |parametersOf| + |writable?| |e01bef| |f04arf| |hostByteOrder| |complete| + |monicDecomposeIfCan| |e02daf| |polygon| |f02adf| |sqfree| + |whitePoint| |OMgetSymbol| |freeOf?| |monicModulo| |denominators| + |functionIsContinuousAtEndPoints| |clearTheFTable| |float?| |sdf2lst| + |complexElementary| |basisOfNucleus| |basis| |movedPoints| + |lazyPseudoDivide| |basisOfCentroid| |central?| |common| |Vectorise| + |hclf| |ptFunc| |biRank| |byteBuffer| |pmintegrate| |setProperties!| + |extensionDegree| |formula| |makeTerm| |c02aff| |f04asf| + |extractBottom!| |hcrf| |key| |principal?| |rCoord| |factorOfDegree| + |lexTriangular| |uniform01| |definingEquations| |mainMonomials| + |super| |nextColeman| |OMputEndBind| |objectOf| |coefficient| + |computeBasis| |d01aqf| |vectorise| |groebner?| |goodPoint| |filename| + |FormatArabic| |writeByte!| |inverseLaplace| |conjugate| |region| + |isOp| |selectPDERoutines| |ScanFloatIgnoreSpacesIfCan| |imagE| + |SturmHabichtMultiple| |startStats!| |index?| |internal?| |nrows| + |zoom| |imagK| |tableau| |lazyPseudoRemainder| |iisqrt2| |parse| + |pointLists| |overbar| |partialDenominators| |oblateSpheroidal| + |ncols| |factorAndSplit| |squareFreePolynomial| |dominantTerm| + |integralCoordinates| |FormatRoman| |solid?| |leftUnit| + |normalElement| |doubleRank| |ip4Address| |integralMatrix| + |constantOperator| |createMultiplicationTable| + |useEisensteinCriterion?| |lyndonIfCan| |sin2csc| |eval| |f01ref| + |zeroSetSplitIntoTriangularSystems| |setStatus| |midpoints| |besselI| + |leadingCoefficientRicDE| |equation| |e02bdf| |typeList| |rightTrace| + |d01anf| |printHeader| |iiacsc| |OMlistSymbols| |factorSquareFree| + |bezoutDiscriminant| |symmetric?| |createThreeSpace| |clikeUniv| + |f04adf| |rubiksGroup| |measure| |arrayStack| |setright!| + |OMconnInDevice| |var2Steps| EQ |kmax| |fixedDivisor| |diag| + |addPointLast| |makeCrit| |antisymmetric?| + |semiResultantReduitEuclidean| |child?| |composites| |janko2| + |compBound| |duplicates| |commutative?| |normalDenom| |sinh2csch| + |isMult| |rootPoly| |monomialIntPoly| |setLabelValue| |datalist| + |completeHermite| |OMputSymbol| |getDatabase| |rightDivide| |tRange| + |f01qcf| |rischDE| |s18adf| |find| |definingPolynomial| + |stopTableGcd!| |stop| |recoverAfterFail| |brillhartIrreducible?| + |mapExponents| |prod| |airyAi| |selectfirst| |curve| |alphabetic| + |extension| |SFunction| |zero| |mathieu11| |expandLog| + |constantKernel| |areEquivalent?| |generalPosition| |evenlambert| + |localIntegralBasis| |genericLeftNorm| |youngGroup| |dmpToHdmp| |pquo| + |unit?| |multiplyCoefficients| |fibonacci| |palgextint| |bottom!| + |LazardQuotient| |ruleset| |genericRightMinimalPolynomial| |minIndex| + |d02gbf| |sylvesterSequence| |And| |cAsinh| |properties| |reflect| + |corrPoly| |index| |taylorQuoByVar| |rootOf| |bandedJacobian| + |totalfract| |numFunEvals3D| |stopMusserTrials| |pow| |deleteRoutine!| + |Or| |OMwrite| |reciprocalPolynomial| |lfextlimint| |is?| |eulerE| + |translate| |lcm| |sequence| |revert| |subscriptedVariables| + |OMputError| |innerint| |Not| |cAcos| + |purelyAlgebraicLeadingMonomial?| |beauzamyBound| + |permutationRepresentation| |changeName| |zeroDimPrime?| |suchThat| + |setleaves!| |identitySquareMatrix| |imagI| |delete| + |quasiMonicPolynomials| |stoseIntegralLastSubResultant| |alternating| + |iisin| |pair| |imports| |append| |d01fcf| |hconcat| |iCompose| + |value| |pseudoQuotient| |unravel| |integers| |s19acf| |var1Steps| + |fortranLiteralLine| |OMputAttr| |linears| |magnitude| |gcd| |airyBi| + |mainCoefficients| |bfEntry| |critBonD| |cAcosh| |npcoef| |powerSum| + |mainKernel| |cycleSplit!| |conditionsForIdempotents| |fixedPoints| + |false| |subresultantSequence| |complexNumericIfCan| |OMconnectTCP| + |nullary?| |setRealSteps| |rk4f| |argument| |setsubMatrix!| |f01rcf| + |repSq| |nodeOf?| |outputAsTex| |partialQuotients| |tower| + |mapUnivariate| |LyndonBasis| |implies| |overlabel| |setImagSteps| + |cosSinInfo| |bitTruth| |inR?| |closedCurve| |rightPower| |setnext!| + |maxPoints3D| |decomposeFunc| |rowEchelonLocal| |iicoth| + |totalGroebner| |unknownEndian| |leftExactQuotient| + |removeIrreducibleRedundantFactors| |rewriteIdealWithHeadRemainder| + |dequeue| |viewport2D| |graeffe| |iiasinh| |interpret| |getOperands| + |addmod| |perfectSqrt| |stack| |quasiRegular| |normalForm| + |collectQuasiMonic| |OMputString| |indiceSubResultantEuclidean| + |leadingExponent| |shiftLeft| |edf2ef| |nodes| |ffactor| + |factorSquareFreeByRecursion| |eulerPhi| |parabolic| |mix| |direction| + |dim| |splitSquarefree| |explicitlyEmpty?| |readByte!| + |stosePrepareSubResAlgo| |extendedSubResultantGcd| |returnTypeOf| + |rootPower| |rightUnit| |swapColumns!| |complexNumeric| |cot2trig| + |zeroVector| |belong?| |genericRightNorm| |squareFreeLexTriangular| + |leftOne| |palgextint0| |lazyPremWithDefault| |meshFun2Var| |d01gaf| + |factorFraction| |rootProduct| |iflist2Result| |logpart| |leftRecip| + |setLegalFortranSourceExtensions| |interpolate| |edf2df| |kernels| + |OMencodingUnknown| |constantCoefficientRicDE| |OMReadError?| + |palgint0| |rightTraceMatrix| |multiset| |printingInfo?| |unitNormal| + |torsion?| |startTable!| |polynomialZeros| |leftExtendedGcd| + |bernoulli| |operator| |intcompBasis| |lazy?| |recolor| |color| + |build| |sample| |infRittWu?| |alphabetic?| |iisinh| |log10| |divide| + |character?| |solveRetract| |multinomial| |postfix| |digit| + |prindINFO| |iiabs| |surface| |selectOrPolynomials| |tanIfCan| + |univariate| |bitand| |csubst| |squareFreeFactors| |cCoth| + |stoseInvertibleSetreg| |rightRank| |irreducible?| |setValue!| + |groebSolve| |symmetricSquare| |algDsolve| |bitior| |solve| + |basisOfMiddleNucleus| |top!| |gensym| |cap| |nextLatticePermutation| + |modTree| |degreeSubResultant| |numFunEvals| + |rewriteIdealWithRemainder| |rischDEsys| F |sorted?| + |tryFunctionalDecomposition| |normalise| |solve1| |printInfo!| |rk4qc| + |prolateSpheroidal| |intersect| |factor| |viewThetaDefault| |f02akf| + |subHeight| |s17dcf| |OMputInteger| |e04naf| |roughBase?| + |algebraicOf| |irreducibleFactor| |mainMonomial| |sqrt| |scan| + |members| |status| |cfirst| |listOfMonoms| |discriminant| + |inputOutputBinaryFile| |headRemainder| |decimal| |null| + |makeViewport3D| |search| |triangSolve| |simpleBounds?| |real| + |indiceSubResultant| |doubleComplex?| |center| |selectPolynomials| + |unitsColorDefault| |PollardSmallFactor| |SturmHabichtSequence| + |tubeRadius| |not| |invertIfCan| |queue| |radicalEigenvector| |imag| + |generalTwoFactor| |cyclePartition| |ldf2lst| |move| |getStream| + |euler| |s21baf| |and| |dihedral| |directProduct| + |tryFunctionalDecomposition?| |nullSpace| |splitNodeOf!| + |numericalOptimization| |leviCivitaSymbol| |separateDegrees| + |diagonalProduct| |subspace| |generalizedContinuumHypothesisAssumed?| + |or| |perspective| |wholePart| |setTex!| |csc2sin| |hitherPlane| + |leftZero| |groebnerIdeal| |bigEndian| |bumprow| |iiexp| |xor| + |branchPointAtInfinity?| |host| |generalizedInverse| |brace| + |putColorInfo| |approxSqrt| |binomThmExpt| |OMencodingSGML| |updatF| + |cscIfCan| |rroot| |case| |integerBound| + |rewriteIdealWithQuasiMonicGenerators| |seriesToOutputForm| |destruct| + |bitLength| |OMserve| |setPosition| |nullity| |zeroDim?| |subTriSet?| + |f04mcf| |Zero| |groebnerFactorize| |contains?| + |removeSuperfluousQuasiComponents| |leftFactor| |acoshIfCan| + |leastAffineMultiple| |univariatePolynomialsGcds| |linkToFortran| + |putGraph| |One| |blue| |distFact| |antiAssociative?| |c06gsf| + |abelianGroup| |lastSubResultantElseSplit| |exprHasWeightCosWXorSinWX| + |listOfLists| |pair?| |cyclicEntries| |stirling2| + |reduceBasisAtInfinity| |partialFraction| |fullDisplay| + |virtualDegree| |getCurve| |coerce| |pseudoDivide| Y |factorials| + |leftTrace| |mapDown!| |invmod| |monomial| |quartic| |fTable| + |notelem| |construct| |increasePrecision| |s14aaf| |OMreadStr| + |divideIfCan| |OMmakeConn| |back| |multivariate| |reduced?| + |eigenvectors| |myDegree| |read!| |asinIfCan| |identityMatrix| + |enterInCache| |dec| |explogs2trigs| |variables| |setOrder| |separate| + |inputBinaryFile| |iicosh| |conjug| |nextItem| |viewDeltaYDefault| + |RittWuCompare| |scaleRoots| |explicitEntries?| |hessian| |elRow2!| + |setMinPoints| |selectODEIVPRoutines| |linearMatrix| + |resultantEuclideannaif| |computeInt| |expint| |cyclicCopy| + |nextSublist| |univariateSolve| |graphImage| |idealiserMatrix| + |alternatingGroup| |inverse| |showSummary| |connectTo| |OMputAtp| + |lastSubResultantEuclidean| |positiveRemainder| |clip| |obj| + |ellipticCylindrical| |conjugates| |rationalApproximation| |vspace| + |lexGroebner| |quoByVar| |palglimint| |monomRDE| |socf2socdf| + |exactQuotient| |axes| |OMputEndAtp| |cache| |showAttributes| |eq?| + |binaryTournament| |squareTop| |taylor| |LazardQuotient2| + |lieAdmissible?| |leftRankPolynomial| |f04mbf| |linGenPos| |mathieu24| + |critMonD1| |trivialIdeal?| |laurent| |stFunc1| |primlimitedint| + |OMputEndError| |laurentRep| |getGraph| |e02aef| |evaluateInverse| + |selectOptimizationRoutines| |c05nbf| |chiSquare1| |puiseux| |s17aef| + |newSubProgram| |f01rdf| |diff| |bombieriNorm| |curryRight| |simpsono| + |writeLine!| |nullary| |invertible?| |subQuasiComponent?| |df2ef| + |delay| |quadraticForm| |readUInt16!| |inv| |insertionSort!| |name| + |rightOne| |rootKerSimp| |powerAssociative?| |viewPosDefault| + |internalIntegrate0| |partition| |prime?| |ground?| |normFactors| + |totalLex| |body| |fixedPointExquo| |curry| |principalAncestors| + |completeEval| |reducedForm| |linear?| |linearDependence| |nthFactor| + |fullPartialFraction| |besselJ| |monomialIntegrate| |remove| |droot| + |critB| |vertConcat| |noLinearFactor?| |coerceL| |primintegrate| + |extract!| |removeConstantTerm| |po| |trapezoidal| |polygon?| + |withPredicates| |factorset| |mainValue| |duplicates?| + |cRationalPower| |removeZero| |integral| |last| |setErrorBound| + |quoted?| |gramschmidt| |rationalPoints| |internalInfRittWu?| + |insertTop!| |assoc| |imagj| |maxrow| |viewport3D| |associatedSystem| + |number?| |generateIrredPoly| |showIntensityFunctions| |cSec| + |alternative?| |halfExtendedSubResultantGcd2| |finiteBasis| |cross| + |minPol| |removeSquaresIfCan| |isTimes| |symbolTable| |check| + |lazyPquo| |asinhIfCan| |pointData| |upperCase?| |geometric| |cAsec| + |outputList| |writeUInt8!| |subNode?| |atoms| |rightExactQuotient| + |leadingBasisTerm| |interactiveEnv| |OMgetEndAttr| |viewpoint| + |pushFortranOutputStack| |makeSeries| |OMopenString| |ParCond| + |coerceImages| |currentSubProgram| |order| |hypergeometric0F1| + |complement| |popFortranOutputStack| LODO2FUN |modularFactor| |graphs| + |f01bsf| |OMreadFile| |spherical| |makeMulti| |getExplanations| + |lazyPrem| BY |inverseIntegralMatrix| |s17ahf| + |primPartElseUnitCanonical| |outputAsFortran| |minPoly| |deepestTail| + |reverse!| |enterPointData| |isNot| |showClipRegion| |triangular?| + |one?| |diagonal?| |saturate| |more?| |constantRight| + |linearPolynomials| |pointPlot| |coHeight| |exprToXXP| + |numberOfOperations| |debug3D| |Frobenius| |depth| |product| + |setAttributeButtonStep| |prinb| |parseString| |quasiRegular?| |init| + |quotient| |cSinh| |pseudoRemainder| |arguments| |lambert| + |lowerPolynomial| |rangeIsFinite| |cycle| |subset?| |showAllElements| + |coordinates| |lookupFunction| |extractIfCan| |goto| |setref| + |integralMatrixAtInfinity| |primintfldpoly| |att2Result| + |mergeFactors| |crest| |adaptive3D?| |viewDeltaXDefault| + |indicialEquation| |leaf?| |entries| |padicallyExpand| + |OMconnOutDevice| |leftFactorIfCan| |useEisensteinCriterion| |df2st| + |generalInfiniteProduct| |s17def| |optAttributes| |cPower| NOT + |leftRank| |removeRoughlyRedundantFactorsInPols| |seriesSolve| + |rightNorm| |diophantineSystem| |makeGraphImage| |bandedHessian| + |polyred| |iiperm| |pomopo!| OR |ratpart| |sign| |padicFraction| + |printTypes| |exptMod| |distribute| |blankSeparate| |roughBasicSet| + |basisOfCommutingElements| |radPoly| AND |jordanAlgebra?| |entry| + |basisOfLeftNucloid| |viewPhiDefault| |antiCommutator| |every?| + |bivariateSLPEBR| |unaryFunction| |integralDerivationMatrix| + |listYoungTableaus| |radicalRoots| |radicalOfLeftTraceForm| + |subResultantGcd| |debug| |setfirst!| |has?| |bitCoef| |ratPoly| + |leftDiscriminant| |weakBiRank| |consnewpol| |stirling1| |pToHdmp| D + |thetaCoord| |nextSubsetGray| |relationsIdeal| |lintgcd| |phiCoord| + |pdf2ef| |rquo| |internalSubQuasiComponent?| |upperCase!| |contract| + |intChoose| |isList| |vector| |addMatchRestricted| |mapExpon| + |charClass| |squareFreePart| |basisOfCenter| |complexEigenvalues| + |iidprod| |numerator| |differentiate| |scale| |divisorCascade| + |cAtanh| |accuracyIF| |maxdeg| |btwFact| |hermite| |cardinality| + |nilFactor| |trueEqual| |createNormalElement| |currentCategoryFrame| + |parametric?| |largest| |indicialEquations| |latex| |list?| + |linearDependenceOverZ| |zeroDimensional?| |resetVariableOrder| + |quickSort| |odd?| |genericLeftMinimalPolynomial| |s20acf| + |trace2PowMod| |monicRightFactorIfCan| |domainTemplate| |stFunc2| + |getButtonValue| |trigs2explogs| |cCos| |char| |Ci| |leadingSupport| + |lighting| |primextintfrac| |isAnd| |binding| |makeFloatFunction| + |removeRedundantFactors| |clearTheIFTable| |sizeMultiplication| * + |firstSubsetGray| |infinite?| |reducedQPowers| |invertibleSet| |f2st| + |plusInfinity| |getMatch| |nextPrime| |extendedIntegrate| |d01amf| + |delta| |cycleRagits| |sh| |logGamma| |goodnessOfFit| |sumSquares| + |integerIfCan| |minusInfinity| |multisect| |mapSolve| |rem| + |lazyResidueClass| |createLowComplexityTable| |normInvertible?| + |headReduce| |fintegrate| |print| |setProperty| |logical?| |medialSet| + |integralAtInfinity?| |repeatUntilLoop| |quo| |sec2cos| = |llprop| + |OMread| |selectIntegrationRoutines| |resolve| |rarrow| |hexDigit| + |selectNonFiniteRoutines| |sts2stst| |startTableGcd!| |expintfldpoly| + |subNodeOf?| |cotIfCan| |endSubProgram| |empty| |leadingIdeal| + |f07fef| |getProperties| |minimize| |heap| |rowEchLocal| |div| < + |components| |c06gcf| |float| |binaryTree| |closedCurve?| + |changeWeightLevel| |prevPrime| |exponents| |lifting| |exquo| + |moduleSum| > |s18dcf| |externalList| |retractIfCan| |type| |maxint| + |showTheFTable| |showTheRoutinesTable| |rightAlternative?| |matrixGcd| + |readInt8!| ~= |e02adf| <= |callForm?| |polyRDE| |lambda| |shufflein| + |oddintegers| |Hausdorff| |groebgen| |plenaryPower| |leaves| |#| >= + |exactQuotient!| |tan2trig| |numer| |twoFactor| |axesColorDefault| + |cyclotomicDecomposition| |factorsOfDegree| |makeViewport2D| + |alphanumeric| |resetAttributeButtons| ~ |c06gbf| |signature| + |OMputEndObject| |denom| |processTemplate| |times!| + |mainDefiningPolynomial| |flexible?| |charpol| |polygamma| |addPoint2| + |leftMult| |wholeRagits| |sinhcosh| |pile| |powern| |erf| |repeating?| + |semiSubResultantGcdEuclidean1| |findCycle| |numericIfCan| + |exportedOperators| |e02dff| |root?| + |pi| |insertBottom!| + |validExponential| |rationalPoint?| |oddInfiniteProduct| |tanAn| + |exp1| |derivationCoordinates| |numberOfDivisors| |/\\| |s15aef| + |rightLcm| - |infinity| |bracket| |symmetricTensors| |clipParametric| + |generalizedEigenvectors| |midpoint| |highCommonTerms| + |normalizedAssociate| |inverseIntegralMatrixAtInfinity| + |createMultiplicationMatrix| |\\/| |max| |unrankImproperPartitions1| / + |redmat| GE |dilog| |extractProperty| |remove!| |typeLists| |ptree| + |cycleLength| |e01sef| |rowEchelon| |s14baf| |light| GT |htrigs| |sin| + |map| |aQuadratic| |exteriorDifferential| |encodingDirectory| |size?| + |bits| |kernel| |endOfFile?| |squareFreePrim| + |removeRedundantFactorsInContents| |setvalue!| LE |cos| |Gamma| + |s13adf| |primitiveElement| |overlap| |draw| |fi2df| |shift| + |mainVariables| |evaluate| LT |cot2tan| |characteristicSerie| |tan| + |bat| |cAsech| |commutativeEquality| |rightScalarTimes!| |e02baf| + |denomLODE| |makeop| |multiple?| |sturmSequence| |cot| |isQuotient| + |mathieu22| |tab1| |rationalPower| |unvectorise| |iiasec| |inspect| + |Ei| |bounds| |before?| |sec| |sinhIfCan| |generic| |pushuconst| + |leadingTerm| |real?| |genericPosition| |autoReduced?| |hdmpToP| + |merge| |csc| |convert| |property| FG2F |qelt| |s21bdf| + |argumentListOf| |OMsupportsCD?| |makeObject| + |clearFortranOutputStack| |presuper| |tanSum| |epilogue| |asin| + |qsetelt| |currentEnv| |reducedDiscriminant| |smith| |besselY| + |rightRecip| |pdf2df| |cond| |atanhIfCan| |stoseInvertible?sqfreg| + |coef| |indicialEquationAtInfinity| |digits| |acos| |script| |xRange| + |supDimElseRittWu?| |simplify| |rightFactorIfCan| + |mainCharacterization| |s17agf| |s17dlf| |OMgetError| |subSet| + |updateStatus!| |atan| |height| |units| |yRange| |shallowCopy| + |genericLeftTrace| |initTable!| |radicalSolve| |quadraticNorm| + |content| |pointColorDefault| |gcdprim| |transform| |acot| |eof?| + |elem?| |removeSinhSq| |f04maf| |palgLODE| |totolex| |makeCos| |Beta| + |asec| |tex| |chvar| |e02dcf| |prefixRagits| |lieAlgebra?| |e01bgf| + |just| |e01daf| |alphanumeric?| |binaryFunction| |acsc| |graphState| + |rightRankPolynomial| |baseRDEsys| |difference| |elements| |iroot| + |initializeGroupForWordProblem| |ldf2vmf| |slash| |sinh| + |numberOfNormalPoly| |divideIfCan!| |isOpen?| |xCoord| |s19adf| |key?| + |signatureAst| |cosh| |setprevious!| |code| |subst| |isConnected?| + |poisson| |radicalEigenvectors| |SturmHabichtCoefficients| |f02bjf| + |degreeSubResultantEuclidean| |localUnquote| |OMsend| |tanh| |box| + |constDsolve| |modularGcd| |f04jgf| |bright| |permutationGroup| + |block| |realEigenvalues| |nand| |copyInto!| |returns| |complexForm| + |coth| |OMgetEndObject| |exponent| |minimumDegree| |cyclotomic| + |s19abf| |clearTable!| |OMputEndBVar| + |unprotectedRemoveRedundantFactors| |headReduced?| + |transcendenceDegree| |sech| |mathieu23| |optpair| |mainPrimitivePart| + |factorsOfCyclicGroupSize| |palgRDE0| |zeroOf| |minRowIndex| |csch| + |pushup| |s20adf| |mainExpression| |getZechTable| |failed| + |conditionP| |resetBadValues| |setMaxPoints3D| |newReduc| |function| + |semiSubResultantGcdEuclidean2| |asinh| |factorial| |complexIntegrate| + |decompose| |neglist| |declare| |isExpt| |convergents| + |stoseInvertible?| |newLine| |realEigenvectors| |sort| |acosh| |dom| + |allRootsOf| |perfectNthPower?| |s17dhf| |objects| |OMgetFloat| + |identity| |getProperty| |safetyMargin| |tail| |atanh| |unparse| + |getMeasure| |changeThreshhold| |base| |f02ajf| |removeSinSq| |bag| + |comparison| |toseSquareFreePart| |setEpilogue!| |acoth| |pushdterm| + |OMputBVar| |gderiv| |inf| |extractTop!| |f2df| |cAcsch| + |computeCycleEntry| |LyndonWordsList| |asech| |lhs| F2FG + |fillPascalTriangle| |dAndcExp| |rules| + |stoseInternalLastSubResultant| |external?| |subResultantChain| + |colorDef| |setelt!| |lazyPseudoQuotient| |random| |rhs| |ef2edf| + |yellow| |mainVariable| |signAround| |parent| |unknown| |rename!| + |toseLastSubResultant| |monicDivide| |multiple| |setTopPredicate| + |title| |measure2Result| |sin?| |drawStyle| |normalizeIfCan| + |dioSolve| |algintegrate| |elColumn2!| |unexpand| |applyQuote| |zag| + |c06ebf| |s17adf| |zeroDimPrimary?| |elliptic?| |fortranInteger| + |monomRDEsys| |OMgetBind| |setAdaptive3D| |double| |fractRadix| + |meshPar1Var| |rational| |diagonals| |parts| |boundOfCauchy| |iisech| + |nextsubResultant2| |tValues| |initiallyReduced?| |e| |discreteLog| + |nary?| |lazyIntegrate| |fortranReal| |rotatey| |quotientByP| + |prologue| |flexibleArray| |shuffle| |fracPart| |getCode| |s18def| + |selectMultiDimensionalRoutines| |log2| |fprindINFO| |lfunc| + |readUInt8!| |li| |halfExtendedResultant1| |true| |lex| + |solveLinearlyOverQ| |c06fuf| |OMreceive| |createNormalPoly| + |outputMeasure| |distdfact| |completeSmith| |sturmVariationsOf| + |controlPanel| |style| |nothing| |legendreP| |cAcoth| |denominator| + |OMgetEndBVar| |degreePartition| |reopen!| |transcendent?| + |lowerCase?| |outputArgs| |getConstant| |rootNormalize| + |purelyTranscendental?| |previous| |leastPower| |infieldIntegrate| + |sort!| |any?| |makeUnit| |patternVariable| |testModulus| |sequences| + |multiplyExponents| |intensity| |listLoops| |rightDiscriminant| + |pascalTriangle| |pdct| |lowerCase!| |declare!| |recur| |infinityNorm| + |modularGcdPrimitive| |rootRadius| |moebiusMu| |pushNewContour| + |aLinear| |innerSolve| |setEmpty!| |primitive?| |c06ecf| + |viewWriteDefault| |getRef| |logIfCan| |dualSignature| + |strongGenerators| |separant| |OMgetEndError| |e04dgf| + |minimumExponent| |extractIndex| |yCoordinates| |directory| |width| + |pop!| |nthFractionalTerm| |integralLastSubResultant| |weight| + |mergeDifference| |unitNormalize| |cycles| |compound?| |d02raf| + |split| |idealiser| |positiveSolve| |mapmult| |readLine!| |gethi| + |OMgetEndApp| |supRittWu?| |powmod| |quatern| |splitConstant| + |laplace| |s19aaf| |shanksDiscLogAlgorithm| |iFTable| |call| |test| + |e02agf| |cTan| |mainVariable?| |s18aff| |closed?| |derivative| + |pushucoef| |nthFlag| |useSingleFactorBound?| |infLex?| |iitan| + |fortranComplex| |tanintegrate| |lo| |univariatePolynomial| + |numberOfMonomials| |LiePolyIfCan| |HenselLift| + |transcendentalDecompose| |open| |segment| |HermiteIntegrate| + |factor1| |sech2cosh| |topPredicate| |d03faf| |iiasech| |cCot| + |relerror| |possiblyNewVariety?| |cSech| |cAtan| |viewZoomDefault| + |nthr| |precision| |eq| |unmakeSUP| |computeCycleLength| + |rationalFunction| |readBytes!| |minrank| |ground| |buildSyntax| + |multiEuclideanTree| |asecIfCan| |mesh?| |createZechTable| |iter| + |s17acf| |standardBasisOfCyclicSubmodule| |optional| |prefix| |roman| + |extractClosed| |iidsum| |leadingMonomial| |pack!| |OMputEndApp| + |mkAnswer| |flatten| |reduction| |associator| |firstUncouplingMatrix| + |reify| |ramifiedAtInfinity?| |operations| |d02cjf| + |leadingCoefficient| |critpOrder| |solveid| |factorList| + |cyclotomicFactorization| |OMcloseConn| |aCubic| |Si| |coshIfCan| + |kovacic| |primitiveMonomials| |iprint| |RemainderList| |aromberg| + |octon| |currentScope| |newTypeLists| |e01bff| |ode| |ratDenom| + |reductum| |associatorDependence| |OMgetAtp| |plot| |twist| |getlo| + |physicalLength| |rightMinimalPolynomial| |rotate!| |select!| |output| + |mapUp!| |pol| |ddFact| |fortran| |f02axf| |headAst| + |numberOfFractionalTerms| |leftNorm| |d02kef| |fortranLinkerArgs| + |weights| |rischNormalize| |showTheSymbolTable| |checkPrecision| + |outlineRender| |startPolynomial| |c06fpf| |lexico| |hasoln| + |rightMult| |updatD| |acothIfCan| |imaginary| |elliptic| |nil| |exp| + |genericRightTraceForm| |graphStates| |prinpolINFO| |matrixConcat3D| + |dimensionsOf| SEGMENT |insertRoot!| |euclideanGroebner| + |removeCoshSq| |OMgetVariable| |setLength!| |null?| |primeFrobenius| + |polCase| |normalizeAtInfinity| |chiSquare| |meshPar2Var| |polyRicDE| + |stiffnessAndStabilityOfODEIF| |e01saf| |directSum| |f02wef| + |arbitrary| |moreAlgebraic?| |generalizedEigenvector| |unitVector| + |frst| |part?| |lflimitedint| |outerProduct| |d01ajf| |approximate| + |makeVariable| |OMencodingBinary| |LyndonCoordinates| |usingTable?| + |lfextendedint| |multiEuclidean| |harmonic| |unitCanonical| |complex| + |sncndn| |asechIfCan| |changeMeasure| |isPower| |setPrologue!| + |rename| |component| |cyclicEqual?| |dequeue!| |any| + |dimensionOfIrreducibleRepresentation| |prepareDecompose| + |leftQuotient| |log| |rootBound| |addBadValue| |innerSolve1| + |divisors| |dimensions| |operators| |doublyTransitive?| |varselect| + |e01sbf| |totalDegree| |equiv| |compactFraction| + |stiffnessAndStabilityFactor| |partitions| |bumptab1| |prem| + |getIdentifier| |f04axf| |PDESolve| |sechIfCan| |tan2cot| + |createNormalPrimitivePoly| |OMUnknownSymbol?| |moduloP| + |nonLinearPart| |untab| |viewDefaults| |traverse| |complexNormalize| + |sum| |readLineIfCan!| |curryLeft| |scalarMatrix| |mainForm| + |OMsupportsSymbol?| |concat| |e02def| |f01qef| |outputFixed| + |leastMonomial| |coordinate| |capacity| |sup| |lookup| + |incrementKthElement| |critT| |realZeros| |rowEch| |rational?| + |zCoord| |iiacot| |complementaryBasis| |normalDeriv| |showTheIFTable| + |interval| UP2UTS |pointColor| |c05adf| |OMunhandledSymbol| + |critMTonD1| |d02bhf| |d03edf| |UnVectorise| |normalizedDivide| + |definingInequation| |aspFilename| |bivariate?| + |semiResultantEuclidean2| |hostPlatform| |mindegTerm| |OMbindTCP| |lp| + |sPol| |fixPredicate| |raisePolynomial| |diagonalMatrix| |coleman| + |exprex| |f04faf| |OMgetObject| |linear| |characteristicSet| + |inGroundField?| |f07adf| |low| |normal?| |commutator| |satisfy?| + |e04ucf| |d01apf| |univariate?| |ParCondList| |stronglyReduce| + |bfKeys| |OMgetString| |bothWays| |systemCommand| |simpson| |source| + |polynomial| |associatedEquations| |acschIfCan| |chainSubResultants| + |rewriteSetWithReduction| |rightQuotient| |clearDenominator| + |category| |setOfMinN| |symmetricGroup| |bsolve| |binarySearchTree| + |setClosed| |atanIfCan| |basisOfRightNucloid| |bezoutResultant| + |domain| |bytes| |removeSuperfluousCases| |scripted?| |solid| |iilog| + |toroidal| |root| |normal| |getOrder| |package| |characteristic| + |makeRecord| |exponentialOrder| |e01baf| |rotatex| |rationalIfCan| + |show| |appendPoint| |unit| |transpose| |zeroSquareMatrix| + |triangulate| |prepareSubResAlgo| |pmComplexintegrate| |mapBivariate| + |quasiComponent| |internalIntegrate| |target| |setProperty!| |submod| + |rightCharacteristicPolynomial| |cosIfCan| |trace| |exprToGenUPS| + |expressIdealMember| |getPickedPoints| |tracePowMod| |length| + |homogeneous?| |s01eaf| |f07aef| |dihedralGroup| |makeEq| |rightZero| + |critM| |exists?| |scripts| |opeval| |leftLcm| |outputForm| + |setVariableOrder| |next| |over| |BumInSepFFE| |infieldint| |makeSUP| + |weierstrass| |charthRoot| |internalLastSubResultant| |rootsOf| + |setClipValue| |OMlistCDs| |combineFeatureCompatibility| |ravel| + |e04gcf| |meatAxe| |qualifier| |reverse| |radix| |stFuncN| + |basisOfLeftNucleus| |factorGroebnerBasis| |commaSeparate| |resetNew| + |safeFloor| |reshape| |rule| |argumentList!| |systemSizeIF| |yCoord| + |cn| |linearAssociatedLog| |open?| |coefficients| |limitPlus| + |permutation| |birth| |generalizedContinuumHypothesisAssumed| + |normalize| |setelt| |interReduce| |algebraicSort| |top| + |matrixDimensions| |dictionary| |leftAlternative?| |leftUnits| |less?| + |arg1| |rootSplit| |high| |c06ekf| |screenResolution| |symbolTableOf| + |realElementary| |representationType| |comp| |vedf2vef| |primeFactor| + |arg2| |copy| |cyclicParents| |write!| |lllip| |ScanArabic| + |kroneckerDelta| |hyperelliptic| |showFortranOutputStack| + |OMencodingXML| |scanOneDimSubspaces| |element?| |deepestInitial| + |continue| |shallowExpand| |schema| |update| |nor| |e04fdf| + |conditions| |isImplies| |whatInfinity| |nonQsign| |scalarTypeOf| + |ReduceOrder| |leader| |numeric| |numberOfIrreduciblePoly| + |rootDirectory| |jacobi| |randomR| |cyclic| |match| |makeYoungTableau| + |autoCoerce| |minimalPolynomial| |prime| |integralRepresents| |list| + |radical| |complex?| |const| |lyndon?| |stoseSquareFreePart| + |createPrimitiveNormalPoly| |sizePascalTriangle| |car| |hdmpToDmp| + |semicolonSeparate| |quotedOperators| |readable?| |jacobian| |red| + |argscript| |rootSimp| |keys| |structuralConstants| |mapMatrixIfCan| + |redpps| |traceMatrix| |cdr| |primaryDecomp| |tab| |e02bcf| |zero?| + |f04atf| |cycleElt| |say| |point?| |create| |string?| |setDifference| + |factorSFBRlcUnit| |e04jaf| |position| |expandPower| |setMinPoints3D| + |ref| |Is| |functorData| |qfactor| |setIntersection| |contractSolve| + |insertMatch| |stoseInvertibleSet| |nthRoot| |henselFact| + |fortranLogical| |qinterval| |patternMatchTimes| + |leftMinimalPolynomial| |rightRemainder| |hex| |f02aef| |setUnion| + |deriv| |match?| |summation| |degree| |elementary| |showAll?| + |contours| |tree| |escape| |vconcat| |result| |minGbasis| + |viewWriteAvailable| |apply| |rightFactorCandidate| + |pointColorPalette| |semiLastSubResultantEuclidean| |iiacosh| |gbasis| + |routines| |iiacoth| |f02aaf| |regime| |simplifyPower| |invmultisect| + |overset?| |stoseInvertible?reg| |ScanFloatIgnoreSpaces| |findBinding| + |associative?| |push| |mapUnivariateIfCan| |child| |reset| + |tubePointsDefault| |ideal| |size| |frobenius| |xn| |nextPartition| + |ran| |modulus| |tablePow| |algint| |hash| + |semiDegreeSubResultantEuclidean| |removeRoughlyRedundantFactorsInPol| + |ramified?| |primextendedint| |branchPoint?| |pole?| + |functionIsOscillatory| |categoryFrame| |imagJ| |predicate| |count| + |monicRightDivide| |showScalarValues| |shiftRight| |write| |green| + |showRegion| |singularAtInfinity?| |ScanRoman| |bipolarCylindrical| + |romberg| |lfinfieldint| |createGenericMatrix| |sn| |save| + |makingStats?| |hasPredicate?| |lazyIrreducibleFactors| |first| + |OMgetEndAtp| |BasicMethod| |d03eef| |ratDsolve| |generator| + |writeBytes!| |wholeRadix| |numberOfChildren| + |getMultiplicationMatrix| |square?| |coerceListOfPairs| |column| + |coercePreimagesImages| |rest| |exprToUPS| |curve?| |limitedint| + |orbit| |eigenvector| |iisqrt3| |rectangularMatrix| |substitute| + |hasSolution?| |slex| |tanNa| |numerators| |genericLeftDiscriminant| + |selectAndPolynomials| |bivariatePolynomials| + |nextNormalPrimitivePoly| |removeDuplicates| |tube| |lyndon| + |extractPoint| |sumOfDivisors| |stripCommentsAndBlanks| |UP2ifCan| + |e02bbf| |lfintegrate| |minset| |f01brf| |setCondition!| |mapGen| + |maxColIndex| |univcase| |screenResolution3D| |basisOfRightNucleus| + |discriminantEuclidean| |ksec| |tanhIfCan| |e02ahf| + |oneDimensionalArray| |lSpaceBasis| |setPredicates| |integrate| + |lazyEvaluate| |generate| |mathieu12| |replace| |choosemon| + |solveLinearPolynomialEquationByFractions| |rst| |OMopenFile| + |subtractIfCan| |genus| |isTerm| |node?| |removeDuplicates!| |mesh| + |repeating| |rightGcd| |row| |parameters| |An| |complexRoots| + |factorPolynomial| |getSyntaxFormsFromFile| |extractSplittingLeaf| + |expPot| |incrementBy| |edf2efi| |extendedResultant| + |subresultantVector| |singular?| |exQuo| |weighted| |iiatanh| + |isEquiv| |antisymmetricTensors| |enumerate| |upDateBranches| |expand| + |level| |inRadical?| |setScreenResolution| |setColumn!| + |nextNormalPoly| |approximants| |ode1| |outputFloating| |gradient| + |irreducibleRepresentation| |filterWhile| |internalZeroSetSplit| + |constant?| |minPoints3D| |secIfCan| |operation| |leftPower| |e02gaf| + |fortranCompilerName| |B1solve| |bat1| |filterUntil| + |totalDifferential| |localReal?| |roughUnitIdeal?| |rur| |conical| + |schwerpunkt| |cTanh| |roughSubIdeal?| |variationOfParameters| + |select| |subResultantsChain| |normal01| |reducedContinuedFraction| + |fortranTypeOf| |position!| |iExquo| |replaceKthElement| |empty?| + |bumptab| |rk4a| |uniform| |matrix| |iitanh| |reduceByQuasiMonic| + |quasiAlgebraicSet| |GospersMethod| |c02agf| |expextendedint| + |singRicDE| |edf2fi| |ricDsolve| |drawComplex| |toseInvertible?| + |OMUnknownCD?| |physicalLength!| |wronskianMatrix| |countable?| + |loopPoints| |factorByRecursion| |getVariableOrder| |reseed| |cubic| + |Aleph| |gcdcofact| |e02ajf| |dfRange| |e01bhf| |id| |cAcsc| |c05pbf| + |shiftRoots| |isOr| |computePowers| |addMatch| |toseInvertibleSet| + |f01qdf| |tanh2trigh| |incr| |setleft!| |factors| |d02bbf| + |removeRedundantFactorsInPols| |categories| |identification| + |whileLoop| |closeComponent| |in?| |d02gaf| |loadNativeModule| |table| + |inverseColeman| |primitivePart| |anticoord| |realSolve| |parents| + |OMgetApp| |subCase?| |generalSqFr| |asimpson| |resultantReduit| |new| + |hi| |iifact| |normalized?| |ocf2ocdf| |figureUnits| |setAdaptive| + |omError| |insert!| |mkIntegral| |scopes| |insert| |readUInt32!| + |swapRows!| |calcRanges| |selectSumOfSquaresRoutines| |tubePlot| + |leadingIndex| |f04qaf| |fglmIfCan| |expIfCan| |unary?| |leftGcd| + |useSingleFactorBound| |readIfCan!| |qroot| |clearCache| |cosh2sech| + |basicSet| |nsqfree| |collect| |options| |fortranDouble| |setrest!| + |fortranDoubleComplex| |completeHensel| |composite| |ipow| GF2FG + |numberOfComposites| |taylorRep| |limit| |second| |messagePrint| + |plotPolar| |numberOfComponents| |selectFiniteRoutines| + |outputSpacing| |zeroMatrix| |domainOf| |rdregime| |knownInfBasis| + |third| |nlde| |rootOfIrreduciblePoly| |numberOfVariables| + |var2StepsDefault| |iicsc| |f01maf| |functionIsFracPolynomial?| + |floor| |string| |gcdPolynomial| |branchIfCan| |infix| |sincos| + |UpTriBddDenomInv| |tableForDiscreteLogarithm| |doubleFloatFormat| + |entry?| |linearlyDependent?| |hMonic| |probablyZeroDim?| |divisor| + |jacobiIdentity?| |LowTriBddDenomInv| |leftRegularRepresentation| + |paren| |f02fjf| |primes| |inHallBasis?| |imagk| |denomRicDE| |rspace| + |head| |OMputApp| |invertibleElseSplit?| |range| |evenInfiniteProduct| + |listexp| |besselK| |decrease| |exponential1| |lift| + |intermediateResultsIF| |coth2trigh| |retractable?| |void| + |companionBlocks| |mapdiv| |left| |bezoutMatrix| |s21bbf| + |clipBoolean| |completeEchelonBasis| |reduce| + |semiResultantEuclideannaif| |mapCoef| |s13aaf| + |getMultiplicationTable| |monomial?| |right| |cyclicGroup| + |infiniteProduct| |expintegrate| |countRealRoots| |f02bbf| + |stopTable!| |groebner| |deepCopy| |singleFactorBound| + |listRepresentation| |palgint| |round| |morphism| |forLoop| + |OMgetAttr| |powers| |maxRowIndex| |elt| |LyndonWordsList1| + |defineProperty| |iicsch| |stronglyReduced?| |setStatus!| + |safeCeiling| |f02aff| |variable?| |front| |internalSubPolSet?| + |laurentIfCan| |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) ((-454) -2805 (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-495) |has| |#1| (-1199)) ((-516 (-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((-516 |#1| |#1|) |has| |#1| (-310 |#1|)) ((-558) -2805 (|has| |#1| (-558)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-646 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-646 (-566)) . T) ((-646 |#1|) . T) ((-646 $) . T) ((-648 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-648 |#1|) . T) ((-648 $) . T) ((-640 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-640 |#1|) . T) ((-640 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-639 (-566)) |has| |#1| (-639 (-566))) ((-639 |#1|) . T) ((-717 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-717 |#1|) . T) ((-717 $) -2805 (|has| |#1| (-558)) (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-724 |#1| #1#) . T) ((-726) . T) ((-900 (-1175)) |has| |#1| (-900 (-1175))) ((-886 (-381)) |has| |#1| (-886 (-381))) ((-886 (-566)) |has| |#1| (-886 (-566))) ((-884 |#1|) . T) ((-909) -12 (|has| |#1| (-308)) (|has| |#1| (-909))) ((-920) -2805 (|has| |#1| (-351)) (|has| |#1| (-365)) (|has| |#1| (-308))) ((-1002) -12 (|has| |#1| (-1002)) (|has| |#1| (-1199))) ((-1038 (-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((-1038 (-566)) |has| |#1| (-1038 (-566))) ((-1038 |#1|) . T) ((-1051 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1051 |#1|) . T) ((-1051 $) . T) ((-1056 #0#) -2805 (|has| |#1| (-351)) (|has| |#1| (-365))) ((-1056 |#1|) . T) ((-1056 $) . T) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . T) ((-1150) |has| |#1| (-351)) ((-1199) |has| |#1| (-1199)) ((-1202) |has| |#1| (-1199)) ((-1214) . 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(|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2700 (|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|) -2700 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2700 (|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)) -2700 (|has| |#2| (-1049)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-616 |#2|) -2700 (|has| |#2| (-1099)) (|has| |#2| (-172))) ((-613 (-862)) -2700 (|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)) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 |#2|) -2700 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 $) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-648 |#2|) -2700 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-648 $) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-640 |#2|) -2700 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-639 (-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049))) ((-639 |#2|) |has| |#2| (-1049)) ((-717 |#2|) -2700 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-726) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-791) |has| |#2| (-848)) ((-792) -2700 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-793) |has| |#2| (-793)) ((-794) -2700 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-795) -2700 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-848) |has| |#2| (-848)) ((-850) -2700 (|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|) -2700 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1056 |#2|) -2700 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1056 $) |has| |#2| (-172)) ((-1049) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2700 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1214) . T) ((-1271 |#2|) |has| |#2| (-365))) -((-2559 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-3802 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2982 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2559 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3802 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2982 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1214) (-1214)) (T -239)) -((-2982 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *7 (-1214)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-3802 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1214)) (-4 *2 (-1214)) (-5 *1 (-239 *5 *6 *2)))) (-2559 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1214)) (-4 *5 (-1214)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-726)) (PROGN (-6 (-726)) (-15 * ($ |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 -4414)) (-6 -4414) |%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) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-23) -2805 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2805 (|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) -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))) +((-2403 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-4362 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3077 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2403 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4362 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3077 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1214) (-1214)) (T -239)) +((-3077 (*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)))) (-4362 (*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)))) (-2403 (*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) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-409 (-566)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #0#) -2700 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 |#1|) . T) ((-616 |#2|) . T) ((-616 |#3|) . T) ((-616 $) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-613 (-862)) . T) ((-172) -2700 (|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) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-310 $) . T) ((-327 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-454) -2700 (|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) -2700 (|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 $) -2700 (|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 $) -2700 (|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 $) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1056 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2700 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-409 (-566)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #0#) -2805 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 |#1|) . T) ((-616 |#2|) . T) ((-616 |#3|) . T) ((-616 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-613 (-862)) . T) ((-172) -2805 (|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) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-310 $) . T) ((-327 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-454) -2805 (|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) -2805 (|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 $) -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) . 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T) ((-172) -2700 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-614 (-225)) -12 (|has| |#1| (-365)) (|has| |#2| (-1022))) ((-614 (-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-1022))) ((-614 (-538)) -12 (|has| |#1| (-365)) (|has| |#2| (-614 (-538)))) ((-614 (-892 (-381))) -12 (|has| |#1| (-365)) (|has| |#2| (-614 (-892 (-381))))) ((-614 (-892 (-566))) -12 (|has| |#1| (-365)) (|has| |#2| (-614 (-892 (-566))))) ((-231 |#2|) |has| |#1| (-365)) ((-233) -2700 (-12 (|has| |#1| (-365)) (|has| |#2| (-233))) (|has| |#1| (-15 * (|#1| (-566) |#1|)))) ((-243) |has| |#1| (-365)) ((-285) |has| |#1| (-38 (-409 (-566)))) ((-287 |#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) ((-287 $ $) |has| (-566) (-1111)) ((-291) -2700 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-310 |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-310 |#2|))) ((-365) |has| |#1| (-365)) ((-340 |#2|) |has| |#1| (-365)) ((-379 |#2|) |has| |#1| (-365)) ((-402 |#2|) |has| |#1| (-365)) ((-454) |has| |#1| (-365)) ((-495) |has| |#1| (-38 (-409 (-566)))) ((-516 (-1175) |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-516 (-1175) |#2|))) ((-516 |#2| |#2|) -12 (|has| |#1| (-365)) (|has| |#2| (-310 |#2|))) ((-558) -2700 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-646 #1#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-646 (-566)) . T) ((-646 |#1|) . T) ((-646 |#2|) |has| |#1| (-365)) ((-646 $) . T) ((-648 #1#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-648 |#1|) . T) ((-648 |#2|) |has| |#1| (-365)) ((-648 $) . T) ((-640 #1#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-640 |#1|) |has| |#1| (-172)) ((-640 |#2|) |has| |#1| (-365)) ((-640 $) -2700 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-639 (-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-639 (-566)))) ((-639 |#2|) |has| |#1| (-365)) ((-717 #1#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-717 |#1|) |has| |#1| (-172)) ((-717 |#2|) |has| |#1| (-365)) ((-717 $) -2700 (|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) -2700 (-12 (|has| |#1| (-365)) (|has| |#2| (-850))) (-12 (|has| |#1| (-365)) (|has| |#2| (-820)))) ((-900 (-1175)) -2700 (-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#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1051 |#1|) . T) ((-1051 |#2|) |has| |#1| (-365)) ((-1051 $) -2700 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1056 #1#) -2700 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-1056 |#1|) . T) ((-1056 |#2|) |has| |#1| (-365)) ((-1056 $) -2700 (|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) ((-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) . 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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 $) -2700 (|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 $) -2700 (|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 $) -2700 (|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 $) -2700 (|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))) -((-2439 (((-644 (-1081)) $) 34)) (-3527 (($ $) 31)) (-2417 (($ |#2| |#3|) NIL) (($ $ (-1081) |#3|) 28) (($ $ (-644 (-1081)) (-644 |#3|)) 27)) (-3488 (($ $) 14)) (-3503 ((|#2| $) 12)) (-3125 ((|#3| $) 10))) -(((-1241 |#1| |#2| |#3|) (-10 -8 (-15 -2439 ((-644 (-1081)) |#1|)) (-15 -2417 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -2417 (|#1| |#1| (-1081) |#3|)) (-15 -3527 (|#1| |#1|)) (-15 -2417 (|#1| |#2| |#3|)) (-15 -3125 (|#3| |#1|)) (-15 -3488 (|#1| |#1|)) (-15 -3503 (|#2| |#1|))) (-1242 |#2| |#3|) (-1049) (-792)) (T -1241)) -NIL -(-10 -8 (-15 -2439 ((-644 (-1081)) |#1|)) (-15 -2417 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -2417 (|#1| |#1| (-1081) |#3|)) (-15 -3527 (|#1| |#1|)) (-15 -2417 (|#1| |#2| |#3|)) (-15 -3125 (|#3| |#1|)) (-15 -3488 (|#1| |#1|)) (-15 -3503 (|#2| |#1|))) -((-2892 (((-112) $ $) 7)) (-3743 (((-112) $) 17)) (-2439 (((-644 (-1081)) $) 86)) (-1351 (((-1175) $) 115)) (-2852 (((-2 (|:| -3550 $) (|:| 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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 $) -2805 (|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 $ $) -2805 (|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#) -2805 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 #2=(-1081)) . T) ((-616 |#1|) . T) ((-616 $) -2805 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-613 (-862)) . T) ((-172) -2805 (|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) -2805 (|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) -2805 (|has| |#1| (-909)) (|has| |#1| (-454)) (|has| |#1| (-365))) ((-516 #2# |#1|) . T) ((-516 #2# $) . T) ((-516 $ $) . T) ((-558) -2805 (|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 $) -2805 (|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 $) -2805 (|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 $) -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) . T) ((-1150) |has| |#1| (-1150)) ((-1218) |has| |#1| (-909))) +((-2540 (((-644 (-1081)) $) 34)) (-3577 (($ $) 31)) (-2519 (($ |#2| |#3|) NIL) (($ $ (-1081) |#3|) 28) (($ $ (-644 (-1081)) (-644 |#3|)) 27)) (-3545 (($ $) 14)) (-3557 ((|#2| $) 12)) (-3992 ((|#3| $) 10))) +(((-1241 |#1| |#2| |#3|) (-10 -8 (-15 -2540 ((-644 (-1081)) |#1|)) (-15 -2519 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -2519 (|#1| |#1| (-1081) |#3|)) (-15 -3577 (|#1| |#1|)) (-15 -2519 (|#1| |#2| |#3|)) (-15 -3992 (|#3| |#1|)) (-15 -3545 (|#1| |#1|)) (-15 -3557 (|#2| |#1|))) (-1242 |#2| |#3|) (-1049) (-792)) (T -1241)) +NIL +(-10 -8 (-15 -2540 ((-644 (-1081)) |#1|)) (-15 -2519 (|#1| |#1| (-644 (-1081)) (-644 |#3|))) (-15 -2519 (|#1| |#1| (-1081) |#3|)) (-15 -3577 (|#1| |#1|)) (-15 -2519 (|#1| |#2| |#3|)) (-15 -3992 (|#3| |#1|)) (-15 -3545 (|#1| |#1|)) (-15 -3557 (|#2| |#1|))) +((-2985 (((-112) $ $) 7)) (-3958 (((-112) $) 17)) (-2540 (((-644 (-1081)) $) 86)) (-1353 (((-1175) $) 115)) (-2330 (((-2 (|:| -3803 $) (|:| 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NIL 2945843 NIL) (-1217 2944324 2944370 2944465 "UFD-" 2944470 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2943406 2943589 2943805 "UDVO" 2944130 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2941222 2941631 2942102 "UDPO" 2942970 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2941155 2941160 2941190 "TYPE" 2941195 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940915 2941110 2941141 "TYPEAST" 2941146 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939886 2940088 2940328 "TWOFACT" 2940709 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938909 2939295 2939530 "TUPLE" 2939686 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936600 2937119 2937658 "TUBETOOL" 2938392 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935449 2935654 2935895 "TUBE" 2936393 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2930178 2934421 2934704 "TS" 2935201 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918818 2922937 2923034 "TSETCAT" 2928303 NIL TSETCAT (NIL T T T T) -9 NIL 2929834 NIL) (-1206 2913550 2915150 2917041 "TSETCAT-" 2917046 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2908189 2909036 2909965 "TRMANIP" 2912686 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907630 2907693 2907856 "TRIMAT" 2908121 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905496 2905733 2906090 "TRIGMNIP" 2907379 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2905016 2905129 2905159 "TRIGCAT" 2905372 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904685 2904764 2904905 "TRIGCAT-" 2904910 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901530 2903543 2903824 "TREE" 2904439 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900804 2901332 2901362 "TRANFUN" 2901397 T TRANFUN (NIL) -9 NIL 2901463 NIL) (-1198 2900083 2900274 2900554 "TRANFUN-" 2900559 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899887 2899919 2899980 "TOPSP" 2900044 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2899235 2899350 2899504 "TOOLSIGN" 2899768 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897869 2898412 2898651 "TEXTFILE" 2899018 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895781 2896322 2896751 "TEX" 2897462 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895562 2895593 2895665 "TEX1" 2895744 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2895210 2895273 2895363 "TEMUTL" 2895494 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2893364 2893644 2893969 "TBCMPPK" 2894933 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2885141 2891524 2891580 "TBAGG" 2891980 NIL TBAGG (NIL T T) -9 NIL 2892191 NIL) (-1189 2880211 2881699 2883453 "TBAGG-" 2883458 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879595 2879702 2879847 "TANEXP" 2880100 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872985 2879452 2879545 "TABLE" 2879550 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2872397 2872496 2872634 "TABLEAU" 2872882 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2867005 2868225 2869473 "TABLBUMP" 2871183 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2866227 2866374 2866555 "SYSTEM" 2866846 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862686 2863385 2864168 "SYSSOLP" 2865478 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861730 2862235 2862354 "SYSNNI" 2862540 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862625) (-1181 2861037 2861496 2861575 "SYSINT" 2861635 NIL SYSINT (NIL NIL) -8 NIL NIL 2861680) (-1180 2857369 2858315 2859025 "SYNTAX" 2860349 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854527 2855129 2855761 "SYMTAB" 2856759 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849776 2850678 2851661 "SYMS" 2853566 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2847011 2849234 2849464 "SYMPOLY" 2849581 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846528 2846603 2846726 "SYMFUNC" 2846923 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842547 2843840 2844653 "SYMBOL" 2845737 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2836086 2837775 2839495 "SWITCH" 2840849 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829320 2834907 2835210 "SUTS" 2835841 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821386 2828567 2828840 "SUPXS" 2829105 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2813145 2821004 2821130 "SUP" 2821295 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812304 2812431 2812648 "SUPFRACF" 2813013 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811925 2811984 2812097 "SUP2" 2812239 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810373 2810647 2811003 "SUMRF" 2811624 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809708 2809774 2809966 "SUMFS" 2810294 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793675 2808885 2809136 "SULS" 2809515 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793277 2793497 2793567 "SUCHTAST" 2793627 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792572 2792802 2792942 "SUCH" 2793185 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786438 2787478 2788437 "SUBSPACE" 2791660 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785868 2785958 2786122 "SUBRESP" 2786326 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2779233 2780533 2781844 "STTF" 2784604 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773406 2774526 2775673 "STTFNC" 2778133 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764716 2766588 2768382 "STTAYLOR" 2771647 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757846 2764580 2764663 "STRTBL" 2764668 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2753210 2757801 2757832 "STRING" 2757837 T STRING (NIL) -8 NIL NIL NIL) (-1156 2748071 2752583 2752613 "STRICAT" 2752672 T STRICAT (NIL) -9 NIL 2752734 NIL) (-1155 2740824 2745690 2746301 "STREAM" 2747495 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740334 2740411 2740555 "STREAM3" 2740741 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739316 2739499 2739734 "STREAM2" 2740147 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2739004 2739056 2739149 "STREAM1" 2739258 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2738020 2738201 2738432 "STINPROD" 2738820 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737572 2737782 2737812 "STEP" 2737892 T STEP (NIL) -9 NIL 2737970 NIL) (-1149 2731004 2737471 2737548 "STBL" 2737553 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2726130 2730225 2730268 "STAGG" 2730421 NIL STAGG (NIL T) -9 NIL 2730510 NIL) (-1147 2723832 2724434 2725306 "STAGG-" 2725311 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721979 2723602 2723694 "STACK" 2723775 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714674 2720120 2720576 "SREGSET" 2721609 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2707099 2708468 2709981 "SRDCMPK" 2713280 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2700016 2704539 2704569 "SRAGG" 2705872 T SRAGG (NIL) -9 NIL 2706480 NIL) (-1142 2699033 2699288 2699667 "SRAGG-" 2699672 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693493 2697980 2698401 "SQMATRIX" 2698659 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2687178 2690211 2690938 "SPLTREE" 2692838 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2683141 2683834 2684480 "SPLNODE" 2686604 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2682188 2682421 2682451 "SPFCAT" 2682895 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680925 2681135 2681399 "SPECOUT" 2681946 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672551 2674321 2674351 "SPADXPT" 2678743 T SPADXPT (NIL) -9 NIL 2680777 NIL) (-1135 2672312 2672352 2672421 "SPADPRSR" 2672504 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670467 2672267 2672298 "SPADAST" 2672303 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662412 2664185 2664228 "SPACEC" 2668601 NIL SPACEC (NIL T) -9 NIL 2670417 NIL) (-1132 2660542 2662344 2662393 "SPACE3" 2662398 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659294 2659465 2659756 "SORTPAK" 2660347 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657386 2657689 2658101 "SOLVETRA" 2658958 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656436 2656658 2656919 "SOLVESER" 2657159 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651740 2652628 2653623 "SOLVERAD" 2655488 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647555 2648164 2648893 "SOLVEFOR" 2651107 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641825 2646904 2647001 "SNTSCAT" 2647006 NIL SNTSCAT (NIL T T T T) -9 NIL 2647076 NIL) (-1125 2635931 2640148 2640539 "SMTS" 2641515 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630615 2635819 2635896 "SMP" 2635901 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628774 2629075 2629473 "SMITH" 2630312 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621487 2625683 2625786 "SMATCAT" 2627137 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627687 NIL) (-1121 2618427 2619250 2620428 "SMATCAT-" 2620433 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2616093 2617663 2617706 "SKAGG" 2617967 NIL SKAGG (NIL T) -9 NIL 2618102 NIL) (-1119 2612404 2615509 2615704 "SINT" 2615891 T SINT (NIL) -8 NIL NIL 2616064) (-1118 2612176 2612214 2612280 "SIMPAN" 2612360 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611455 2611711 2611851 "SIG" 2612058 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610293 2610514 2610789 "SIGNRF" 2611214 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2609126 2609277 2609561 "SIGNEF" 2610122 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608432 2608709 2608833 "SIGAST" 2609024 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2606121 2606576 2607082 "SHP" 2607973 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599973 2606022 2606098 "SHDP" 2606103 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599546 2599738 2599768 "SGROUP" 2599861 T SGROUP (NIL) -9 NIL 2599923 NIL) (-1110 2599404 2599430 2599503 "SGROUP-" 2599508 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596239 2596937 2597660 "SGCF" 2598703 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590607 2595686 2595783 "SFRTCAT" 2595788 NIL SFRTCAT (NIL T T T T) -9 NIL 2595827 NIL) (-1107 2584028 2585046 2586182 "SFRGCD" 2589590 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2577154 2578227 2579413 "SFQCMPK" 2582961 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576774 2576863 2576974 "SFORT" 2577095 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575892 2576614 2576735 "SEXOF" 2576740 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574999 2575773 2575841 "SEX" 2575846 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570512 2571227 2571322 "SEXCAT" 2574259 NIL SEXCAT (NIL T T T T T) -9 NIL 2574837 NIL) (-1101 2567665 2570446 2570494 "SET" 2570499 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565889 2566378 2566683 "SETMN" 2567406 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565385 2565537 2565567 "SETCAT" 2565743 T SETCAT (NIL) -9 NIL 2565853 NIL) (-1098 2565077 2565155 2565285 "SETCAT-" 2565290 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561438 2563538 2563581 "SETAGG" 2564451 NIL SETAGG (NIL T) -9 NIL 2564791 NIL) (-1096 2560896 2561012 2561249 "SETAGG-" 2561254 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560339 2560592 2560693 "SEQAST" 2560817 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559538 2559832 2559893 "SEGXCAT" 2560179 NIL SEGXCAT (NIL T T) -9 NIL 2560299 NIL) (-1093 2558544 2559204 2559386 "SEG" 2559391 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557523 2557737 2557780 "SEGCAT" 2558302 NIL SEGCAT (NIL T) -9 NIL 2558523 NIL) (-1091 2556524 2556902 2557102 "SEGBIND" 2557358 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2556145 2556204 2556317 "SEGBIND2" 2556459 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555718 2555946 2556023 "SEGAST" 2556090 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554937 2555063 2555267 "SEG2" 2555562 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554347 2554872 2554919 "SDVAR" 2554924 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546874 2554117 2554247 "SDPOL" 2554252 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545467 2545733 2546052 "SCPKG" 2546589 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544631 2544803 2544995 "SCOPE" 2545297 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543851 2543985 2544164 "SCACHE" 2544486 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543497 2543683 2543713 "SASTCAT" 2543718 T SASTCAT (NIL) -9 NIL 2543731 NIL) (-1081 2542984 2543332 2543408 "SAOS" 2543443 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542549 2542584 2542757 "SAERFFC" 2542943 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536488 2542446 2542526 "SAE" 2542531 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2536081 2536116 2536275 "SAEFACT" 2536447 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534402 2534716 2535117 "RURPK" 2535747 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2533039 2533345 2533650 "RULESET" 2534236 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530262 2530792 2531250 "RULE" 2532720 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529874 2530056 2530139 "RULECOLD" 2530214 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529664 2529692 2529763 "RTVALUE" 2529825 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2529135 2529381 2529475 "RSTRCAST" 2529592 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523983 2524778 2525698 "RSETGCD" 2528334 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2513213 2518292 2518389 "RSETCAT" 2522508 NIL RSETCAT (NIL T T T T) -9 NIL 2523605 NIL) (-1069 2511140 2511679 2512503 "RSETCAT-" 2512508 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503525 2504902 2506422 "RSDCMPK" 2509739 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501504 2501971 2502045 "RRCC" 2503131 NIL RRCC (NIL T T) -9 NIL 2503475 NIL) (-1066 2500855 2501029 2501308 "RRCC-" 2501313 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500298 2500551 2500652 "RPTAST" 2500776 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2474149 2483506 2483573 "RPOLCAT" 2494237 NIL RPOLCAT (NIL T T T) -9 NIL 2497396 NIL) (-1063 2465647 2467987 2471109 "RPOLCAT-" 2471114 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456578 2463858 2464340 "ROUTINE" 2465187 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453376 2456204 2456344 "ROMAN" 2456460 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451620 2452236 2452496 "ROIRC" 2453181 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447852 2450136 2450166 "RNS" 2450470 T RNS (NIL) -9 NIL 2450744 NIL) (-1058 2446361 2446744 2447278 "RNS-" 2447353 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445764 2446172 2446202 "RNG" 2446207 T RNG (NIL) -9 NIL 2446228 NIL) (-1056 2445163 2445551 2445594 "RMODULE" 2445599 NIL RMODULE (NIL T) -9 NIL 2445626 NIL) (-1055 2443999 2444093 2444429 "RMCAT2" 2445064 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440849 2443345 2443642 "RMATRIX" 2443761 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433676 2435936 2436051 "RMATCAT" 2439410 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440392 NIL) (-1052 2433051 2433198 2433505 "RMATCAT-" 2433510 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432452 2432673 2432716 "RLINSET" 2432910 NIL RLINSET (NIL T) -9 NIL 2433001 NIL) (-1050 2432019 2432094 2432222 "RINTERP" 2432371 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2431077 2431631 2431661 "RING" 2431717 T RING (NIL) -9 NIL 2431809 NIL) (-1048 2430869 2430913 2431010 "RING-" 2431015 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429710 2429947 2430205 "RIDIST" 2430633 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420999 2429178 2429384 "RGCHAIN" 2429558 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420349 2420755 2420796 "RGBCSPC" 2420854 NIL RGBCSPC (NIL T) -9 NIL 2420906 NIL) (-1044 2419507 2419888 2419929 "RGBCMDL" 2420161 NIL RGBCMDL (NIL T) -9 NIL 2420275 NIL) (-1043 2416501 2417115 2417785 "RF" 2418871 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2416147 2416210 2416313 "RFFACTOR" 2416432 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415872 2415907 2416004 "RFFACT" 2416106 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413989 2414353 2414735 "RFDIST" 2415512 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413442 2413534 2413697 "RETSOL" 2413891 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2413078 2413158 2413201 "RETRACT" 2413334 NIL RETRACT (NIL T) -9 NIL 2413421 NIL) (-1037 2412927 2412952 2413039 "RETRACT-" 2413044 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412529 2412749 2412819 "RETAST" 2412879 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405267 2412182 2412309 "RESULT" 2412424 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403858 2404536 2404735 "RESRING" 2405170 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403494 2403543 2403641 "RESLATC" 2403795 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2403199 2403234 2403341 "REPSQ" 2403453 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400621 2401201 2401803 "REP" 2402619 T REP (NIL) -7 NIL NIL NIL) (-1030 2400318 2400353 2400464 "REPDB" 2400580 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2394218 2395607 2396830 "REP2" 2399130 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390595 2391276 2392084 "REP1" 2393445 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383291 2388736 2389192 "REGSET" 2390225 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2382056 2382439 2382689 "REF" 2383076 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381433 2381536 2381703 "REDORDER" 2381940 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377401 2380646 2380873 "RECLOS" 2381261 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376453 2376634 2376849 "REALSOLV" 2377208 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376299 2376340 2376370 "REAL" 2376375 T REAL (NIL) -9 NIL 2376410 NIL) (-1021 2372782 2373584 2374468 "REAL0Q" 2375464 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368383 2369371 2370432 "REAL0" 2371763 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367854 2368100 2368194 "RDUCEAST" 2368311 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367259 2367331 2367538 "RDIV" 2367776 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366327 2366501 2366714 "RDIST" 2367081 NIL RDIST (NIL T) -7 NIL NIL NIL) 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NIL NIL) (-1004 2338938 2344655 2344965 "RADIX" 2345546 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330557 2338780 2338910 "RADFF" 2338915 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1002 2330204 2330279 2330309 "RADCAT" 2330469 T RADCAT (NIL) -9 NIL NIL NIL) (-1001 2329986 2330034 2330134 "RADCAT-" 2330139 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1000 2328086 2329758 2329849 "QUEUE" 2329930 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-999 2324627 2328023 2328068 "QUAT" 2328073 NIL QUAT (NIL T) -8 NIL NIL NIL) (-998 2324265 2324308 2324435 "QUATCT2" 2324578 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2317727 2321072 2321112 "QUATCAT" 2321892 NIL QUATCAT (NIL T) -9 NIL 2322658 NIL) (-996 2313871 2314908 2316295 "QUATCAT-" 2316389 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-995 2311344 2312955 2312996 "QUAGG" 2313371 NIL QUAGG (NIL T) -9 NIL 2313546 NIL) (-994 2310949 2311169 2311237 "QQUTAST" 2311296 T QQUTAST (NIL) -8 NIL NIL NIL) (-993 2309847 2310347 2310519 "QFORM" 2310821 NIL QFORM (NIL 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NIL) (-874 2036422 2036766 2036994 "PALETTE" 2037437 T PALETTE (NIL) -8 NIL NIL NIL) (-873 2034815 2035427 2035787 "PAIR" 2036108 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-872 2028685 2034074 2034268 "PADICRC" 2034670 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-871 2021914 2028031 2028215 "PADICRAT" 2028533 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-870 2020229 2021851 2021896 "PADIC" 2021901 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-869 2017339 2018903 2018943 "PADICCT" 2019524 NIL PADICCT (NIL NIL) -9 NIL 2019806 NIL) (-868 2016296 2016496 2016764 "PADEPAC" 2017126 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-867 2015508 2015641 2015847 "PADE" 2016158 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-866 2013895 2014716 2014996 "OWP" 2015312 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-865 2013388 2013601 2013698 "OVERSET" 2013818 T OVERSET (NIL) -8 NIL NIL NIL) (-864 2012434 2012993 2013165 "OVAR" 2013256 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-863 2011698 2011819 2011980 "OUT" 2012293 T OUT (NIL) -7 NIL NIL NIL) (-862 2000570 2002807 2005007 "OUTFORM" 2009518 T OUTFORM (NIL) -8 NIL NIL NIL) (-861 1999906 2000167 2000294 "OUTBFILE" 2000463 T OUTBFILE (NIL) -8 NIL NIL NIL) (-860 1999213 1999378 1999406 "OUTBCON" 1999724 T OUTBCON (NIL) -9 NIL 1999890 NIL) (-859 1998814 1998926 1999083 "OUTBCON-" 1999088 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1998194 1998543 1998632 "OSI" 1998745 T OSI (NIL) -8 NIL NIL NIL) (-857 1997724 1998062 1998090 "OSGROUP" 1998095 T OSGROUP (NIL) -9 NIL 1998117 NIL) (-856 1996469 1996696 1996981 "ORTHPOL" 1997471 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1994020 1996304 1996425 "OREUP" 1996430 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991423 1993711 1993838 "ORESUP" 1993962 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988951 1989451 1990012 "OREPCTO" 1990912 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982637 1984838 1984879 "OREPCAT" 1987227 NIL OREPCAT (NIL T) -9 NIL 1988331 NIL) (-851 1979784 1980566 1981624 "OREPCAT-" 1981629 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978935 1979233 1979261 "ORDSET" 1979570 T ORDSET (NIL) -9 NIL 1979734 NIL) (-849 1978366 1978514 1978738 "ORDSET-" 1978743 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976931 1977722 1977750 "ORDRING" 1977952 T ORDRING (NIL) -9 NIL 1978077 NIL) (-847 1976576 1976670 1976814 "ORDRING-" 1976819 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975956 1976419 1976447 "ORDMON" 1976452 T ORDMON (NIL) -9 NIL 1976473 NIL) (-845 1975118 1975265 1975460 "ORDFUNS" 1975805 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974456 1974875 1974903 "ORDFIN" 1974968 T ORDFIN (NIL) -9 NIL 1975042 NIL) (-843 1971015 1973042 1973451 "ORDCOMP" 1974080 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1970281 1970408 1970594 "ORDCOMP2" 1970875 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966862 1967772 1968586 "OPTPROB" 1969487 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963664 1964303 1965007 "OPTPACK" 1966178 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961351 1962117 1962145 "OPTCAT" 1962964 T OPTCAT (NIL) -9 NIL 1963614 NIL) (-838 1960735 1961028 1961133 "OPSIG" 1961266 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960503 1960542 1960608 "OPQUERY" 1960689 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957634 1958814 1959318 "OP" 1960032 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1957008 1957234 1957275 "OPERCAT" 1957487 NIL OPERCAT (NIL T) -9 NIL 1957584 NIL) (-834 1956763 1956819 1956936 "OPERCAT-" 1956941 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953576 1955560 1955929 "ONECOMP" 1956427 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952881 1952996 1953170 "ONECOMP2" 1953448 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952300 1952406 1952536 "OMSERVER" 1952771 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1949162 1951740 1951780 "OMSAGG" 1951841 NIL OMSAGG (NIL T) -9 NIL 1951905 NIL) (-829 1947785 1948048 1948330 "OMPKG" 1948900 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1947215 1947318 1947346 "OM" 1947645 T OM (NIL) -9 NIL NIL NIL) (-827 1945762 1946764 1946933 "OMLO" 1947096 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944722 1944869 1945089 "OMEXPR" 1945588 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1944013 1944268 1944404 "OMERR" 1944606 T OMERR (NIL) -8 NIL NIL NIL) (-824 1943164 1943434 1943594 "OMERRK" 1943873 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942615 1942841 1942949 "OMENC" 1943076 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936510 1937695 1938866 "OMDEV" 1941464 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935579 1935750 1935944 "OMCONN" 1936336 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1934100 1935076 1935104 "OINTDOM" 1935109 T OINTDOM (NIL) -9 NIL 1935130 NIL) (-819 1929879 1931090 1931806 "OFMONOID" 1933416 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929290 1929816 1929861 "ODVAR" 1929866 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926713 1929035 1929190 "ODR" 1929195 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919294 1926489 1926615 "ODPOL" 1926620 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1913116 1919166 1919271 "ODP" 1919276 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911882 1912097 1912372 "ODETOOLS" 1912890 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908849 1909507 1910223 "ODESYS" 1911215 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903731 1904639 1905664 "ODERTRIC" 1907924 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1903157 1903239 1903433 "ODERED" 1903643 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1900045 1900593 1901270 "ODERAT" 1902580 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1897002 1897469 1898066 "ODEPRRIC" 1899574 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894945 1895541 1896027 "ODEPROB" 1896536 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891465 1891950 1892597 "ODEPRIM" 1894424 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890714 1890816 1891076 "ODEPAL" 1891357 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886876 1887667 1888531 "ODEPACK" 1889870 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885937 1886044 1886266 "ODEINT" 1886765 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1880038 1881463 1882910 "ODEIFTBL" 1884510 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875436 1876222 1877174 "ODEEF" 1879197 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874785 1874874 1875097 "ODECONST" 1875341 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872910 1873571 1873599 "ODECAT" 1874204 T ODECAT (NIL) -9 NIL 1874735 NIL) (-799 1869782 1872622 1872741 "OCT" 1872823 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869420 1869463 1869590 "OCTCT2" 1869733 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1864069 1866504 1866544 "OC" 1867641 NIL OC (NIL T) -9 NIL 1868499 NIL) (-796 1861296 1862044 1863034 "OC-" 1863128 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860648 1861116 1861144 "OCAMON" 1861149 T OCAMON (NIL) -9 NIL 1861170 NIL) (-794 1860179 1860520 1860548 "OASGP" 1860553 T OASGP (NIL) -9 NIL 1860573 NIL) (-793 1859440 1859929 1859957 "OAMONS" 1859997 T OAMONS (NIL) -9 NIL 1860040 NIL) (-792 1858854 1859287 1859315 "OAMON" 1859320 T OAMON (NIL) -9 NIL 1859340 NIL) (-791 1858112 1858630 1858658 "OAGROUP" 1858663 T OAGROUP (NIL) -9 NIL 1858683 NIL) (-790 1857802 1857852 1857940 "NUMTUBE" 1858056 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851375 1852893 1854429 "NUMQUAD" 1856286 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1847131 1848119 1849144 "NUMODE" 1850370 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844486 1845366 1845394 "NUMINT" 1846317 T NUMINT (NIL) -9 NIL 1847081 NIL) (-786 1843434 1843631 1843849 "NUMFMT" 1844288 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829793 1832738 1835270 "NUMERIC" 1840941 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1824163 1829242 1829337 "NTSCAT" 1829342 NIL NTSCAT (NIL T T T T) -9 NIL 1829381 NIL) (-783 1823357 1823522 1823715 "NTPOLFN" 1824002 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811434 1820182 1820994 "NSUP" 1822578 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1811066 1811123 1811232 "NSUP2" 1811371 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801294 1810840 1810973 "NSMP" 1810978 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799726 1800027 1800384 "NREP" 1800982 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798317 1798569 1798927 "NPCOEF" 1799469 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797383 1797498 1797714 "NORMRETR" 1798198 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795424 1795714 1796123 "NORMPK" 1797091 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1795109 1795137 1795261 "NORMMA" 1795390 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794909 1795066 1795095 "NONE" 1795100 T NONE (NIL) -8 NIL NIL NIL) (-773 1794698 1794727 1794796 "NONE1" 1794873 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1794195 1794257 1794436 "NODE1" 1794630 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792480 1793331 1793586 "NNI" 1793933 T NNI (NIL) -8 NIL NIL 1794168) (-770 1790900 1791213 1791577 "NLINSOL" 1792148 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1787141 1788136 1789035 "NIPROB" 1790021 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785898 1786132 1786434 "NFINTBAS" 1786903 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1785072 1785548 1785589 "NETCLT" 1785761 NIL NETCLT (NIL T) -9 NIL 1785843 NIL) (-766 1783780 1784011 1784292 "NCODIV" 1784840 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783542 1783579 1783654 "NCNTFRAC" 1783737 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781722 1782086 1782506 "NCEP" 1783167 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780573 1781346 1781374 "NASRING" 1781484 T NASRING (NIL) -9 NIL 1781564 NIL) (-762 1780368 1780412 1780506 "NASRING-" 1780511 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779475 1780000 1780028 "NARNG" 1780145 T NARNG (NIL) -9 NIL 1780236 NIL) (-760 1779167 1779234 1779368 "NARNG-" 1779373 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1778046 1778253 1778488 "NAGSP" 1778952 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769318 1771002 1772675 "NAGS" 1776393 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767866 1768174 1768505 "NAGF07" 1769007 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762404 1763695 1765002 "NAGF04" 1766579 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755372 1756986 1758619 "NAGF02" 1760791 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750596 1751696 1752813 "NAGF01" 1754275 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1744224 1745790 1747375 "NAGE04" 1749031 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735393 1737514 1739644 "NAGE02" 1742114 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731346 1732293 1733257 "NAGE01" 1734449 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1729141 1729675 1730233 "NAGD03" 1730808 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720891 1722819 1724773 "NAGD02" 1727207 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714702 1716127 1717567 "NAGD01" 1719471 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710911 1711733 1712570 "NAGC06" 1713885 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709376 1709708 1710064 "NAGC05" 1710575 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708752 1708871 1709015 "NAGC02" 1709252 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707711 1708294 1708334 "NAALG" 1708413 NIL NAALG (NIL T) -9 NIL 1708474 NIL) (-743 1707546 1707575 1707665 "NAALG-" 1707670 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701496 1702604 1703791 "MULTSQFR" 1706442 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700815 1700890 1701074 "MULTFACT" 1701408 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693539 1697452 1697505 "MTSCAT" 1698575 NIL MTSCAT (NIL T T) -9 NIL 1699090 NIL) (-739 1693251 1693305 1693397 "MTHING" 1693479 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1693043 1693076 1693136 "MSYSCMD" 1693211 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1689125 1691798 1692118 "MSET" 1692756 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1686194 1688686 1688727 "MSETAGG" 1688732 NIL MSETAGG (NIL T) -9 NIL 1688766 NIL) (-735 1682035 1683573 1684318 "MRING" 1685494 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681601 1681668 1681799 "MRF2" 1681962 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1681219 1681254 1681398 "MRATFAC" 1681560 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678831 1679126 1679557 "MPRFF" 1680924 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1673128 1678685 1678782 "MPOLY" 1678787 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672618 1672653 1672861 "MPCPF" 1673087 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1672132 1672175 1672359 "MPC3" 1672569 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671327 1671408 1671629 "MPC2" 1672047 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669628 1669965 1670355 "MONOTOOL" 1670987 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668853 1669170 1669198 "MONOID" 1669417 T MONOID (NIL) -9 NIL 1669564 NIL) (-725 1668399 1668518 1668699 "MONOID-" 1668704 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658874 1664825 1664884 "MONOGEN" 1665558 NIL MONOGEN (NIL T T) -9 NIL 1666014 NIL) (-723 1656092 1656827 1657827 "MONOGEN-" 1657946 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654925 1655371 1655399 "MONADWU" 1655791 T MONADWU (NIL) -9 NIL 1656029 NIL) (-721 1654297 1654456 1654704 "MONADWU-" 1654709 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653656 1653900 1653928 "MONAD" 1654135 T MONAD (NIL) -9 NIL 1654247 NIL) (-719 1653341 1653419 1653551 "MONAD-" 1653556 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651630 1652254 1652533 "MOEBIUS" 1653094 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650908 1651312 1651352 "MODULE" 1651357 NIL MODULE (NIL T) -9 NIL 1651396 NIL) (-716 1650476 1650572 1650762 "MODULE-" 1650767 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1648156 1648840 1649167 "MODRING" 1650300 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1645100 1646261 1646782 "MODOP" 1647685 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643688 1644167 1644444 "MODMONOM" 1644963 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633729 1641979 1642393 "MODMON" 1643325 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630885 1632573 1632849 "MODFIELD" 1633604 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629862 1630166 1630356 "MMLFORM" 1630715 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629388 1629431 1629610 "MMAP" 1629813 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627467 1628234 1628275 "MLO" 1628698 NIL MLO (NIL T) -9 NIL 1628940 NIL) (-707 1624833 1625349 1625951 "MLIFT" 1626948 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1624224 1624308 1624462 "MKUCFUNC" 1624744 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623823 1623893 1624016 "MKRECORD" 1624147 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622870 1623032 1623260 "MKFUNC" 1623634 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622258 1622362 1622518 "MKFLCFN" 1622753 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621535 1621637 1621822 "MKBCFUNC" 1622151 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618242 1621089 1621225 "MINT" 1621419 T MINT (NIL) -8 NIL NIL NIL) (-700 1617054 1617297 1617574 "MHROWRED" 1617997 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612433 1615589 1615994 "MFLOAT" 1616669 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611790 1611866 1612037 "MFINFACT" 1612345 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1608105 1608953 1609837 "MESH" 1610926 T MESH (NIL) -7 NIL NIL NIL) (-696 1606495 1606807 1607160 "MDDFACT" 1607792 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603290 1605654 1605695 "MDAGG" 1605950 NIL MDAGG (NIL T) -9 NIL 1606093 NIL) (-694 1593030 1602583 1602790 "MCMPLX" 1603103 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1592171 1592317 1592517 "MCDEN" 1592879 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1590061 1590331 1590711 "MCALCFN" 1591901 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588986 1589226 1589459 "MAYBE" 1589867 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586598 1587121 1587683 "MATSTOR" 1588457 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582555 1585970 1586218 "MATRIX" 1586383 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578319 1579028 1579764 "MATLIN" 1581912 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568425 1571611 1571688 "MATCAT" 1576568 NIL MATCAT (NIL T T T) -9 NIL 1577985 NIL) (-686 1564781 1565802 1567158 "MATCAT-" 1567163 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563375 1563528 1563861 "MATCAT2" 1564616 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561487 1561811 1562195 "MAPPKG3" 1563050 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560468 1560641 1560863 "MAPPKG2" 1561311 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558967 1559251 1559578 "MAPPKG1" 1560174 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1558046 1558373 1558550 "MAPPAST" 1558810 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557657 1557715 1557838 "MAPHACK3" 1557982 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557249 1557310 1557424 "MAPHACK2" 1557589 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556686 1556790 1556932 "MAPHACK1" 1557140 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554765 1555386 1555690 "MAGMA" 1556414 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554244 1554489 1554580 "MACROAST" 1554694 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550662 1552483 1552944 "M3D" 1553816 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544768 1549031 1549072 "LZSTAGG" 1549854 NIL LZSTAGG (NIL T) -9 NIL 1550149 NIL) (-673 1540725 1541899 1543356 "LZSTAGG-" 1543361 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537812 1538616 1539103 "LWORD" 1540270 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537388 1537616 1537691 "LSTAST" 1537757 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530554 1537159 1537293 "LSQM" 1537298 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529778 1529917 1530145 "LSPP" 1530409 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527590 1527891 1528347 "LSMP" 1529467 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524369 1525043 1525773 "LSMP1" 1526892 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518246 1523536 1523577 "LSAGG" 1523639 NIL LSAGG (NIL T) -9 NIL 1523717 NIL) (-665 1514941 1515865 1517078 "LSAGG-" 1517083 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512540 1514085 1514334 "LPOLY" 1514736 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1512122 1512207 1512330 "LPEFRAC" 1512449 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510443 1511216 1511469 "LO" 1511954 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1510095 1510207 1510235 "LOGIC" 1510346 T LOGIC (NIL) -9 NIL 1510427 NIL) (-660 1509957 1509980 1510051 "LOGIC-" 1510056 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1509150 1509290 1509483 "LODOOPS" 1509813 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506573 1509066 1509132 "LODO" 1509137 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1505111 1505346 1505699 "LODOF" 1506320 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501329 1503760 1503801 "LODOCAT" 1504239 NIL LODOCAT (NIL T) -9 NIL 1504450 NIL) (-655 1501062 1501120 1501247 "LODOCAT-" 1501252 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498382 1500903 1501021 "LODO2" 1501026 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495817 1498319 1498364 "LODO1" 1498369 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494698 1494863 1495168 "LODEEF" 1495640 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489937 1492828 1492869 "LNAGG" 1493816 NIL LNAGG (NIL T) -9 NIL 1494260 NIL) (-650 1489084 1489298 1489640 "LNAGG-" 1489645 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1485220 1486009 1486648 "LMOPS" 1488499 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484623 1485011 1485052 "LMODULE" 1485057 NIL LMODULE (NIL T) -9 NIL 1485083 NIL) (-647 1481821 1484268 1484391 "LMDICT" 1484533 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1481227 1481448 1481489 "LLINSET" 1481680 NIL LLINSET (NIL T) -9 NIL 1481771 NIL) (-645 1480926 1481135 1481195 "LITERAL" 1481200 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1474109 1479872 1480170 "LIST" 1480661 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473634 1473708 1473847 "LIST3" 1474029 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472641 1472819 1473047 "LIST2" 1473452 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470775 1471087 1471486 "LIST2MAP" 1472288 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470371 1470608 1470649 "LINSET" 1470654 NIL LINSET (NIL T) -9 NIL 1470688 NIL) (-639 1469032 1469702 1469743 "LINEXP" 1469998 NIL LINEXP (NIL T) -9 NIL 1470147 NIL) (-638 1467679 1467939 1468236 "LINDEP" 1468784 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464446 1465165 1465942 "LIMITRF" 1466934 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462749 1463045 1463454 "LIMITPS" 1464141 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1457177 1462260 1462488 "LIE" 1462570 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1456125 1456594 1456634 "LIECAT" 1456774 NIL LIECAT (NIL T) -9 NIL 1456925 NIL) (-633 1455966 1455993 1456081 "LIECAT-" 1456086 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448462 1455415 1455580 "LIB" 1455821 T LIB (NIL) -8 NIL NIL NIL) (-631 1444097 1444980 1445915 "LGROBP" 1447579 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1442095 1442369 1442719 "LF" 1443818 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440935 1441627 1441655 "LFCAT" 1441862 T LFCAT (NIL) -9 NIL 1442001 NIL) (-628 1437837 1438467 1439155 "LEXTRIPK" 1440299 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434581 1435407 1435910 "LEXP" 1437417 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1434057 1434302 1434394 "LETAST" 1434509 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432455 1432768 1433169 "LEADCDET" 1433739 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431645 1431719 1431948 "LAZM3PK" 1432376 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426562 1429722 1430260 "LAUPOL" 1431157 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1426141 1426185 1426346 "LAPLACE" 1426512 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1424080 1425242 1425493 "LA" 1425974 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1423074 1423658 1423699 "LALG" 1423761 NIL LALG (NIL T) -9 NIL 1423820 NIL) (-619 1422788 1422847 1422983 "LALG-" 1422988 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422623 1422647 1422688 "KVTFROM" 1422750 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421546 1421990 1422175 "KTVLOGIC" 1422458 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421381 1421405 1421446 "KRCFROM" 1421508 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420285 1420472 1420771 "KOVACIC" 1421181 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1420120 1420144 1420185 "KONVERT" 1420247 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419955 1419979 1420020 "KOERCE" 1420082 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417785 1418548 1418925 "KERNEL" 1419611 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417281 1417362 1417494 "KERNEL2" 1417699 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1411051 1415820 1415874 "KDAGG" 1416251 NIL KDAGG (NIL T T) -9 NIL 1416457 NIL) (-609 1410580 1410704 1410909 "KDAGG-" 1410914 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403728 1410241 1410396 "KAFILE" 1410458 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1398156 1403239 1403467 "JORDAN" 1403549 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397535 1397805 1397926 "JOINAST" 1398055 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397381 1397440 1397495 "JAVACODE" 1397500 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393633 1395586 1395640 "IXAGG" 1396569 NIL IXAGG (NIL T T) -9 NIL 1397028 NIL) (-603 1392552 1392858 1393277 "IXAGG-" 1393282 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1388082 1392474 1392533 "IVECTOR" 1392538 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386848 1387085 1387351 "ITUPLE" 1387849 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385350 1385527 1385822 "ITRIGMNP" 1386670 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1384095 1384299 1384582 "ITFUN3" 1385126 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383727 1383784 1383893 "ITFUN2" 1384032 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381529 1382589 1382888 "ITAYLOR" 1383461 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370474 1375666 1376829 "ISUPS" 1380399 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369578 1369718 1369954 "ISUMP" 1370321 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364792 1369379 1369458 "ISTRING" 1369531 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364268 1364513 1364605 "ISAST" 1364720 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363477 1363559 1363775 "IRURPK" 1364182 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362413 1362614 1362854 "IRSN" 1363257 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360484 1360839 1361268 "IRRF2F" 1362051 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1360231 1360269 1360345 "IRREDFFX" 1360440 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358846 1359105 1359404 "IROOT" 1359964 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355450 1356530 1357222 "IR" 1358186 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1353063 1353558 1354124 "IR2" 1354928 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1352163 1352276 1352490 "IR2F" 1352946 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351954 1351988 1352048 "IPRNTPK" 1352123 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348533 1351843 1351912 "IPF" 1351917 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346860 1348458 1348515 "IPADIC" 1348520 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1346172 1346420 1346550 "IP4ADDR" 1346750 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345645 1345876 1345986 "IOMODE" 1346082 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344718 1345242 1345369 "IOBFILE" 1345538 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1344206 1344622 1344650 "IOBCON" 1344655 T IOBCON (NIL) -9 NIL 1344676 NIL) (-577 1343717 1343775 1343958 "INVLAPLA" 1344142 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333365 1335719 1338105 "INTTR" 1341381 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329700 1330442 1331307 "INTTOOLS" 1332550 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329286 1329377 1329494 "INTSLPE" 1329603 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327239 1329209 1329268 "INTRVL" 1329273 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324841 1325353 1325928 "INTRF" 1326724 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324252 1324349 1324491 "INTRET" 1324739 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322249 1322638 1323108 "INTRAT" 1323860 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319512 1320095 1320714 "INTPM" 1321734 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316257 1316856 1317594 "INTPAF" 1318898 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311436 1312398 1313449 "INTPACK" 1315226 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308316 1311165 1311292 "INT" 1311329 T INT (NIL) -8 NIL NIL NIL) (-565 1307568 1307720 1307928 "INTHERTR" 1308158 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1307007 1307087 1307275 "INTHERAL" 1307482 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304853 1305296 1305753 "INTHEORY" 1306570 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296259 1297880 1299652 "INTG0" 1303205 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276832 1281622 1286432 "INTFTBL" 1291469 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1276081 1276219 1276392 "INTFACT" 1276691 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273508 1273954 1274511 "INTEF" 1275635 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271875 1272614 1272642 "INTDOM" 1272943 T INTDOM (NIL) -9 NIL 1273150 NIL) (-557 1271244 1271418 1271660 "INTDOM-" 1271665 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267632 1269560 1269614 "INTCAT" 1270413 NIL INTCAT (NIL T) -9 NIL 1270734 NIL) (-555 1267104 1267207 1267335 "INTBIT" 1267524 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265803 1265957 1266264 "INTALG" 1266949 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265286 1265376 1265533 "INTAF" 1265707 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258629 1265096 1265236 "INTABL" 1265241 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257970 1258436 1258501 "INT8" 1258535 T INT8 (NIL) -8 NIL NIL 1258580) (-550 1257310 1257776 1257841 "INT64" 1257875 T INT64 (NIL) -8 NIL NIL 1257920) (-549 1256650 1257116 1257181 "INT32" 1257215 T INT32 (NIL) -8 NIL NIL 1257260) (-548 1255990 1256456 1256521 "INT16" 1256555 T INT16 (NIL) -8 NIL NIL 1256600) (-547 1250900 1253613 1253641 "INS" 1254575 T INS (NIL) -9 NIL 1255240 NIL) (-546 1248140 1248911 1249885 "INS-" 1249958 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246915 1247142 1247440 "INPSIGN" 1247893 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1246033 1246150 1246347 "INPRODPF" 1246795 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244927 1245044 1245281 "INPRODFF" 1245913 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243927 1244079 1244339 "INNMFACT" 1244763 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1243124 1243221 1243409 "INMODGCD" 1243826 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241632 1241877 1242201 "INFSP" 1242869 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240816 1240933 1241116 "INFPROD0" 1241512 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237671 1238881 1239396 "INFORM" 1240309 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237281 1237341 1237439 "INFORM1" 1237606 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236804 1236893 1237007 "INFINITY" 1237187 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235980 1236524 1236625 "INETCLTS" 1236723 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234596 1234846 1235167 "INEP" 1235728 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233845 1234493 1234558 "INDE" 1234563 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233409 1233477 1233594 "INCRMAPS" 1233772 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1232227 1232678 1232884 "INBFILE" 1233223 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227526 1228463 1229407 "INBFF" 1231315 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226434 1226703 1226731 "INBCON" 1227244 T INBCON (NIL) -9 NIL 1227510 NIL) (-528 1225686 1225909 1226185 "INBCON-" 1226190 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1225165 1225410 1225501 "INAST" 1225615 T INAST (NIL) -8 NIL NIL NIL) (-526 1224592 1224844 1224950 "IMPTAST" 1225079 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1221038 1224436 1224540 "IMATRIX" 1224545 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219750 1219873 1220188 "IMATQF" 1220894 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217970 1218197 1218534 "IMATLIN" 1219506 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212548 1217894 1217952 "ILIST" 1217957 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210453 1212408 1212521 "IIARRAY2" 1212526 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205851 1210364 1210428 "IFF" 1210433 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1205198 1205468 1205584 "IFAST" 1205755 T IFAST (NIL) -8 NIL NIL NIL) (-518 1200193 1204490 1204678 "IFARRAY" 1205055 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199373 1200097 1200170 "IFAMON" 1200175 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198957 1199022 1199076 "IEVALAB" 1199283 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198632 1198700 1198860 "IEVALAB-" 1198865 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198263 1198546 1198609 "IDPO" 1198614 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197513 1198152 1198227 "IDPOAMS" 1198232 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196820 1197402 1197477 "IDPOAM" 1197482 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195879 1196155 1196208 "IDPC" 1196621 NIL IDPC (NIL T T) -9 NIL 1196770 NIL) (-510 1195348 1195771 1195844 "IDPAM" 1195849 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194724 1195240 1195313 "IDPAG" 1195318 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194369 1194560 1194635 "IDENT" 1194669 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190624 1191472 1192367 "IDECOMP" 1193526 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183462 1184547 1185594 "IDEAL" 1189660 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182626 1182738 1182937 "ICDEN" 1183346 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181697 1182106 1182253 "ICARD" 1182499 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179757 1180070 1180475 "IBPTOOLS" 1181374 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175364 1179377 1179490 "IBITS" 1179676 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1172087 1172663 1173358 "IBATOOL" 1174781 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169866 1170328 1170861 "IBACHIN" 1171622 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167695 1169712 1169815 "IARRAY2" 1169820 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163801 1167621 1167678 "IARRAY1" 1167683 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157910 1162213 1162694 "IAN" 1163340 T IAN (NIL) -8 NIL NIL NIL) (-496 1157421 1157478 1157651 "IALGFACT" 1157847 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156949 1157062 1157090 "HYPCAT" 1157297 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156487 1156604 1156790 "HYPCAT-" 1156795 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1156082 1156282 1156365 "HOSTNAME" 1156424 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155927 1155964 1156005 "HOMOTOP" 1156010 NIL HOMOTOP (NIL T) -9 NIL 1156043 NIL) (-491 1152559 1153937 1153978 "HOAGG" 1154959 NIL HOAGG (NIL T) -9 NIL 1155638 NIL) (-490 1151153 1151552 1152078 "HOAGG-" 1152083 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1145157 1150748 1150897 "HEXADEC" 1151024 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143904 1144127 1144390 "HEUGCD" 1144934 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142980 1143741 1143871 "HELLFDIV" 1143876 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1141159 1142757 1142845 "HEAP" 1142924 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140422 1140711 1140845 "HEADAST" 1141045 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134288 1140337 1140399 "HDP" 1140404 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128276 1133923 1134075 "HDMP" 1134189 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127600 1127740 1127904 "HB" 1128132 T HB (NIL) -7 NIL NIL NIL) (-481 1120986 1127446 1127550 "HASHTBL" 1127555 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120462 1120707 1120799 "HASAST" 1120914 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118240 1120084 1120266 "HACKPI" 1120300 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113908 1118093 1118206 "GTSET" 1118211 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107323 1113786 1113884 "GSTBL" 1113889 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099601 1106354 1106619 "GSERIES" 1107114 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098742 1099159 1099187 "GROUP" 1099390 T GROUP (NIL) -9 NIL 1099524 NIL) (-474 1098108 1098267 1098518 "GROUP-" 1098523 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096475 1096796 1097183 "GROEBSOL" 1097785 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095389 1095677 1095728 "GRMOD" 1096257 NIL GRMOD (NIL T T) -9 NIL 1096425 NIL) (-471 1095157 1095193 1095321 "GRMOD-" 1095326 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090447 1091511 1092511 "GRIMAGE" 1094177 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088913 1089174 1089498 "GRDEF" 1090143 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088357 1088473 1088614 "GRAY" 1088792 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087544 1087950 1088001 "GRALG" 1088154 NIL GRALG (NIL T T) -9 NIL 1088247 NIL) (-466 1087205 1087278 1087441 "GRALG-" 1087446 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083982 1086790 1086968 "GPOLSET" 1087112 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083336 1083393 1083651 "GOSPER" 1083919 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1079068 1079774 1080300 "GMODPOL" 1083035 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1078073 1078257 1078495 "GHENSEL" 1078880 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1072229 1073072 1074092 "GENUPS" 1077157 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071926 1071977 1072066 "GENUFACT" 1072172 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071338 1071415 1071580 "GENPGCD" 1071844 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070812 1070847 1071060 "GENMFACT" 1071297 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069378 1069635 1069942 "GENEEZ" 1070555 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063524 1068989 1069151 "GDMP" 1069301 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052866 1057295 1058401 "GCNAALG" 1062507 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1051193 1052055 1052083 "GCDDOM" 1052338 T GCDDOM (NIL) -9 NIL 1052495 NIL) (-453 1050663 1050790 1051005 "GCDDOM-" 1051010 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049335 1049520 1049824 "GB" 1050442 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037951 1040281 1042673 "GBINTERN" 1047026 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035788 1036080 1036501 "GBF" 1037626 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034569 1034734 1035001 "GBEUCLID" 1035604 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033918 1034043 1034192 "GAUSSFAC" 1034440 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032285 1032587 1032901 "GALUTIL" 1033637 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030593 1030867 1031191 "GALPOLYU" 1032012 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027958 1028248 1028655 "GALFACTU" 1030290 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019763 1021263 1022871 "GALFACT" 1026390 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1017151 1017809 1017837 "FVFUN" 1018993 T FVFUN (NIL) -9 NIL 1019713 NIL) (-442 1016417 1016599 1016627 "FVC" 1016918 T FVC (NIL) -9 NIL 1017101 NIL) (-441 1016060 1016242 1016310 "FUNDESC" 1016369 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015675 1015857 1015938 "FUNCTION" 1016012 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013419 1013997 1014463 "FT" 1015229 T FT (NIL) -8 NIL NIL NIL) (-438 1012210 1012720 1012923 "FTEM" 1013236 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010501 1010790 1011187 "FSUPFACT" 1011901 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008898 1009187 1009519 "FST" 1010189 T FST (NIL) -8 NIL NIL NIL) (-435 1008097 1008203 1008391 "FSRED" 1008780 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006796 1007052 1007399 "FSPRMELT" 1007812 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1004102 1004540 1005026 "FSPECF" 1006359 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985740 994071 994112 "FS" 997996 NIL FS (NIL T) -9 NIL 1000285 NIL) (-431 974383 977376 981433 "FS-" 981733 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973911 973965 974135 "FSINT" 974324 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 972203 972904 973207 "FSERIES" 973690 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971245 971361 971585 "FSCINT" 972083 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967453 970189 970230 "FSAGG" 970600 NIL FSAGG (NIL T) -9 NIL 970859 NIL) (-426 965215 965816 966612 "FSAGG-" 966707 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964257 964400 964627 "FSAGG2" 965068 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961939 962219 962766 "FS2UPS" 963975 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961573 961616 961745 "FS2" 961890 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960451 960622 960924 "FS2EXPXP" 961398 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959877 959992 960144 "FRUTIL" 960331 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951290 955372 956730 "FR" 958551 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946259 948933 948973 "FRNAALG" 950369 NIL FRNAALG (NIL T) -9 NIL 950976 NIL) (-418 941932 943008 944283 "FRNAALG-" 945033 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941570 941613 941740 "FRNAAF2" 941883 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939950 940424 940719 "FRMOD" 941382 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937701 938333 938650 "FRIDEAL" 939741 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936896 936983 937272 "FRIDEAL2" 937608 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 936029 936443 936484 "FRETRCT" 936489 NIL FRETRCT (NIL T) -9 NIL 936665 NIL) (-412 935141 935372 935723 "FRETRCT-" 935728 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 932229 933439 933498 "FRAMALG" 934380 NIL FRAMALG (NIL T T) -9 NIL 934672 NIL) (-410 930363 930818 931448 "FRAMALG-" 931671 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924284 929838 930114 "FRAC" 930119 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923920 923977 924084 "FRAC2" 924221 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923556 923613 923720 "FR2" 923857 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 918069 920962 920990 "FPS" 922109 T FPS (NIL) -9 NIL 922666 NIL) (-405 917518 917627 917791 "FPS-" 917937 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914820 916489 916517 "FPC" 916742 T FPC (NIL) -9 NIL 916884 NIL) (-403 914613 914653 914750 "FPC-" 914755 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913403 914101 914142 "FPATMAB" 914147 NIL FPATMAB (NIL T) -9 NIL 914299 NIL) (-401 911076 911579 912005 "FPARFRAC" 913040 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906469 906968 907650 "FORTRAN" 910508 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 904185 904685 905224 "FORT" 905950 T FORT (NIL) -7 NIL NIL NIL) (-398 901861 902423 902451 "FORTFN" 903511 T FORTFN (NIL) -9 NIL 904135 NIL) (-397 901625 901675 901703 "FORTCAT" 901762 T FORTCAT (NIL) -9 NIL 901824 NIL) (-396 899731 900241 900631 "FORMULA" 901255 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899519 899549 899618 "FORMULA1" 899695 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 899042 899094 899267 "FORDER" 899461 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 898138 898302 898495 "FOP" 898869 T FOP (NIL) -7 NIL NIL NIL) (-392 896719 897418 897592 "FNLA" 898020 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895448 895863 895891 "FNCAT" 896351 T FNCAT (NIL) -9 NIL 896611 NIL) (-390 894987 895407 895435 "FNAME" 895440 T FNAME (NIL) -8 NIL NIL NIL) (-389 893550 894513 894541 "FMTC" 894546 T FMTC (NIL) -9 NIL 894582 NIL) (-388 889883 891073 891702 "FMONOID" 892954 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 889075 889625 889774 "FM" 889779 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886499 887145 887173 "FMFUN" 888317 T FMFUN (NIL) -9 NIL 889025 NIL) (-385 885768 885949 885977 "FMC" 886267 T FMC (NIL) -9 NIL 886449 NIL) (-384 882847 883707 883761 "FMCAT" 884956 NIL FMCAT (NIL T T) -9 NIL 885451 NIL) (-383 881713 882613 882713 "FM1" 882792 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879487 879903 880397 "FLOATRP" 881264 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 873062 877216 877837 "FLOAT" 878886 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870500 871000 871578 "FLOATCP" 872529 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869240 870078 870119 "FLINEXP" 870124 NIL FLINEXP (NIL T) -9 NIL 870217 NIL) (-378 868394 868629 868957 "FLINEXP-" 868962 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867470 867614 867838 "FLASORT" 868246 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864586 865454 865506 "FLALG" 866733 NIL FLALG (NIL T T) -9 NIL 867200 NIL) (-375 858322 862072 862113 "FLAGG" 863375 NIL FLAGG (NIL T) -9 NIL 864027 NIL) (-374 857048 857387 857877 "FLAGG-" 857882 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 856090 856233 856460 "FLAGG2" 856901 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852941 853949 854008 "FINRALG" 855136 NIL FINRALG (NIL T T) -9 NIL 855644 NIL) (-371 852101 852330 852669 "FINRALG-" 852674 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851481 851720 851748 "FINITE" 851944 T FINITE (NIL) -9 NIL 852051 NIL) (-369 843838 846025 846065 "FINAALG" 849732 NIL FINAALG (NIL T) -9 NIL 851185 NIL) (-368 839170 840220 841364 "FINAALG-" 842743 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838538 838925 839028 "FILE" 839100 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837196 837534 837588 "FILECAT" 838272 NIL FILECAT (NIL T T) -9 NIL 838488 NIL) (-365 834912 836440 836468 "FIELD" 836508 T FIELD (NIL) -9 NIL 836588 NIL) (-364 833532 833917 834428 "FIELD-" 834433 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831382 832167 832514 "FGROUP" 833218 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830472 830636 830856 "FGLMICPK" 831214 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826304 830397 830454 "FFX" 830459 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825905 825966 826101 "FFSLPE" 826237 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821894 822677 823473 "FFPOLY" 825141 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821398 821434 821643 "FFPOLY2" 821852 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817241 821317 821380 "FFP" 821385 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812639 817152 817216 "FF" 817221 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807765 811982 812172 "FFNBX" 812493 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802694 806900 807158 "FFNBP" 807619 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797327 801978 802189 "FFNB" 802527 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 796159 796357 796672 "FFINTBAS" 797124 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792228 794448 794476 "FFIELDC" 795096 T FFIELDC (NIL) -9 NIL 795472 NIL) (-350 790890 791261 791758 "FFIELDC-" 791763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790459 790505 790629 "FFHOM" 790832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 788154 788641 789158 "FFF" 789974 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783772 787896 787997 "FFCGX" 788097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779393 783504 783611 "FFCGP" 783715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774576 779120 779228 "FFCG" 779329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755972 765053 765139 "FFCAT" 770304 NIL FFCAT (NIL T T T) -9 NIL 771755 NIL) (-343 751170 752217 753531 "FFCAT-" 754761 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750581 750624 750859 "FFCAT2" 751121 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739902 743553 744773 "FEXPR" 749433 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738902 739337 739378 "FEVALAB" 739462 NIL FEVALAB (NIL T) -9 NIL 739723 NIL) (-339 738061 738271 738609 "FEVALAB-" 738614 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736627 737444 737647 "FDIV" 737960 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733647 734388 734503 "FDIVCAT" 736071 NIL FDIVCAT (NIL T T T T) -9 NIL 736508 NIL) (-336 733409 733436 733606 "FDIVCAT-" 733611 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732629 732716 732993 "FDIV2" 733316 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731631 731945 732140 "FCTRDATA" 732454 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730317 730576 730865 "FCPAK1" 731362 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729416 729817 729958 "FCOMP" 730208 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 713118 716566 720104 "FC" 725898 T FC (NIL) -8 NIL NIL NIL) (-330 705481 709509 709549 "FAXF" 711351 NIL FAXF (NIL T) -9 NIL 712043 NIL) (-329 702757 703415 704240 "FAXF-" 704705 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697809 702133 702309 "FARRAY" 702614 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692703 694770 694823 "FAMR" 695846 NIL FAMR (NIL T T) -9 NIL 696306 NIL) (-326 691593 691895 692330 "FAMR-" 692335 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690762 691515 691568 "FAMONOID" 691573 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688548 689258 689311 "FAMONC" 690252 NIL FAMONC (NIL T T) -9 NIL 690638 NIL) (-323 687212 688302 688439 "FAGROUP" 688444 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 685007 685326 685729 "FACUTIL" 686893 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 684106 684291 684513 "FACTFUNC" 684817 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676528 683409 683608 "EXPUPXS" 683962 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 674011 674551 675137 "EXPRTUBE" 675962 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670282 670874 671604 "EXPRODE" 673350 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655767 668931 669360 "EXPR" 669886 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650321 650908 651714 "EXPR2UPS" 655065 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649953 650010 650119 "EXPR2" 650258 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641343 649106 649396 "EXPEXPAN" 649790 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 641143 641300 641329 "EXIT" 641334 T EXIT (NIL) -8 NIL NIL NIL) (-312 640623 640867 640958 "EXITAST" 641072 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640250 640312 640425 "EVALCYC" 640555 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639791 639909 639950 "EVALAB" 640120 NIL EVALAB (NIL T) -9 NIL 640224 NIL) (-309 639272 639394 639615 "EVALAB-" 639620 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636640 637942 637970 "EUCDOM" 638525 T EUCDOM (NIL) -9 NIL 638875 NIL) (-307 635045 635487 636077 "EUCDOM-" 636082 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622583 625343 628093 "ESTOOLS" 632315 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622215 622272 622381 "ESTOOLS2" 622520 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621966 622008 622088 "ESTOOLS1" 622167 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 616003 617611 617639 "ES" 620407 T ES (NIL) -9 NIL 621817 NIL) (-302 610950 612237 614054 "ES-" 614218 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607324 608085 608865 "ESCONT" 610190 T ESCONT (NIL) -7 NIL NIL NIL) (-300 607069 607101 607183 "ESCONT1" 607286 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606744 606794 606894 "ES2" 607013 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606374 606432 606541 "ES1" 606680 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605590 605719 605895 "ERROR" 606218 T ERROR (NIL) -7 NIL NIL NIL) (-296 598982 605449 605540 "EQTBL" 605545 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591485 594296 595745 "EQ" 597566 NIL -2013 (NIL T) -8 NIL NIL NIL) (-294 591117 591174 591283 "EQ2" 591422 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586406 587455 588548 "EP" 590056 NIL EP (NIL T) -7 NIL NIL NIL) (-292 585006 585297 585603 "ENV" 586120 T ENV (NIL) -8 NIL NIL NIL) (-291 584100 584654 584682 "ENTIRER" 584687 T ENTIRER (NIL) -9 NIL 584733 NIL) (-290 580567 582055 582425 "EMR" 583899 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579711 579896 579950 "ELTAGG" 580330 NIL ELTAGG (NIL T T) -9 NIL 580541 NIL) (-288 579430 579492 579633 "ELTAGG-" 579638 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579219 579248 579302 "ELTAB" 579386 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578345 578491 578690 "ELFUTS" 579070 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 578087 578143 578171 "ELEMFUN" 578276 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577957 577978 578046 "ELEMFUN-" 578051 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572801 576057 576098 "ELAGG" 577038 NIL ELAGG (NIL T) -9 NIL 577501 NIL) (-282 571086 571520 572183 "ELAGG-" 572188 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569751 570029 570322 "ELABEXPR" 570813 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562615 564418 565245 "EFUPXS" 569027 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 556065 557866 558676 "EFULS" 561891 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553550 553908 554380 "EFSTRUC" 555697 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543341 544907 546455 "EF" 552065 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542415 542826 542975 "EAB" 543212 T EAB (NIL) -8 NIL NIL NIL) (-275 541597 542374 542402 "E04UCFA" 542407 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540779 541556 541584 "E04NAFA" 541589 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539961 540738 540766 "E04MBFA" 540771 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 539143 539920 539948 "E04JAFA" 539953 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538327 539102 539130 "E04GCFA" 539135 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537511 538286 538314 "E04FDFA" 538319 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536693 537470 537498 "E04DGFA" 537503 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530866 532218 533582 "E04AGNT" 535349 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529546 530052 530092 "DVARCAT" 530567 NIL DVARCAT (NIL T) -9 NIL 530766 NIL) (-266 528750 528962 529276 "DVARCAT-" 529281 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521887 528549 528678 "DSMP" 528683 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516668 517832 518900 "DROPT" 520839 T DROPT (NIL) -8 NIL NIL NIL) (-263 516333 516392 516490 "DROPT1" 516603 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511448 512574 513711 "DROPT0" 515216 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509793 510118 510504 "DRAWPT" 511082 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504380 505303 506382 "DRAW" 508767 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 504013 504066 504184 "DRAWHACK" 504321 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502744 503013 503304 "DRAWCX" 503742 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502259 502328 502479 "DRAWCURV" 502670 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492727 494689 496804 "DRAWCFUN" 500164 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489493 491422 491463 "DQAGG" 492092 NIL DQAGG (NIL T) -9 NIL 492365 NIL) (-254 477617 484086 484169 "DPOLCAT" 486021 NIL DPOLCAT (NIL T T T T) -9 NIL 486566 NIL) (-253 472453 473802 475760 "DPOLCAT-" 475765 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465575 472314 472412 "DPMO" 472417 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458600 465355 465522 "DPMM" 465527 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 458078 458292 458390 "DOMTMPLT" 458522 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457511 457880 457960 "DOMCTOR" 458018 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456779 457033 457170 "DOMAIN" 457394 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450767 456414 456566 "DMP" 456680 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450367 450423 450567 "DLP" 450705 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444189 449694 449884 "DLIST" 450209 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440986 443042 443083 "DLAGG" 443633 NIL DLAGG (NIL T) -9 NIL 443863 NIL) (-243 439662 440326 440354 "DIVRING" 440446 T DIVRING (NIL) -9 NIL 440529 NIL) (-242 438899 439089 439389 "DIVRING-" 439394 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437001 437358 437764 "DISPLAY" 438513 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430889 436915 436978 "DIRPROD" 436983 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429737 429940 430205 "DIRPROD2" 430682 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418512 424518 424571 "DIRPCAT" 424981 NIL DIRPCAT (NIL NIL T) -9 NIL 425821 NIL) (-237 415838 416480 417361 "DIRPCAT-" 417698 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415125 415285 415471 "DIOSP" 415672 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411780 414037 414078 "DIOPS" 414512 NIL DIOPS (NIL T) -9 NIL 414741 NIL) (-234 411329 411443 411634 "DIOPS-" 411639 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410152 410780 410808 "DIFRING" 410995 T DIFRING (NIL) -9 NIL 411105 NIL) (-232 409798 409875 410027 "DIFRING-" 410032 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407534 408806 408847 "DIFEXT" 409210 NIL DIFEXT (NIL T) -9 NIL 409504 NIL) (-230 405819 406247 406913 "DIFEXT-" 406918 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403094 405351 405392 "DIAGG" 405397 NIL DIAGG (NIL T) -9 NIL 405417 NIL) (-228 402478 402635 402887 "DIAGG-" 402892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397895 401437 401714 "DHMATRIX" 402247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393507 394416 395426 "DFSFUN" 396905 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388585 392438 392750 "DFLOAT" 393215 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386848 387129 387518 "DFINTTLS" 388293 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383877 384869 385269 "DERHAM" 386514 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381678 383652 383741 "DEQUEUE" 383821 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380932 381065 381248 "DEGRED" 381540 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377362 378107 378953 "DEFINTRF" 380160 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374917 375386 375978 "DEFINTEF" 376881 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374267 374537 374652 "DEFAST" 374822 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368271 373862 374011 "DECIMAL" 374138 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365783 366241 366747 "DDFACT" 367815 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365379 365422 365573 "DBLRESP" 365734 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363251 363612 363972 "DBASE" 365146 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362493 362731 362877 "DATAARY" 363150 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361599 362452 362480 "D03FAFA" 362485 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360706 361558 361586 "D03EEFA" 361591 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358656 359122 359611 "D03AGNT" 360237 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357945 358615 358643 "D02EJFA" 358648 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357234 357904 357932 "D02CJFA" 357937 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356523 357193 357221 "D02BHFA" 357226 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355812 356482 356510 "D02BBFA" 356515 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349009 350598 352204 "D02AGNT" 354226 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346777 347300 347846 "D01WGTS" 348483 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345844 346736 346764 "D01TRNS" 346769 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344912 345803 345831 "D01GBFA" 345836 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343980 344871 344899 "D01FCFA" 344904 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343048 343939 343967 "D01ASFA" 343972 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342116 343007 343035 "D01AQFA" 343040 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341184 342075 342103 "D01APFA" 342108 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340252 341143 341171 "D01ANFA" 341176 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339320 340211 340239 "D01AMFA" 340244 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338388 339279 339307 "D01ALFA" 339312 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337456 338347 338375 "D01AKFA" 338380 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336524 337415 337443 "D01AJFA" 337448 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329819 331372 332933 "D01AGNT" 334983 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329156 329284 329436 "CYCLOTOM" 329687 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325890 326604 327331 "CYCLES" 328449 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325202 325336 325507 "CVMP" 325751 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323043 323301 323670 "CTRIGMNP" 324930 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322479 322837 322910 "CTOR" 322990 T CTOR (NIL) -8 NIL NIL NIL) (-186 321988 322210 322311 "CTORKIND" 322398 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321279 321595 321623 "CTORCAT" 321805 T CTORCAT (NIL) -9 NIL 321918 NIL) (-184 320877 320988 321147 "CTORCAT-" 321152 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320366 320580 320678 "CTORCALL" 320799 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319740 319839 319992 "CSTTOOLS" 320263 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315539 316196 316954 "CRFP" 319052 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315014 315260 315352 "CRCEAST" 315467 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314061 314246 314474 "CRAPACK" 314818 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313445 313546 313750 "CPMATCH" 313937 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313170 313198 313304 "CPIMA" 313411 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309518 310190 310909 "COORDSYS" 312505 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308930 309051 309193 "CONTOUR" 309396 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304821 306933 307425 "CONTFRAC" 308470 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304701 304722 304750 "CONDUIT" 304787 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303789 304343 304371 "COMRING" 304376 T COMRING (NIL) -9 NIL 304428 NIL) (-171 302843 303147 303331 "COMPPROP" 303625 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302504 302539 302667 "COMPLPAT" 302802 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292795 302313 302422 "COMPLEX" 302427 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292431 292488 292595 "COMPLEX2" 292732 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292149 292184 292282 "COMPFACT" 292390 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276229 286223 286263 "COMPCAT" 287267 NIL COMPCAT (NIL T) -9 NIL 288615 NIL) (-165 265741 268668 272295 "COMPCAT-" 272651 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265470 265498 265601 "COMMUPC" 265707 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265264 265298 265357 "COMMONOP" 265431 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264820 265015 265102 "COMM" 265197 T COMM (NIL) -8 NIL NIL NIL) (-161 264396 264624 264699 "COMMAAST" 264765 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263645 263839 263867 "COMBOPC" 264205 T COMBOPC (NIL) -9 NIL 264380 NIL) (-159 262541 262751 262993 "COMBINAT" 263435 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258998 259572 260199 "COMBF" 261963 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257756 258114 258349 "COLOR" 258783 T COLOR (NIL) -8 NIL NIL NIL) (-156 257232 257477 257569 "COLONAST" 257684 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256872 256919 257044 "CMPLXRT" 257179 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256320 256572 256671 "CLLCTAST" 256793 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251818 252850 253930 "CLIP" 255260 T CLIP (NIL) -7 NIL NIL NIL) (-152 250164 250924 251163 "CLIF" 251645 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246339 248310 248351 "CLAGG" 249280 NIL CLAGG (NIL T) -9 NIL 249816 NIL) (-150 244761 245218 245801 "CLAGG-" 245806 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244305 244390 244530 "CINTSLPE" 244670 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241806 242277 242825 "CHVAR" 243833 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240980 241534 241562 "CHARZ" 241567 T CHARZ (NIL) -9 NIL 241582 NIL) (-146 240734 240774 240852 "CHARPOL" 240934 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239792 240379 240407 "CHARNZ" 240454 T CHARNZ (NIL) -9 NIL 240510 NIL) (-144 237758 238482 238817 "CHAR" 239477 T CHAR (NIL) -8 NIL NIL NIL) (-143 237484 237545 237573 "CFCAT" 237684 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236729 236840 237022 "CDEN" 237368 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232694 235882 236162 "CCLASS" 236469 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232001 232144 232307 "CATEGORY" 232551 T -10 (NIL) -8 NIL NIL NIL) (-139 231574 231920 231968 "CATCTOR" 231973 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231025 231277 231375 "CATAST" 231496 T CATAST (NIL) -8 NIL NIL NIL) (-137 230501 230746 230838 "CASEAST" 230953 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225510 226530 227283 "CARTEN" 229804 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224618 224766 224987 "CARTEN2" 225357 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222934 223768 224025 "CARD" 224381 T CARD (NIL) -8 NIL NIL NIL) (-133 222510 222738 222813 "CAPSLAST" 222879 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222014 222222 222250 "CACHSET" 222382 T CACHSET (NIL) -9 NIL 222460 NIL) (-131 221484 221806 221834 "CABMON" 221884 T CABMON (NIL) -9 NIL 221940 NIL) (-130 220957 221188 221298 "BYTEORD" 221394 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219936 220491 220633 "BYTE" 220796 T BYTE (NIL) -8 NIL NIL 220918) (-128 215286 219441 219613 "BYTEBUF" 219784 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212795 214978 215085 "BTREE" 215212 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210244 212443 212565 "BTOURN" 212705 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207614 209714 209755 "BTCAT" 209823 NIL BTCAT (NIL T) -9 NIL 209900 NIL) (-124 207281 207361 207510 "BTCAT-" 207515 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202546 206424 206452 "BTAGG" 206674 T BTAGG (NIL) -9 NIL 206835 NIL) (-122 202036 202161 202367 "BTAGG-" 202372 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199031 201314 201529 "BSTREE" 201853 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198169 198295 198479 "BRILL" 198887 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194821 196895 196936 "BRAGG" 197585 NIL BRAGG (NIL T) -9 NIL 197843 NIL) (-118 193350 193756 194311 "BRAGG-" 194316 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186579 192696 192880 "BPADICRT" 193198 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184894 186516 186561 "BPADIC" 186566 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184592 184622 184736 "BOUNDZRO" 184858 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179820 181018 181930 "BOP" 183700 T BOP (NIL) -8 NIL NIL NIL) (-113 177601 178005 178480 "BOP1" 179378 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176426 177175 177324 "BOOLEAN" 177472 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175705 176109 176163 "BMODULE" 176168 NIL BMODULE (NIL T T) -9 NIL 176233 NIL) (-110 171506 175503 175576 "BITS" 175652 T BITS (NIL) -8 NIL NIL NIL) (-109 170927 171046 171186 "BINDING" 171386 T BINDING (NIL) -8 NIL NIL NIL) (-108 164934 170524 170672 "BINARY" 170799 T BINARY (NIL) -8 NIL NIL NIL) (-107 162714 164189 164230 "BGAGG" 164490 NIL BGAGG (NIL T) -9 NIL 164627 NIL) (-106 162545 162577 162668 "BGAGG-" 162673 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161616 161929 162134 "BFUNCT" 162360 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160306 160484 160772 "BEZOUT" 161440 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156775 159158 159488 "BBTREE" 160009 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156509 156562 156590 "BASTYPE" 156709 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156361 156390 156463 "BASTYPE-" 156468 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155795 155871 156023 "BALFACT" 156272 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154651 155210 155396 "AUTOMOR" 155640 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154377 154382 154408 "ATTREG" 154413 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152629 153074 153426 "ATTRBUT" 154043 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152237 152457 152523 "ATTRAST" 152581 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151773 151886 151912 "ATRIG" 152113 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151582 151623 151710 "ATRIG-" 151715 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151227 151413 151439 "ASTCAT" 151444 T ASTCAT (NIL) -9 NIL 151474 NIL) (-92 150954 151013 151132 "ASTCAT-" 151137 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149103 150730 150818 "ASTACK" 150897 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147608 147905 148270 "ASSOCEQ" 148785 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146640 147267 147391 "ASP9" 147515 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146403 146588 146627 "ASP8" 146632 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145271 146008 146150 "ASP80" 146292 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144169 144906 145038 "ASP7" 145170 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143123 143846 143964 "ASP78" 144082 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142092 142803 142920 "ASP77" 143037 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141004 141730 141861 "ASP74" 141992 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139904 140639 140771 "ASP73" 140903 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139008 139730 139830 "ASP6" 139835 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137952 138685 138803 "ASP55" 138921 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136901 137626 137745 "ASP50" 137864 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135989 136602 136712 "ASP4" 136822 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135077 135690 135800 "ASP49" 135910 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133861 134616 134784 "ASP42" 134966 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132637 133394 133564 "ASP41" 133748 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131587 132314 132432 "ASP35" 132550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131352 131535 131574 "ASP34" 131579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131089 131156 131232 "ASP33" 131307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129982 130724 130856 "ASP31" 130988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129747 129930 129969 "ASP30" 129974 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129482 129551 129627 "ASP29" 129702 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129247 129430 129469 "ASP28" 129474 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129012 129195 129234 "ASP27" 129239 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128096 128710 128821 "ASP24" 128932 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127172 127898 128010 "ASP20" 128015 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126260 126873 126983 "ASP1" 127093 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125202 125934 126053 "ASP19" 126172 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124939 125006 125082 "ASP12" 125157 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123791 124538 124682 "ASP10" 124826 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121642 123635 123726 "ARRAY2" 123731 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117407 121290 121404 "ARRAY1" 121559 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116439 116612 116833 "ARRAY12" 117230 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110751 112669 112744 "ARR2CAT" 115374 NIL ARR2CAT (NIL T T T) -9 NIL 116132 NIL) (-56 108185 108929 109883 "ARR2CAT-" 109888 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107502 107812 107937 "ARITY" 108078 T ARITY (NIL) -8 NIL NIL NIL) (-54 106278 106430 106729 "APPRULE" 107338 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105929 105977 106096 "APPLYORE" 106224 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105194 105389 "ANY" 105752 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 3221321 3221326 3221331 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3221306 3221311 3221316 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3221291 3221296 3221301 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3221276 3221281 3221286 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1292 3220419 3221151 3221228 "ZMOD" 3221233 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1291 3219529 3219693 3219902 "ZLINDEP" 3220251 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1290 3208829 3210597 3212569 "ZDSOLVE" 3217659 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1289 3208075 3208216 3208405 "YSTREAM" 3208675 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1288 3205849 3207376 3207580 "XRPOLY" 3207918 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1287 3202402 3203720 3204295 "XPR" 3205321 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1286 3200123 3201733 3201937 "XPOLY" 3202233 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1285 3197776 3199144 3199199 "XPOLYC" 3199487 NIL XPOLYC (NIL T T) -9 NIL 3199600 NIL) (-1284 3194151 3196293 3196681 "XPBWPOLY" 3197434 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1283 3189846 3192141 3192183 "XF" 3192804 NIL XF (NIL T) -9 NIL 3193204 NIL) (-1282 3189467 3189555 3189724 "XF-" 3189729 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1281 3184663 3185952 3186007 "XFALG" 3188179 NIL XFALG (NIL T T) -9 NIL 3188968 NIL) (-1280 3183796 3183900 3184105 "XEXPPKG" 3184555 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1279 3181905 3183646 3183742 "XDPOLY" 3183747 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3180712 3181312 3181355 "XALG" 3181360 NIL XALG (NIL T) -9 NIL 3181471 NIL) (-1277 3174154 3178689 3179183 "WUTSET" 3180304 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1276 3172410 3173206 3173529 "WP" 3173965 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1275 3172012 3172232 3172302 "WHILEAST" 3172362 T WHILEAST (NIL) -8 NIL NIL NIL) (-1274 3171484 3171729 3171823 "WHEREAST" 3171940 T WHEREAST (NIL) -8 NIL NIL NIL) (-1273 3170370 3170568 3170863 "WFFINTBS" 3171281 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1272 3168274 3168701 3169163 "WEIER" 3169942 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1271 3167320 3167770 3167812 "VSPACE" 3167948 NIL VSPACE (NIL T) -9 NIL 3168022 NIL) (-1270 3167158 3167185 3167276 "VSPACE-" 3167281 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1269 3166966 3167009 3167077 "VOID" 3167112 T VOID (NIL) -8 NIL NIL NIL) (-1268 3165102 3165461 3165867 "VIEW" 3166582 T VIEW (NIL) -7 NIL NIL NIL) (-1267 3161526 3162165 3162902 "VIEWDEF" 3164387 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1266 3150830 3153074 3155247 "VIEW3D" 3159375 T VIEW3D (NIL) -8 NIL NIL NIL) (-1265 3143081 3144741 3146320 "VIEW2D" 3149273 T VIEW2D (NIL) -8 NIL NIL NIL) (-1264 3138433 3142851 3142943 "VECTOR" 3143024 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1263 3137010 3137269 3137587 "VECTOR2" 3138163 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1262 3130484 3134791 3134834 "VECTCAT" 3135829 NIL VECTCAT (NIL T) -9 NIL 3136416 NIL) (-1261 3129498 3129752 3130142 "VECTCAT-" 3130147 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1260 3128952 3129149 3129269 "VARIABLE" 3129413 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1259 3128885 3128890 3128920 "UTYPE" 3128925 T UTYPE (NIL) -9 NIL NIL NIL) (-1258 3127715 3127869 3128131 "UTSODETL" 3128711 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1257 3125155 3125615 3126139 "UTSODE" 3127256 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1256 3116992 3122781 3123270 "UTS" 3124724 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1255 3107866 3113233 3113276 "UTSCAT" 3114388 NIL UTSCAT (NIL T) -9 NIL 3115146 NIL) (-1254 3105213 3105936 3106925 "UTSCAT-" 3106930 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1253 3104840 3104883 3105016 "UTS2" 3105164 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1252 3099066 3101678 3101721 "URAGG" 3103791 NIL URAGG (NIL T) -9 NIL 3104514 NIL) (-1251 3096005 3096868 3097991 "URAGG-" 3097996 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1250 3091714 3094640 3095105 "UPXSSING" 3095669 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1249 3083780 3090961 3091234 "UPXS" 3091499 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1248 3076853 3083684 3083756 "UPXSCONS" 3083761 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1247 3066598 3073391 3073453 "UPXSCCA" 3074027 NIL UPXSCCA (NIL T T) -9 NIL 3074260 NIL) (-1246 3066236 3066321 3066495 "UPXSCCA-" 3066500 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1245 3055833 3062399 3062442 "UPXSCAT" 3063090 NIL UPXSCAT (NIL T) -9 NIL 3063699 NIL) (-1244 3055263 3055342 3055521 "UPXS2" 3055748 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1243 3053917 3054170 3054521 "UPSQFREE" 3055006 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1242 3047338 3050395 3050450 "UPSCAT" 3051611 NIL UPSCAT (NIL T T) -9 NIL 3052385 NIL) (-1241 3046542 3046749 3047076 "UPSCAT-" 3047081 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1240 3032197 3039965 3040008 "UPOLYC" 3042109 NIL UPOLYC (NIL T) -9 NIL 3043330 NIL) (-1239 3023525 3025951 3029098 "UPOLYC-" 3029103 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1238 3023152 3023195 3023328 "UPOLYC2" 3023476 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1237 3014963 3022835 3022964 "UP" 3023071 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1236 3014302 3014409 3014573 "UPMP" 3014852 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1235 3013855 3013936 3014075 "UPDIVP" 3014215 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1234 3012423 3012672 3012988 "UPDECOMP" 3013604 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1233 3011658 3011770 3011955 "UPCDEN" 3012307 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1232 3011177 3011246 3011395 "UP2" 3011583 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1231 3009644 3010381 3010658 "UNISEG" 3010935 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1230 3008859 3008986 3009191 "UNISEG2" 3009487 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1229 3007919 3008099 3008325 "UNIFACT" 3008675 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1228 2991851 3007096 3007347 "ULS" 3007726 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1227 2979849 2991755 2991827 "ULSCONS" 2991832 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1226 2961868 2973853 2973915 "ULSCCAT" 2974553 NIL ULSCCAT (NIL T T) -9 NIL 2974841 NIL) (-1225 2960918 2961163 2961551 "ULSCCAT-" 2961556 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1224 2950292 2956772 2956815 "ULSCAT" 2957678 NIL ULSCAT (NIL T) -9 NIL 2958409 NIL) (-1223 2949722 2949801 2949980 "ULS2" 2950207 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1222 2948849 2949359 2949466 "UINT8" 2949577 T UINT8 (NIL) -8 NIL NIL 2949662) (-1221 2947975 2948485 2948592 "UINT64" 2948703 T UINT64 (NIL) -8 NIL NIL 2948788) (-1220 2947101 2947611 2947718 "UINT32" 2947829 T UINT32 (NIL) -8 NIL NIL 2947914) (-1219 2946227 2946737 2946844 "UINT16" 2946955 T UINT16 (NIL) -8 NIL NIL 2947040) (-1218 2944530 2945487 2945517 "UFD" 2945729 T UFD (NIL) -9 NIL 2945843 NIL) (-1217 2944324 2944370 2944465 "UFD-" 2944470 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1216 2943406 2943589 2943805 "UDVO" 2944130 T UDVO (NIL) -7 NIL NIL NIL) (-1215 2941222 2941631 2942102 "UDPO" 2942970 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1214 2941155 2941160 2941190 "TYPE" 2941195 T TYPE (NIL) -9 NIL NIL NIL) (-1213 2940915 2941110 2941141 "TYPEAST" 2941146 T TYPEAST (NIL) -8 NIL NIL NIL) (-1212 2939886 2940088 2940328 "TWOFACT" 2940709 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1211 2938909 2939295 2939530 "TUPLE" 2939686 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1210 2936600 2937119 2937658 "TUBETOOL" 2938392 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1209 2935449 2935654 2935895 "TUBE" 2936393 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1208 2930178 2934421 2934704 "TS" 2935201 NIL TS (NIL T) -8 NIL NIL NIL) (-1207 2918818 2922937 2923034 "TSETCAT" 2928303 NIL TSETCAT (NIL T T T T) -9 NIL 2929834 NIL) (-1206 2913550 2915150 2917041 "TSETCAT-" 2917046 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1205 2908189 2909036 2909965 "TRMANIP" 2912686 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1204 2907630 2907693 2907856 "TRIMAT" 2908121 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1203 2905496 2905733 2906090 "TRIGMNIP" 2907379 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1202 2905016 2905129 2905159 "TRIGCAT" 2905372 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1201 2904685 2904764 2904905 "TRIGCAT-" 2904910 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1200 2901530 2903543 2903824 "TREE" 2904439 NIL TREE (NIL T) -8 NIL NIL NIL) (-1199 2900804 2901332 2901362 "TRANFUN" 2901397 T TRANFUN (NIL) -9 NIL 2901463 NIL) (-1198 2900083 2900274 2900554 "TRANFUN-" 2900559 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1197 2899887 2899919 2899980 "TOPSP" 2900044 T TOPSP (NIL) -7 NIL NIL NIL) (-1196 2899235 2899350 2899504 "TOOLSIGN" 2899768 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1195 2897869 2898412 2898651 "TEXTFILE" 2899018 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1194 2895781 2896322 2896751 "TEX" 2897462 T TEX (NIL) -8 NIL NIL NIL) (-1193 2895562 2895593 2895665 "TEX1" 2895744 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1192 2895210 2895273 2895363 "TEMUTL" 2895494 T TEMUTL (NIL) -7 NIL NIL NIL) (-1191 2893364 2893644 2893969 "TBCMPPK" 2894933 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1190 2885141 2891524 2891580 "TBAGG" 2891980 NIL TBAGG (NIL T T) -9 NIL 2892191 NIL) (-1189 2880211 2881699 2883453 "TBAGG-" 2883458 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1188 2879595 2879702 2879847 "TANEXP" 2880100 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1187 2872985 2879452 2879545 "TABLE" 2879550 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1186 2872397 2872496 2872634 "TABLEAU" 2872882 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1185 2867005 2868225 2869473 "TABLBUMP" 2871183 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1184 2866227 2866374 2866555 "SYSTEM" 2866846 T SYSTEM (NIL) -8 NIL NIL NIL) (-1183 2862686 2863385 2864168 "SYSSOLP" 2865478 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1182 2861730 2862235 2862354 "SYSNNI" 2862540 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862625) (-1181 2861037 2861496 2861575 "SYSINT" 2861635 NIL SYSINT (NIL NIL) -8 NIL NIL 2861680) (-1180 2857369 2858315 2859025 "SYNTAX" 2860349 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854527 2855129 2855761 "SYMTAB" 2856759 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849776 2850678 2851661 "SYMS" 2853566 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2847011 2849234 2849464 "SYMPOLY" 2849581 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846528 2846603 2846726 "SYMFUNC" 2846923 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842547 2843840 2844653 "SYMBOL" 2845737 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2836086 2837775 2839495 "SWITCH" 2840849 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829320 2834907 2835210 "SUTS" 2835841 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821386 2828567 2828840 "SUPXS" 2829105 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2813145 2821004 2821130 "SUP" 2821295 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812304 2812431 2812648 "SUPFRACF" 2813013 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811925 2811984 2812097 "SUP2" 2812239 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810373 2810647 2811003 "SUMRF" 2811624 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809708 2809774 2809966 "SUMFS" 2810294 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793675 2808885 2809136 "SULS" 2809515 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793277 2793497 2793567 "SUCHTAST" 2793627 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792572 2792802 2792942 "SUCH" 2793185 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786438 2787478 2788437 "SUBSPACE" 2791660 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785868 2785958 2786122 "SUBRESP" 2786326 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2779233 2780533 2781844 "STTF" 2784604 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773406 2774526 2775673 "STTFNC" 2778133 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764716 2766588 2768382 "STTAYLOR" 2771647 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757846 2764580 2764663 "STRTBL" 2764668 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2753210 2757801 2757832 "STRING" 2757837 T STRING (NIL) -8 NIL NIL NIL) (-1156 2748071 2752583 2752613 "STRICAT" 2752672 T STRICAT (NIL) -9 NIL 2752734 NIL) (-1155 2740824 2745690 2746301 "STREAM" 2747495 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740334 2740411 2740555 "STREAM3" 2740741 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739316 2739499 2739734 "STREAM2" 2740147 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2739004 2739056 2739149 "STREAM1" 2739258 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2738020 2738201 2738432 "STINPROD" 2738820 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737572 2737782 2737812 "STEP" 2737892 T STEP (NIL) -9 NIL 2737970 NIL) (-1149 2731004 2737471 2737548 "STBL" 2737553 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2726130 2730225 2730268 "STAGG" 2730421 NIL STAGG (NIL T) -9 NIL 2730510 NIL) (-1147 2723832 2724434 2725306 "STAGG-" 2725311 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721979 2723602 2723694 "STACK" 2723775 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714674 2720120 2720576 "SREGSET" 2721609 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2707099 2708468 2709981 "SRDCMPK" 2713280 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2700016 2704539 2704569 "SRAGG" 2705872 T SRAGG (NIL) -9 NIL 2706480 NIL) (-1142 2699033 2699288 2699667 "SRAGG-" 2699672 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693493 2697980 2698401 "SQMATRIX" 2698659 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2687178 2690211 2690938 "SPLTREE" 2692838 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2683141 2683834 2684480 "SPLNODE" 2686604 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2682188 2682421 2682451 "SPFCAT" 2682895 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680925 2681135 2681399 "SPECOUT" 2681946 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672551 2674321 2674351 "SPADXPT" 2678743 T SPADXPT (NIL) -9 NIL 2680777 NIL) (-1135 2672312 2672352 2672421 "SPADPRSR" 2672504 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670467 2672267 2672298 "SPADAST" 2672303 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662412 2664185 2664228 "SPACEC" 2668601 NIL SPACEC (NIL T) -9 NIL 2670417 NIL) (-1132 2660542 2662344 2662393 "SPACE3" 2662398 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659294 2659465 2659756 "SORTPAK" 2660347 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657386 2657689 2658101 "SOLVETRA" 2658958 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656436 2656658 2656919 "SOLVESER" 2657159 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651740 2652628 2653623 "SOLVERAD" 2655488 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647555 2648164 2648893 "SOLVEFOR" 2651107 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641825 2646904 2647001 "SNTSCAT" 2647006 NIL SNTSCAT (NIL T T T T) -9 NIL 2647076 NIL) (-1125 2635931 2640148 2640539 "SMTS" 2641515 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630615 2635819 2635896 "SMP" 2635901 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628774 2629075 2629473 "SMITH" 2630312 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621487 2625683 2625786 "SMATCAT" 2627137 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627687 NIL) (-1121 2618427 2619250 2620428 "SMATCAT-" 2620433 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2616093 2617663 2617706 "SKAGG" 2617967 NIL SKAGG (NIL T) -9 NIL 2618102 NIL) (-1119 2612404 2615509 2615704 "SINT" 2615891 T SINT (NIL) -8 NIL NIL 2616064) (-1118 2612176 2612214 2612280 "SIMPAN" 2612360 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611455 2611711 2611851 "SIG" 2612058 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610293 2610514 2610789 "SIGNRF" 2611214 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2609126 2609277 2609561 "SIGNEF" 2610122 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608432 2608709 2608833 "SIGAST" 2609024 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2606121 2606576 2607082 "SHP" 2607973 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599973 2606022 2606098 "SHDP" 2606103 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599546 2599738 2599768 "SGROUP" 2599861 T SGROUP (NIL) -9 NIL 2599923 NIL) (-1110 2599404 2599430 2599503 "SGROUP-" 2599508 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596239 2596937 2597660 "SGCF" 2598703 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590607 2595686 2595783 "SFRTCAT" 2595788 NIL SFRTCAT (NIL T T T T) -9 NIL 2595827 NIL) (-1107 2584028 2585046 2586182 "SFRGCD" 2589590 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2577154 2578227 2579413 "SFQCMPK" 2582961 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576774 2576863 2576974 "SFORT" 2577095 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575892 2576614 2576735 "SEXOF" 2576740 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574999 2575773 2575841 "SEX" 2575846 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570512 2571227 2571322 "SEXCAT" 2574259 NIL SEXCAT (NIL T T T T T) -9 NIL 2574837 NIL) (-1101 2567665 2570446 2570494 "SET" 2570499 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565889 2566378 2566683 "SETMN" 2567406 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565385 2565537 2565567 "SETCAT" 2565743 T SETCAT (NIL) -9 NIL 2565853 NIL) (-1098 2565077 2565155 2565285 "SETCAT-" 2565290 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561438 2563538 2563581 "SETAGG" 2564451 NIL SETAGG (NIL T) -9 NIL 2564791 NIL) (-1096 2560896 2561012 2561249 "SETAGG-" 2561254 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560339 2560592 2560693 "SEQAST" 2560817 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559538 2559832 2559893 "SEGXCAT" 2560179 NIL SEGXCAT (NIL T T) -9 NIL 2560299 NIL) (-1093 2558544 2559204 2559386 "SEG" 2559391 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557523 2557737 2557780 "SEGCAT" 2558302 NIL SEGCAT (NIL T) -9 NIL 2558523 NIL) (-1091 2556524 2556902 2557102 "SEGBIND" 2557358 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2556145 2556204 2556317 "SEGBIND2" 2556459 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555718 2555946 2556023 "SEGAST" 2556090 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554937 2555063 2555267 "SEG2" 2555562 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554347 2554872 2554919 "SDVAR" 2554924 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546874 2554117 2554247 "SDPOL" 2554252 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545467 2545733 2546052 "SCPKG" 2546589 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544631 2544803 2544995 "SCOPE" 2545297 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543851 2543985 2544164 "SCACHE" 2544486 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543497 2543683 2543713 "SASTCAT" 2543718 T SASTCAT (NIL) -9 NIL 2543731 NIL) (-1081 2542984 2543332 2543408 "SAOS" 2543443 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542549 2542584 2542757 "SAERFFC" 2542943 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536488 2542446 2542526 "SAE" 2542531 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2536081 2536116 2536275 "SAEFACT" 2536447 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534402 2534716 2535117 "RURPK" 2535747 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2533039 2533345 2533650 "RULESET" 2534236 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530262 2530792 2531250 "RULE" 2532720 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529874 2530056 2530139 "RULECOLD" 2530214 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529664 2529692 2529763 "RTVALUE" 2529825 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2529135 2529381 2529475 "RSTRCAST" 2529592 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523983 2524778 2525698 "RSETGCD" 2528334 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2513213 2518292 2518389 "RSETCAT" 2522508 NIL RSETCAT (NIL T T T T) -9 NIL 2523605 NIL) (-1069 2511140 2511679 2512503 "RSETCAT-" 2512508 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503525 2504902 2506422 "RSDCMPK" 2509739 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501504 2501971 2502045 "RRCC" 2503131 NIL RRCC (NIL T T) -9 NIL 2503475 NIL) (-1066 2500855 2501029 2501308 "RRCC-" 2501313 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500298 2500551 2500652 "RPTAST" 2500776 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2474149 2483506 2483573 "RPOLCAT" 2494237 NIL RPOLCAT (NIL T T T) -9 NIL 2497396 NIL) (-1063 2465647 2467987 2471109 "RPOLCAT-" 2471114 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456578 2463858 2464340 "ROUTINE" 2465187 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453376 2456204 2456344 "ROMAN" 2456460 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451620 2452236 2452496 "ROIRC" 2453181 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447852 2450136 2450166 "RNS" 2450470 T RNS (NIL) -9 NIL 2450744 NIL) (-1058 2446361 2446744 2447278 "RNS-" 2447353 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445764 2446172 2446202 "RNG" 2446207 T RNG (NIL) -9 NIL 2446228 NIL) (-1056 2445163 2445551 2445594 "RMODULE" 2445599 NIL RMODULE (NIL T) -9 NIL 2445626 NIL) (-1055 2443999 2444093 2444429 "RMCAT2" 2445064 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440849 2443345 2443642 "RMATRIX" 2443761 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433676 2435936 2436051 "RMATCAT" 2439410 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440392 NIL) (-1052 2433051 2433198 2433505 "RMATCAT-" 2433510 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432452 2432673 2432716 "RLINSET" 2432910 NIL RLINSET (NIL T) -9 NIL 2433001 NIL) (-1050 2432019 2432094 2432222 "RINTERP" 2432371 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2431077 2431631 2431661 "RING" 2431717 T RING (NIL) -9 NIL 2431809 NIL) (-1048 2430869 2430913 2431010 "RING-" 2431015 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429710 2429947 2430205 "RIDIST" 2430633 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420999 2429178 2429384 "RGCHAIN" 2429558 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420349 2420755 2420796 "RGBCSPC" 2420854 NIL RGBCSPC (NIL T) -9 NIL 2420906 NIL) (-1044 2419507 2419888 2419929 "RGBCMDL" 2420161 NIL RGBCMDL (NIL T) -9 NIL 2420275 NIL) (-1043 2416501 2417115 2417785 "RF" 2418871 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2416147 2416210 2416313 "RFFACTOR" 2416432 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415872 2415907 2416004 "RFFACT" 2416106 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413989 2414353 2414735 "RFDIST" 2415512 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413442 2413534 2413697 "RETSOL" 2413891 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2413078 2413158 2413201 "RETRACT" 2413334 NIL RETRACT (NIL T) -9 NIL 2413421 NIL) (-1037 2412927 2412952 2413039 "RETRACT-" 2413044 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412529 2412749 2412819 "RETAST" 2412879 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405267 2412182 2412309 "RESULT" 2412424 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403858 2404536 2404735 "RESRING" 2405170 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403494 2403543 2403641 "RESLATC" 2403795 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2403199 2403234 2403341 "REPSQ" 2403453 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400621 2401201 2401803 "REP" 2402619 T REP (NIL) -7 NIL NIL NIL) (-1030 2400318 2400353 2400464 "REPDB" 2400580 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2394218 2395607 2396830 "REP2" 2399130 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390595 2391276 2392084 "REP1" 2393445 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383291 2388736 2389192 "REGSET" 2390225 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2382056 2382439 2382689 "REF" 2383076 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381433 2381536 2381703 "REDORDER" 2381940 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377401 2380646 2380873 "RECLOS" 2381261 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376453 2376634 2376849 "REALSOLV" 2377208 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376299 2376340 2376370 "REAL" 2376375 T REAL (NIL) -9 NIL 2376410 NIL) (-1021 2372782 2373584 2374468 "REAL0Q" 2375464 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368383 2369371 2370432 "REAL0" 2371763 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367854 2368100 2368194 "RDUCEAST" 2368311 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367259 2367331 2367538 "RDIV" 2367776 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366327 2366501 2366714 "RDIST" 2367081 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364924 2365211 2365583 "RDETRS" 2366035 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362736 2363190 2363728 "RDETR" 2364466 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2361361 2361639 2362036 "RDEEFS" 2362452 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 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1998814 1998926 1999083 "OUTBCON-" 1999088 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-858 1998194 1998543 1998632 "OSI" 1998745 T OSI (NIL) -8 NIL NIL NIL) (-857 1997724 1998062 1998090 "OSGROUP" 1998095 T OSGROUP (NIL) -9 NIL 1998117 NIL) (-856 1996469 1996696 1996981 "ORTHPOL" 1997471 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-855 1994020 1996304 1996425 "OREUP" 1996430 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-854 1991423 1993711 1993838 "ORESUP" 1993962 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-853 1988951 1989451 1990012 "OREPCTO" 1990912 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-852 1982637 1984838 1984879 "OREPCAT" 1987227 NIL OREPCAT (NIL T) -9 NIL 1988331 NIL) (-851 1979784 1980566 1981624 "OREPCAT-" 1981629 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-850 1978935 1979233 1979261 "ORDSET" 1979570 T ORDSET (NIL) -9 NIL 1979734 NIL) (-849 1978366 1978514 1978738 "ORDSET-" 1978743 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-848 1976931 1977722 1977750 "ORDRING" 1977952 T ORDRING (NIL) -9 NIL 1978077 NIL) (-847 1976576 1976670 1976814 "ORDRING-" 1976819 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975956 1976419 1976447 "ORDMON" 1976452 T ORDMON (NIL) -9 NIL 1976473 NIL) (-845 1975118 1975265 1975460 "ORDFUNS" 1975805 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974456 1974875 1974903 "ORDFIN" 1974968 T ORDFIN (NIL) -9 NIL 1975042 NIL) (-843 1971015 1973042 1973451 "ORDCOMP" 1974080 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1970281 1970408 1970594 "ORDCOMP2" 1970875 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966862 1967772 1968586 "OPTPROB" 1969487 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963664 1964303 1965007 "OPTPACK" 1966178 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961351 1962117 1962145 "OPTCAT" 1962964 T OPTCAT (NIL) -9 NIL 1963614 NIL) (-838 1960735 1961028 1961133 "OPSIG" 1961266 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960503 1960542 1960608 "OPQUERY" 1960689 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957634 1958814 1959318 "OP" 1960032 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1957008 1957234 1957275 "OPERCAT" 1957487 NIL OPERCAT (NIL T) -9 NIL 1957584 NIL) (-834 1956763 1956819 1956936 "OPERCAT-" 1956941 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953576 1955560 1955929 "ONECOMP" 1956427 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952881 1952996 1953170 "ONECOMP2" 1953448 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952300 1952406 1952536 "OMSERVER" 1952771 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1949162 1951740 1951780 "OMSAGG" 1951841 NIL OMSAGG (NIL T) -9 NIL 1951905 NIL) (-829 1947785 1948048 1948330 "OMPKG" 1948900 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1947215 1947318 1947346 "OM" 1947645 T OM (NIL) -9 NIL NIL NIL) (-827 1945762 1946764 1946933 "OMLO" 1947096 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944722 1944869 1945089 "OMEXPR" 1945588 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1944013 1944268 1944404 "OMERR" 1944606 T OMERR (NIL) -8 NIL NIL NIL) (-824 1943164 1943434 1943594 "OMERRK" 1943873 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942615 1942841 1942949 "OMENC" 1943076 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936510 1937695 1938866 "OMDEV" 1941464 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935579 1935750 1935944 "OMCONN" 1936336 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1934100 1935076 1935104 "OINTDOM" 1935109 T OINTDOM (NIL) -9 NIL 1935130 NIL) (-819 1929879 1931090 1931806 "OFMONOID" 1933416 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929290 1929816 1929861 "ODVAR" 1929866 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926713 1929035 1929190 "ODR" 1929195 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919294 1926489 1926615 "ODPOL" 1926620 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1913116 1919166 1919271 "ODP" 1919276 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911882 1912097 1912372 "ODETOOLS" 1912890 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908849 1909507 1910223 "ODESYS" 1911215 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903731 1904639 1905664 "ODERTRIC" 1907924 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1903157 1903239 1903433 "ODERED" 1903643 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1900045 1900593 1901270 "ODERAT" 1902580 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1897002 1897469 1898066 "ODEPRRIC" 1899574 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894945 1895541 1896027 "ODEPROB" 1896536 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891465 1891950 1892597 "ODEPRIM" 1894424 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890714 1890816 1891076 "ODEPAL" 1891357 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886876 1887667 1888531 "ODEPACK" 1889870 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885937 1886044 1886266 "ODEINT" 1886765 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1880038 1881463 1882910 "ODEIFTBL" 1884510 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875436 1876222 1877174 "ODEEF" 1879197 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874785 1874874 1875097 "ODECONST" 1875341 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872910 1873571 1873599 "ODECAT" 1874204 T ODECAT (NIL) -9 NIL 1874735 NIL) (-799 1869782 1872622 1872741 "OCT" 1872823 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869420 1869463 1869590 "OCTCT2" 1869733 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1864069 1866504 1866544 "OC" 1867641 NIL OC (NIL T) -9 NIL 1868499 NIL) (-796 1861296 1862044 1863034 "OC-" 1863128 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860648 1861116 1861144 "OCAMON" 1861149 T OCAMON (NIL) -9 NIL 1861170 NIL) (-794 1860179 1860520 1860548 "OASGP" 1860553 T OASGP (NIL) -9 NIL 1860573 NIL) (-793 1859440 1859929 1859957 "OAMONS" 1859997 T OAMONS (NIL) -9 NIL 1860040 NIL) (-792 1858854 1859287 1859315 "OAMON" 1859320 T OAMON (NIL) -9 NIL 1859340 NIL) (-791 1858112 1858630 1858658 "OAGROUP" 1858663 T OAGROUP (NIL) -9 NIL 1858683 NIL) (-790 1857802 1857852 1857940 "NUMTUBE" 1858056 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851375 1852893 1854429 "NUMQUAD" 1856286 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1847131 1848119 1849144 "NUMODE" 1850370 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844486 1845366 1845394 "NUMINT" 1846317 T NUMINT (NIL) -9 NIL 1847081 NIL) (-786 1843434 1843631 1843849 "NUMFMT" 1844288 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829793 1832738 1835270 "NUMERIC" 1840941 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1824163 1829242 1829337 "NTSCAT" 1829342 NIL NTSCAT (NIL T T T T) -9 NIL 1829381 NIL) (-783 1823357 1823522 1823715 "NTPOLFN" 1824002 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811434 1820182 1820994 "NSUP" 1822578 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1811066 1811123 1811232 "NSUP2" 1811371 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801294 1810840 1810973 "NSMP" 1810978 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799726 1800027 1800384 "NREP" 1800982 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798317 1798569 1798927 "NPCOEF" 1799469 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797383 1797498 1797714 "NORMRETR" 1798198 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795424 1795714 1796123 "NORMPK" 1797091 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1795109 1795137 1795261 "NORMMA" 1795390 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794909 1795066 1795095 "NONE" 1795100 T NONE (NIL) -8 NIL NIL NIL) (-773 1794698 1794727 1794796 "NONE1" 1794873 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1794195 1794257 1794436 "NODE1" 1794630 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792480 1793331 1793586 "NNI" 1793933 T NNI (NIL) -8 NIL NIL 1794168) (-770 1790900 1791213 1791577 "NLINSOL" 1792148 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1787141 1788136 1789035 "NIPROB" 1790021 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785898 1786132 1786434 "NFINTBAS" 1786903 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1785072 1785548 1785589 "NETCLT" 1785761 NIL NETCLT (NIL T) -9 NIL 1785843 NIL) (-766 1783780 1784011 1784292 "NCODIV" 1784840 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783542 1783579 1783654 "NCNTFRAC" 1783737 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781722 1782086 1782506 "NCEP" 1783167 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780573 1781346 1781374 "NASRING" 1781484 T NASRING (NIL) -9 NIL 1781564 NIL) (-762 1780368 1780412 1780506 "NASRING-" 1780511 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779475 1780000 1780028 "NARNG" 1780145 T NARNG (NIL) -9 NIL 1780236 NIL) (-760 1779167 1779234 1779368 "NARNG-" 1779373 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1778046 1778253 1778488 "NAGSP" 1778952 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769318 1771002 1772675 "NAGS" 1776393 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767866 1768174 1768505 "NAGF07" 1769007 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762404 1763695 1765002 "NAGF04" 1766579 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755372 1756986 1758619 "NAGF02" 1760791 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750596 1751696 1752813 "NAGF01" 1754275 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1744224 1745790 1747375 "NAGE04" 1749031 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735393 1737514 1739644 "NAGE02" 1742114 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731346 1732293 1733257 "NAGE01" 1734449 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1729141 1729675 1730233 "NAGD03" 1730808 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720891 1722819 1724773 "NAGD02" 1727207 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714702 1716127 1717567 "NAGD01" 1719471 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710911 1711733 1712570 "NAGC06" 1713885 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709376 1709708 1710064 "NAGC05" 1710575 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708752 1708871 1709015 "NAGC02" 1709252 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707711 1708294 1708334 "NAALG" 1708413 NIL NAALG (NIL T) -9 NIL 1708474 NIL) (-743 1707546 1707575 1707665 "NAALG-" 1707670 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701496 1702604 1703791 "MULTSQFR" 1706442 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700815 1700890 1701074 "MULTFACT" 1701408 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693539 1697452 1697505 "MTSCAT" 1698575 NIL MTSCAT (NIL T T) -9 NIL 1699090 NIL) (-739 1693251 1693305 1693397 "MTHING" 1693479 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1693043 1693076 1693136 "MSYSCMD" 1693211 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1689125 1691798 1692118 "MSET" 1692756 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1686194 1688686 1688727 "MSETAGG" 1688732 NIL MSETAGG (NIL T) -9 NIL 1688766 NIL) (-735 1682035 1683573 1684318 "MRING" 1685494 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681601 1681668 1681799 "MRF2" 1681962 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1681219 1681254 1681398 "MRATFAC" 1681560 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678831 1679126 1679557 "MPRFF" 1680924 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1673128 1678685 1678782 "MPOLY" 1678787 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672618 1672653 1672861 "MPCPF" 1673087 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1672132 1672175 1672359 "MPC3" 1672569 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671327 1671408 1671629 "MPC2" 1672047 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669628 1669965 1670355 "MONOTOOL" 1670987 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668853 1669170 1669198 "MONOID" 1669417 T MONOID (NIL) -9 NIL 1669564 NIL) (-725 1668399 1668518 1668699 "MONOID-" 1668704 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658874 1664825 1664884 "MONOGEN" 1665558 NIL MONOGEN (NIL T T) -9 NIL 1666014 NIL) (-723 1656092 1656827 1657827 "MONOGEN-" 1657946 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654925 1655371 1655399 "MONADWU" 1655791 T MONADWU (NIL) -9 NIL 1656029 NIL) (-721 1654297 1654456 1654704 "MONADWU-" 1654709 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653656 1653900 1653928 "MONAD" 1654135 T MONAD (NIL) -9 NIL 1654247 NIL) (-719 1653341 1653419 1653551 "MONAD-" 1653556 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651630 1652254 1652533 "MOEBIUS" 1653094 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650908 1651312 1651352 "MODULE" 1651357 NIL MODULE (NIL T) -9 NIL 1651396 NIL) (-716 1650476 1650572 1650762 "MODULE-" 1650767 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1648156 1648840 1649167 "MODRING" 1650300 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1645100 1646261 1646782 "MODOP" 1647685 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643688 1644167 1644444 "MODMONOM" 1644963 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633729 1641979 1642393 "MODMON" 1643325 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630885 1632573 1632849 "MODFIELD" 1633604 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629862 1630166 1630356 "MMLFORM" 1630715 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629388 1629431 1629610 "MMAP" 1629813 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627467 1628234 1628275 "MLO" 1628698 NIL MLO (NIL T) -9 NIL 1628940 NIL) (-707 1624833 1625349 1625951 "MLIFT" 1626948 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1624224 1624308 1624462 "MKUCFUNC" 1624744 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623823 1623893 1624016 "MKRECORD" 1624147 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622870 1623032 1623260 "MKFUNC" 1623634 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622258 1622362 1622518 "MKFLCFN" 1622753 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621535 1621637 1621822 "MKBCFUNC" 1622151 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618242 1621089 1621225 "MINT" 1621419 T MINT (NIL) -8 NIL NIL NIL) (-700 1617054 1617297 1617574 "MHROWRED" 1617997 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612433 1615589 1615994 "MFLOAT" 1616669 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611790 1611866 1612037 "MFINFACT" 1612345 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1608105 1608953 1609837 "MESH" 1610926 T MESH (NIL) -7 NIL NIL NIL) (-696 1606495 1606807 1607160 "MDDFACT" 1607792 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603290 1605654 1605695 "MDAGG" 1605950 NIL MDAGG (NIL T) -9 NIL 1606093 NIL) (-694 1593030 1602583 1602790 "MCMPLX" 1603103 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1592171 1592317 1592517 "MCDEN" 1592879 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1590061 1590331 1590711 "MCALCFN" 1591901 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588986 1589226 1589459 "MAYBE" 1589867 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586598 1587121 1587683 "MATSTOR" 1588457 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582555 1585970 1586218 "MATRIX" 1586383 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578319 1579028 1579764 "MATLIN" 1581912 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568425 1571611 1571688 "MATCAT" 1576568 NIL MATCAT (NIL T T T) -9 NIL 1577985 NIL) (-686 1564781 1565802 1567158 "MATCAT-" 1567163 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563375 1563528 1563861 "MATCAT2" 1564616 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561487 1561811 1562195 "MAPPKG3" 1563050 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560468 1560641 1560863 "MAPPKG2" 1561311 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558967 1559251 1559578 "MAPPKG1" 1560174 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1558046 1558373 1558550 "MAPPAST" 1558810 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557657 1557715 1557838 "MAPHACK3" 1557982 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557249 1557310 1557424 "MAPHACK2" 1557589 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556686 1556790 1556932 "MAPHACK1" 1557140 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554765 1555386 1555690 "MAGMA" 1556414 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554244 1554489 1554580 "MACROAST" 1554694 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550662 1552483 1552944 "M3D" 1553816 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544768 1549031 1549072 "LZSTAGG" 1549854 NIL LZSTAGG (NIL T) -9 NIL 1550149 NIL) (-673 1540725 1541899 1543356 "LZSTAGG-" 1543361 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537812 1538616 1539103 "LWORD" 1540270 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537388 1537616 1537691 "LSTAST" 1537757 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530554 1537159 1537293 "LSQM" 1537298 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529778 1529917 1530145 "LSPP" 1530409 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527590 1527891 1528347 "LSMP" 1529467 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524369 1525043 1525773 "LSMP1" 1526892 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518246 1523536 1523577 "LSAGG" 1523639 NIL LSAGG (NIL T) -9 NIL 1523717 NIL) (-665 1514941 1515865 1517078 "LSAGG-" 1517083 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512540 1514085 1514334 "LPOLY" 1514736 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1512122 1512207 1512330 "LPEFRAC" 1512449 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510443 1511216 1511469 "LO" 1511954 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1510095 1510207 1510235 "LOGIC" 1510346 T LOGIC (NIL) -9 NIL 1510427 NIL) (-660 1509957 1509980 1510051 "LOGIC-" 1510056 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1509150 1509290 1509483 "LODOOPS" 1509813 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506573 1509066 1509132 "LODO" 1509137 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1505111 1505346 1505699 "LODOF" 1506320 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501329 1503760 1503801 "LODOCAT" 1504239 NIL LODOCAT (NIL T) -9 NIL 1504450 NIL) (-655 1501062 1501120 1501247 "LODOCAT-" 1501252 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498382 1500903 1501021 "LODO2" 1501026 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495817 1498319 1498364 "LODO1" 1498369 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494698 1494863 1495168 "LODEEF" 1495640 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489937 1492828 1492869 "LNAGG" 1493816 NIL LNAGG (NIL T) -9 NIL 1494260 NIL) (-650 1489084 1489298 1489640 "LNAGG-" 1489645 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1485220 1486009 1486648 "LMOPS" 1488499 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484623 1485011 1485052 "LMODULE" 1485057 NIL LMODULE (NIL T) -9 NIL 1485083 NIL) (-647 1481821 1484268 1484391 "LMDICT" 1484533 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1481227 1481448 1481489 "LLINSET" 1481680 NIL LLINSET (NIL T) -9 NIL 1481771 NIL) (-645 1480926 1481135 1481195 "LITERAL" 1481200 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1474109 1479872 1480170 "LIST" 1480661 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473634 1473708 1473847 "LIST3" 1474029 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472641 1472819 1473047 "LIST2" 1473452 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470775 1471087 1471486 "LIST2MAP" 1472288 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470371 1470608 1470649 "LINSET" 1470654 NIL LINSET (NIL T) -9 NIL 1470688 NIL) (-639 1469032 1469702 1469743 "LINEXP" 1469998 NIL LINEXP (NIL T) -9 NIL 1470147 NIL) (-638 1467679 1467939 1468236 "LINDEP" 1468784 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464446 1465165 1465942 "LIMITRF" 1466934 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462749 1463045 1463454 "LIMITPS" 1464141 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1457177 1462260 1462488 "LIE" 1462570 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1456125 1456594 1456634 "LIECAT" 1456774 NIL LIECAT (NIL T) -9 NIL 1456925 NIL) (-633 1455966 1455993 1456081 "LIECAT-" 1456086 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448462 1455415 1455580 "LIB" 1455821 T LIB (NIL) -8 NIL NIL NIL) (-631 1444097 1444980 1445915 "LGROBP" 1447579 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1442095 1442369 1442719 "LF" 1443818 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440935 1441627 1441655 "LFCAT" 1441862 T LFCAT (NIL) -9 NIL 1442001 NIL) (-628 1437837 1438467 1439155 "LEXTRIPK" 1440299 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434581 1435407 1435910 "LEXP" 1437417 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1434057 1434302 1434394 "LETAST" 1434509 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432455 1432768 1433169 "LEADCDET" 1433739 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431645 1431719 1431948 "LAZM3PK" 1432376 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426562 1429722 1430260 "LAUPOL" 1431157 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1426141 1426185 1426346 "LAPLACE" 1426512 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1424080 1425242 1425493 "LA" 1425974 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1423074 1423658 1423699 "LALG" 1423761 NIL LALG (NIL T) -9 NIL 1423820 NIL) (-619 1422788 1422847 1422983 "LALG-" 1422988 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422623 1422647 1422688 "KVTFROM" 1422750 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421546 1421990 1422175 "KTVLOGIC" 1422458 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421381 1421405 1421446 "KRCFROM" 1421508 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420285 1420472 1420771 "KOVACIC" 1421181 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1420120 1420144 1420185 "KONVERT" 1420247 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419955 1419979 1420020 "KOERCE" 1420082 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417785 1418548 1418925 "KERNEL" 1419611 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417281 1417362 1417494 "KERNEL2" 1417699 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1411051 1415820 1415874 "KDAGG" 1416251 NIL KDAGG (NIL T T) -9 NIL 1416457 NIL) (-609 1410580 1410704 1410909 "KDAGG-" 1410914 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403728 1410241 1410396 "KAFILE" 1410458 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1398156 1403239 1403467 "JORDAN" 1403549 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397535 1397805 1397926 "JOINAST" 1398055 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397381 1397440 1397495 "JAVACODE" 1397500 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393633 1395586 1395640 "IXAGG" 1396569 NIL IXAGG (NIL T T) -9 NIL 1397028 NIL) (-603 1392552 1392858 1393277 "IXAGG-" 1393282 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1388082 1392474 1392533 "IVECTOR" 1392538 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386848 1387085 1387351 "ITUPLE" 1387849 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385350 1385527 1385822 "ITRIGMNP" 1386670 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1384095 1384299 1384582 "ITFUN3" 1385126 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383727 1383784 1383893 "ITFUN2" 1384032 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381529 1382589 1382888 "ITAYLOR" 1383461 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370474 1375666 1376829 "ISUPS" 1380399 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369578 1369718 1369954 "ISUMP" 1370321 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364792 1369379 1369458 "ISTRING" 1369531 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364268 1364513 1364605 "ISAST" 1364720 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363477 1363559 1363775 "IRURPK" 1364182 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362413 1362614 1362854 "IRSN" 1363257 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360484 1360839 1361268 "IRRF2F" 1362051 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1360231 1360269 1360345 "IRREDFFX" 1360440 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358846 1359105 1359404 "IROOT" 1359964 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355450 1356530 1357222 "IR" 1358186 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1353063 1353558 1354124 "IR2" 1354928 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1352163 1352276 1352490 "IR2F" 1352946 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351954 1351988 1352048 "IPRNTPK" 1352123 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348533 1351843 1351912 "IPF" 1351917 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346860 1348458 1348515 "IPADIC" 1348520 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1346172 1346420 1346550 "IP4ADDR" 1346750 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345645 1345876 1345986 "IOMODE" 1346082 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344718 1345242 1345369 "IOBFILE" 1345538 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1344206 1344622 1344650 "IOBCON" 1344655 T IOBCON (NIL) -9 NIL 1344676 NIL) (-577 1343717 1343775 1343958 "INVLAPLA" 1344142 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333365 1335719 1338105 "INTTR" 1341381 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329700 1330442 1331307 "INTTOOLS" 1332550 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329286 1329377 1329494 "INTSLPE" 1329603 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327239 1329209 1329268 "INTRVL" 1329273 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324841 1325353 1325928 "INTRF" 1326724 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324252 1324349 1324491 "INTRET" 1324739 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322249 1322638 1323108 "INTRAT" 1323860 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319512 1320095 1320714 "INTPM" 1321734 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316257 1316856 1317594 "INTPAF" 1318898 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311436 1312398 1313449 "INTPACK" 1315226 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308316 1311165 1311292 "INT" 1311329 T INT (NIL) -8 NIL NIL NIL) (-565 1307568 1307720 1307928 "INTHERTR" 1308158 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1307007 1307087 1307275 "INTHERAL" 1307482 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304853 1305296 1305753 "INTHEORY" 1306570 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296259 1297880 1299652 "INTG0" 1303205 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276832 1281622 1286432 "INTFTBL" 1291469 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1276081 1276219 1276392 "INTFACT" 1276691 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273508 1273954 1274511 "INTEF" 1275635 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271875 1272614 1272642 "INTDOM" 1272943 T INTDOM (NIL) -9 NIL 1273150 NIL) (-557 1271244 1271418 1271660 "INTDOM-" 1271665 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267632 1269560 1269614 "INTCAT" 1270413 NIL INTCAT (NIL T) -9 NIL 1270734 NIL) (-555 1267104 1267207 1267335 "INTBIT" 1267524 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265803 1265957 1266264 "INTALG" 1266949 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265286 1265376 1265533 "INTAF" 1265707 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258629 1265096 1265236 "INTABL" 1265241 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257970 1258436 1258501 "INT8" 1258535 T INT8 (NIL) -8 NIL NIL 1258580) (-550 1257310 1257776 1257841 "INT64" 1257875 T INT64 (NIL) -8 NIL NIL 1257920) (-549 1256650 1257116 1257181 "INT32" 1257215 T INT32 (NIL) -8 NIL NIL 1257260) (-548 1255990 1256456 1256521 "INT16" 1256555 T INT16 (NIL) -8 NIL NIL 1256600) (-547 1250900 1253613 1253641 "INS" 1254575 T INS (NIL) -9 NIL 1255240 NIL) (-546 1248140 1248911 1249885 "INS-" 1249958 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246915 1247142 1247440 "INPSIGN" 1247893 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1246033 1246150 1246347 "INPRODPF" 1246795 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244927 1245044 1245281 "INPRODFF" 1245913 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243927 1244079 1244339 "INNMFACT" 1244763 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1243124 1243221 1243409 "INMODGCD" 1243826 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241632 1241877 1242201 "INFSP" 1242869 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240816 1240933 1241116 "INFPROD0" 1241512 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237671 1238881 1239396 "INFORM" 1240309 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237281 1237341 1237439 "INFORM1" 1237606 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236804 1236893 1237007 "INFINITY" 1237187 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235980 1236524 1236625 "INETCLTS" 1236723 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234596 1234846 1235167 "INEP" 1235728 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233845 1234493 1234558 "INDE" 1234563 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233409 1233477 1233594 "INCRMAPS" 1233772 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1232227 1232678 1232884 "INBFILE" 1233223 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227526 1228463 1229407 "INBFF" 1231315 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226434 1226703 1226731 "INBCON" 1227244 T INBCON (NIL) -9 NIL 1227510 NIL) (-528 1225686 1225909 1226185 "INBCON-" 1226190 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1225165 1225410 1225501 "INAST" 1225615 T INAST (NIL) -8 NIL NIL NIL) (-526 1224592 1224844 1224950 "IMPTAST" 1225079 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1221038 1224436 1224540 "IMATRIX" 1224545 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219750 1219873 1220188 "IMATQF" 1220894 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217970 1218197 1218534 "IMATLIN" 1219506 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212548 1217894 1217952 "ILIST" 1217957 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210453 1212408 1212521 "IIARRAY2" 1212526 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205851 1210364 1210428 "IFF" 1210433 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1205198 1205468 1205584 "IFAST" 1205755 T IFAST (NIL) -8 NIL NIL NIL) (-518 1200193 1204490 1204678 "IFARRAY" 1205055 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199373 1200097 1200170 "IFAMON" 1200175 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198957 1199022 1199076 "IEVALAB" 1199283 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198632 1198700 1198860 "IEVALAB-" 1198865 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198263 1198546 1198609 "IDPO" 1198614 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197513 1198152 1198227 "IDPOAMS" 1198232 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196820 1197402 1197477 "IDPOAM" 1197482 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195879 1196155 1196208 "IDPC" 1196621 NIL IDPC (NIL T T) -9 NIL 1196770 NIL) (-510 1195348 1195771 1195844 "IDPAM" 1195849 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194724 1195240 1195313 "IDPAG" 1195318 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194369 1194560 1194635 "IDENT" 1194669 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190624 1191472 1192367 "IDECOMP" 1193526 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183462 1184547 1185594 "IDEAL" 1189660 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182626 1182738 1182937 "ICDEN" 1183346 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181697 1182106 1182253 "ICARD" 1182499 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179757 1180070 1180475 "IBPTOOLS" 1181374 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175364 1179377 1179490 "IBITS" 1179676 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1172087 1172663 1173358 "IBATOOL" 1174781 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169866 1170328 1170861 "IBACHIN" 1171622 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167695 1169712 1169815 "IARRAY2" 1169820 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163801 1167621 1167678 "IARRAY1" 1167683 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157910 1162213 1162694 "IAN" 1163340 T IAN (NIL) -8 NIL NIL NIL) (-496 1157421 1157478 1157651 "IALGFACT" 1157847 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156949 1157062 1157090 "HYPCAT" 1157297 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156487 1156604 1156790 "HYPCAT-" 1156795 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1156082 1156282 1156365 "HOSTNAME" 1156424 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155927 1155964 1156005 "HOMOTOP" 1156010 NIL HOMOTOP (NIL T) -9 NIL 1156043 NIL) (-491 1152559 1153937 1153978 "HOAGG" 1154959 NIL HOAGG (NIL T) -9 NIL 1155638 NIL) (-490 1151153 1151552 1152078 "HOAGG-" 1152083 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1145157 1150748 1150897 "HEXADEC" 1151024 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143904 1144127 1144390 "HEUGCD" 1144934 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142980 1143741 1143871 "HELLFDIV" 1143876 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1141159 1142757 1142845 "HEAP" 1142924 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140422 1140711 1140845 "HEADAST" 1141045 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134288 1140337 1140399 "HDP" 1140404 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128276 1133923 1134075 "HDMP" 1134189 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127600 1127740 1127904 "HB" 1128132 T HB (NIL) -7 NIL NIL NIL) (-481 1120986 1127446 1127550 "HASHTBL" 1127555 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120462 1120707 1120799 "HASAST" 1120914 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118240 1120084 1120266 "HACKPI" 1120300 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113908 1118093 1118206 "GTSET" 1118211 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107323 1113786 1113884 "GSTBL" 1113889 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099601 1106354 1106619 "GSERIES" 1107114 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098742 1099159 1099187 "GROUP" 1099390 T GROUP (NIL) -9 NIL 1099524 NIL) (-474 1098108 1098267 1098518 "GROUP-" 1098523 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096475 1096796 1097183 "GROEBSOL" 1097785 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095389 1095677 1095728 "GRMOD" 1096257 NIL GRMOD (NIL T T) -9 NIL 1096425 NIL) (-471 1095157 1095193 1095321 "GRMOD-" 1095326 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090447 1091511 1092511 "GRIMAGE" 1094177 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088913 1089174 1089498 "GRDEF" 1090143 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088357 1088473 1088614 "GRAY" 1088792 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087544 1087950 1088001 "GRALG" 1088154 NIL GRALG (NIL T T) -9 NIL 1088247 NIL) (-466 1087205 1087278 1087441 "GRALG-" 1087446 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083982 1086790 1086968 "GPOLSET" 1087112 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083336 1083393 1083651 "GOSPER" 1083919 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1079068 1079774 1080300 "GMODPOL" 1083035 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1078073 1078257 1078495 "GHENSEL" 1078880 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1072229 1073072 1074092 "GENUPS" 1077157 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071926 1071977 1072066 "GENUFACT" 1072172 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071338 1071415 1071580 "GENPGCD" 1071844 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070812 1070847 1071060 "GENMFACT" 1071297 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069378 1069635 1069942 "GENEEZ" 1070555 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063524 1068989 1069151 "GDMP" 1069301 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052866 1057295 1058401 "GCNAALG" 1062507 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1051193 1052055 1052083 "GCDDOM" 1052338 T GCDDOM (NIL) -9 NIL 1052495 NIL) (-453 1050663 1050790 1051005 "GCDDOM-" 1051010 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049335 1049520 1049824 "GB" 1050442 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037951 1040281 1042673 "GBINTERN" 1047026 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035788 1036080 1036501 "GBF" 1037626 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034569 1034734 1035001 "GBEUCLID" 1035604 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033918 1034043 1034192 "GAUSSFAC" 1034440 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032285 1032587 1032901 "GALUTIL" 1033637 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030593 1030867 1031191 "GALPOLYU" 1032012 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027958 1028248 1028655 "GALFACTU" 1030290 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019763 1021263 1022871 "GALFACT" 1026390 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1017151 1017809 1017837 "FVFUN" 1018993 T FVFUN (NIL) -9 NIL 1019713 NIL) (-442 1016417 1016599 1016627 "FVC" 1016918 T FVC (NIL) -9 NIL 1017101 NIL) (-441 1016060 1016242 1016310 "FUNDESC" 1016369 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015675 1015857 1015938 "FUNCTION" 1016012 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013419 1013997 1014463 "FT" 1015229 T FT (NIL) -8 NIL NIL NIL) (-438 1012210 1012720 1012923 "FTEM" 1013236 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010501 1010790 1011187 "FSUPFACT" 1011901 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008898 1009187 1009519 "FST" 1010189 T FST (NIL) -8 NIL NIL NIL) (-435 1008097 1008203 1008391 "FSRED" 1008780 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006796 1007052 1007399 "FSPRMELT" 1007812 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1004102 1004540 1005026 "FSPECF" 1006359 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985740 994071 994112 "FS" 997996 NIL FS (NIL T) -9 NIL 1000285 NIL) (-431 974383 977376 981433 "FS-" 981733 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973911 973965 974135 "FSINT" 974324 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 972203 972904 973207 "FSERIES" 973690 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971245 971361 971585 "FSCINT" 972083 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967453 970189 970230 "FSAGG" 970600 NIL FSAGG (NIL T) -9 NIL 970859 NIL) (-426 965215 965816 966612 "FSAGG-" 966707 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964257 964400 964627 "FSAGG2" 965068 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961939 962219 962766 "FS2UPS" 963975 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961573 961616 961745 "FS2" 961890 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960451 960622 960924 "FS2EXPXP" 961398 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959877 959992 960144 "FRUTIL" 960331 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951290 955372 956730 "FR" 958551 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946259 948933 948973 "FRNAALG" 950369 NIL FRNAALG (NIL T) -9 NIL 950976 NIL) (-418 941932 943008 944283 "FRNAALG-" 945033 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941570 941613 941740 "FRNAAF2" 941883 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939950 940424 940719 "FRMOD" 941382 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937701 938333 938650 "FRIDEAL" 939741 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936896 936983 937272 "FRIDEAL2" 937608 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 936029 936443 936484 "FRETRCT" 936489 NIL FRETRCT (NIL T) -9 NIL 936665 NIL) (-412 935141 935372 935723 "FRETRCT-" 935728 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 932229 933439 933498 "FRAMALG" 934380 NIL FRAMALG (NIL T T) -9 NIL 934672 NIL) (-410 930363 930818 931448 "FRAMALG-" 931671 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924284 929838 930114 "FRAC" 930119 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923920 923977 924084 "FRAC2" 924221 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923556 923613 923720 "FR2" 923857 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 918069 920962 920990 "FPS" 922109 T FPS (NIL) -9 NIL 922666 NIL) (-405 917518 917627 917791 "FPS-" 917937 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914820 916489 916517 "FPC" 916742 T FPC (NIL) -9 NIL 916884 NIL) (-403 914613 914653 914750 "FPC-" 914755 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913403 914101 914142 "FPATMAB" 914147 NIL FPATMAB (NIL T) -9 NIL 914299 NIL) (-401 911076 911579 912005 "FPARFRAC" 913040 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906469 906968 907650 "FORTRAN" 910508 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 904185 904685 905224 "FORT" 905950 T FORT (NIL) -7 NIL NIL NIL) (-398 901861 902423 902451 "FORTFN" 903511 T FORTFN (NIL) -9 NIL 904135 NIL) (-397 901625 901675 901703 "FORTCAT" 901762 T FORTCAT (NIL) -9 NIL 901824 NIL) (-396 899731 900241 900631 "FORMULA" 901255 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899519 899549 899618 "FORMULA1" 899695 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 899042 899094 899267 "FORDER" 899461 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 898138 898302 898495 "FOP" 898869 T FOP (NIL) -7 NIL NIL NIL) (-392 896719 897418 897592 "FNLA" 898020 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895448 895863 895891 "FNCAT" 896351 T FNCAT (NIL) -9 NIL 896611 NIL) (-390 894987 895407 895435 "FNAME" 895440 T FNAME (NIL) -8 NIL NIL NIL) (-389 893550 894513 894541 "FMTC" 894546 T FMTC (NIL) -9 NIL 894582 NIL) (-388 889883 891073 891702 "FMONOID" 892954 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 889075 889625 889774 "FM" 889779 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886499 887145 887173 "FMFUN" 888317 T FMFUN (NIL) -9 NIL 889025 NIL) (-385 885768 885949 885977 "FMC" 886267 T FMC (NIL) -9 NIL 886449 NIL) (-384 882847 883707 883761 "FMCAT" 884956 NIL FMCAT (NIL T T) -9 NIL 885451 NIL) (-383 881713 882613 882713 "FM1" 882792 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879487 879903 880397 "FLOATRP" 881264 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 873062 877216 877837 "FLOAT" 878886 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870500 871000 871578 "FLOATCP" 872529 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869240 870078 870119 "FLINEXP" 870124 NIL FLINEXP (NIL T) -9 NIL 870217 NIL) (-378 868394 868629 868957 "FLINEXP-" 868962 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867470 867614 867838 "FLASORT" 868246 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864586 865454 865506 "FLALG" 866733 NIL FLALG (NIL T T) -9 NIL 867200 NIL) (-375 858322 862072 862113 "FLAGG" 863375 NIL FLAGG (NIL T) -9 NIL 864027 NIL) (-374 857048 857387 857877 "FLAGG-" 857882 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 856090 856233 856460 "FLAGG2" 856901 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852941 853949 854008 "FINRALG" 855136 NIL FINRALG (NIL T T) -9 NIL 855644 NIL) (-371 852101 852330 852669 "FINRALG-" 852674 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851481 851720 851748 "FINITE" 851944 T FINITE (NIL) -9 NIL 852051 NIL) (-369 843838 846025 846065 "FINAALG" 849732 NIL FINAALG (NIL T) -9 NIL 851185 NIL) (-368 839170 840220 841364 "FINAALG-" 842743 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838538 838925 839028 "FILE" 839100 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837196 837534 837588 "FILECAT" 838272 NIL FILECAT (NIL T T) -9 NIL 838488 NIL) (-365 834912 836440 836468 "FIELD" 836508 T FIELD (NIL) -9 NIL 836588 NIL) (-364 833532 833917 834428 "FIELD-" 834433 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831382 832167 832514 "FGROUP" 833218 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830472 830636 830856 "FGLMICPK" 831214 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826304 830397 830454 "FFX" 830459 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825905 825966 826101 "FFSLPE" 826237 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821894 822677 823473 "FFPOLY" 825141 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821398 821434 821643 "FFPOLY2" 821852 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817241 821317 821380 "FFP" 821385 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812639 817152 817216 "FF" 817221 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807765 811982 812172 "FFNBX" 812493 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802694 806900 807158 "FFNBP" 807619 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797327 801978 802189 "FFNB" 802527 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 796159 796357 796672 "FFINTBAS" 797124 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792228 794448 794476 "FFIELDC" 795096 T FFIELDC (NIL) -9 NIL 795472 NIL) (-350 790890 791261 791758 "FFIELDC-" 791763 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790459 790505 790629 "FFHOM" 790832 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 788154 788641 789158 "FFF" 789974 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783772 787896 787997 "FFCGX" 788097 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779393 783504 783611 "FFCGP" 783715 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774576 779120 779228 "FFCG" 779329 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755972 765053 765139 "FFCAT" 770304 NIL FFCAT (NIL T T T) -9 NIL 771755 NIL) (-343 751170 752217 753531 "FFCAT-" 754761 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750581 750624 750859 "FFCAT2" 751121 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739902 743553 744773 "FEXPR" 749433 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738902 739337 739378 "FEVALAB" 739462 NIL FEVALAB (NIL T) -9 NIL 739723 NIL) (-339 738061 738271 738609 "FEVALAB-" 738614 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736627 737444 737647 "FDIV" 737960 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733647 734388 734503 "FDIVCAT" 736071 NIL FDIVCAT (NIL T T T T) -9 NIL 736508 NIL) (-336 733409 733436 733606 "FDIVCAT-" 733611 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732629 732716 732993 "FDIV2" 733316 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731631 731945 732140 "FCTRDATA" 732454 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730317 730576 730865 "FCPAK1" 731362 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729416 729817 729958 "FCOMP" 730208 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 713118 716566 720104 "FC" 725898 T FC (NIL) -8 NIL NIL NIL) (-330 705481 709509 709549 "FAXF" 711351 NIL FAXF (NIL T) -9 NIL 712043 NIL) (-329 702757 703415 704240 "FAXF-" 704705 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697809 702133 702309 "FARRAY" 702614 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692703 694770 694823 "FAMR" 695846 NIL FAMR (NIL T T) -9 NIL 696306 NIL) (-326 691593 691895 692330 "FAMR-" 692335 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690762 691515 691568 "FAMONOID" 691573 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688548 689258 689311 "FAMONC" 690252 NIL FAMONC (NIL T T) -9 NIL 690638 NIL) (-323 687212 688302 688439 "FAGROUP" 688444 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 685007 685326 685729 "FACUTIL" 686893 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 684106 684291 684513 "FACTFUNC" 684817 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676528 683409 683608 "EXPUPXS" 683962 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 674011 674551 675137 "EXPRTUBE" 675962 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670282 670874 671604 "EXPRODE" 673350 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655767 668931 669360 "EXPR" 669886 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650321 650908 651714 "EXPR2UPS" 655065 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649953 650010 650119 "EXPR2" 650258 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641343 649106 649396 "EXPEXPAN" 649790 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 641143 641300 641329 "EXIT" 641334 T EXIT (NIL) -8 NIL NIL NIL) (-312 640623 640867 640958 "EXITAST" 641072 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640250 640312 640425 "EVALCYC" 640555 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639791 639909 639950 "EVALAB" 640120 NIL EVALAB (NIL T) -9 NIL 640224 NIL) (-309 639272 639394 639615 "EVALAB-" 639620 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636640 637942 637970 "EUCDOM" 638525 T EUCDOM (NIL) -9 NIL 638875 NIL) (-307 635045 635487 636077 "EUCDOM-" 636082 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622583 625343 628093 "ESTOOLS" 632315 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622215 622272 622381 "ESTOOLS2" 622520 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621966 622008 622088 "ESTOOLS1" 622167 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 616003 617611 617639 "ES" 620407 T ES (NIL) -9 NIL 621817 NIL) (-302 610950 612237 614054 "ES-" 614218 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607324 608085 608865 "ESCONT" 610190 T ESCONT (NIL) -7 NIL NIL NIL) (-300 607069 607101 607183 "ESCONT1" 607286 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606744 606794 606894 "ES2" 607013 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606374 606432 606541 "ES1" 606680 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605590 605719 605895 "ERROR" 606218 T ERROR (NIL) -7 NIL NIL NIL) (-296 598982 605449 605540 "EQTBL" 605545 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591485 594296 595745 "EQ" 597566 NIL -2097 (NIL T) -8 NIL NIL NIL) (-294 591117 591174 591283 "EQ2" 591422 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586406 587455 588548 "EP" 590056 NIL EP (NIL T) -7 NIL NIL NIL) (-292 585006 585297 585603 "ENV" 586120 T ENV (NIL) -8 NIL NIL NIL) (-291 584100 584654 584682 "ENTIRER" 584687 T ENTIRER (NIL) -9 NIL 584733 NIL) (-290 580567 582055 582425 "EMR" 583899 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579711 579896 579950 "ELTAGG" 580330 NIL ELTAGG (NIL T T) -9 NIL 580541 NIL) (-288 579430 579492 579633 "ELTAGG-" 579638 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579219 579248 579302 "ELTAB" 579386 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578345 578491 578690 "ELFUTS" 579070 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 578087 578143 578171 "ELEMFUN" 578276 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577957 577978 578046 "ELEMFUN-" 578051 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572801 576057 576098 "ELAGG" 577038 NIL ELAGG (NIL T) -9 NIL 577501 NIL) (-282 571086 571520 572183 "ELAGG-" 572188 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569751 570029 570322 "ELABEXPR" 570813 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562615 564418 565245 "EFUPXS" 569027 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 556065 557866 558676 "EFULS" 561891 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553550 553908 554380 "EFSTRUC" 555697 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543341 544907 546455 "EF" 552065 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542415 542826 542975 "EAB" 543212 T EAB (NIL) -8 NIL NIL NIL) (-275 541597 542374 542402 "E04UCFA" 542407 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540779 541556 541584 "E04NAFA" 541589 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539961 540738 540766 "E04MBFA" 540771 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 539143 539920 539948 "E04JAFA" 539953 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538327 539102 539130 "E04GCFA" 539135 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537511 538286 538314 "E04FDFA" 538319 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536693 537470 537498 "E04DGFA" 537503 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530866 532218 533582 "E04AGNT" 535349 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529546 530052 530092 "DVARCAT" 530567 NIL DVARCAT (NIL T) -9 NIL 530766 NIL) (-266 528750 528962 529276 "DVARCAT-" 529281 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521887 528549 528678 "DSMP" 528683 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516668 517832 518900 "DROPT" 520839 T DROPT (NIL) -8 NIL NIL NIL) (-263 516333 516392 516490 "DROPT1" 516603 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511448 512574 513711 "DROPT0" 515216 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509793 510118 510504 "DRAWPT" 511082 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504380 505303 506382 "DRAW" 508767 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 504013 504066 504184 "DRAWHACK" 504321 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502744 503013 503304 "DRAWCX" 503742 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502259 502328 502479 "DRAWCURV" 502670 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492727 494689 496804 "DRAWCFUN" 500164 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489493 491422 491463 "DQAGG" 492092 NIL DQAGG (NIL T) -9 NIL 492365 NIL) (-254 477617 484086 484169 "DPOLCAT" 486021 NIL DPOLCAT (NIL T T T T) -9 NIL 486566 NIL) (-253 472453 473802 475760 "DPOLCAT-" 475765 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465575 472314 472412 "DPMO" 472417 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458600 465355 465522 "DPMM" 465527 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 458078 458292 458390 "DOMTMPLT" 458522 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457511 457880 457960 "DOMCTOR" 458018 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456779 457033 457170 "DOMAIN" 457394 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450767 456414 456566 "DMP" 456680 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450367 450423 450567 "DLP" 450705 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 444189 449694 449884 "DLIST" 450209 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440986 443042 443083 "DLAGG" 443633 NIL DLAGG (NIL T) -9 NIL 443863 NIL) (-243 439662 440326 440354 "DIVRING" 440446 T DIVRING (NIL) -9 NIL 440529 NIL) (-242 438899 439089 439389 "DIVRING-" 439394 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 437001 437358 437764 "DISPLAY" 438513 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430889 436915 436978 "DIRPROD" 436983 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429737 429940 430205 "DIRPROD2" 430682 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418512 424518 424571 "DIRPCAT" 424981 NIL DIRPCAT (NIL NIL T) -9 NIL 425821 NIL) (-237 415838 416480 417361 "DIRPCAT-" 417698 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 415125 415285 415471 "DIOSP" 415672 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411780 414037 414078 "DIOPS" 414512 NIL DIOPS (NIL T) -9 NIL 414741 NIL) (-234 411329 411443 411634 "DIOPS-" 411639 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 410152 410780 410808 "DIFRING" 410995 T DIFRING (NIL) -9 NIL 411105 NIL) (-232 409798 409875 410027 "DIFRING-" 410032 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407534 408806 408847 "DIFEXT" 409210 NIL DIFEXT (NIL T) -9 NIL 409504 NIL) (-230 405819 406247 406913 "DIFEXT-" 406918 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 403094 405351 405392 "DIAGG" 405397 NIL DIAGG (NIL T) -9 NIL 405417 NIL) (-228 402478 402635 402887 "DIAGG-" 402892 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397895 401437 401714 "DHMATRIX" 402247 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393507 394416 395426 "DFSFUN" 396905 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388585 392438 392750 "DFLOAT" 393215 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386848 387129 387518 "DFINTTLS" 388293 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383877 384869 385269 "DERHAM" 386514 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381678 383652 383741 "DEQUEUE" 383821 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380932 381065 381248 "DEGRED" 381540 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377362 378107 378953 "DEFINTRF" 380160 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374917 375386 375978 "DEFINTEF" 376881 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374267 374537 374652 "DEFAST" 374822 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368271 373862 374011 "DECIMAL" 374138 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365783 366241 366747 "DDFACT" 367815 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365379 365422 365573 "DBLRESP" 365734 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 363251 363612 363972 "DBASE" 365146 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362493 362731 362877 "DATAARY" 363150 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361599 362452 362480 "D03FAFA" 362485 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360706 361558 361586 "D03EEFA" 361591 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358656 359122 359611 "D03AGNT" 360237 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357945 358615 358643 "D02EJFA" 358648 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 357234 357904 357932 "D02CJFA" 357937 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356523 357193 357221 "D02BHFA" 357226 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355812 356482 356510 "D02BBFA" 356515 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 349009 350598 352204 "D02AGNT" 354226 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346777 347300 347846 "D01WGTS" 348483 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345844 346736 346764 "D01TRNS" 346769 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344912 345803 345831 "D01GBFA" 345836 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343980 344871 344899 "D01FCFA" 344904 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 343048 343939 343967 "D01ASFA" 343972 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 342116 343007 343035 "D01AQFA" 343040 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 341184 342075 342103 "D01APFA" 342108 T D01APFA (NIL) -8 NIL NIL NIL) (-197 340252 341143 341171 "D01ANFA" 341176 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339320 340211 340239 "D01AMFA" 340244 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338388 339279 339307 "D01ALFA" 339312 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337456 338347 338375 "D01AKFA" 338380 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336524 337415 337443 "D01AJFA" 337448 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329819 331372 332933 "D01AGNT" 334983 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 329156 329284 329436 "CYCLOTOM" 329687 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325890 326604 327331 "CYCLES" 328449 T CYCLES (NIL) -7 NIL NIL NIL) (-189 325202 325336 325507 "CVMP" 325751 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 323043 323301 323670 "CTRIGMNP" 324930 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322479 322837 322910 "CTOR" 322990 T CTOR (NIL) -8 NIL NIL NIL) (-186 321988 322210 322311 "CTORKIND" 322398 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321279 321595 321623 "CTORCAT" 321805 T CTORCAT (NIL) -9 NIL 321918 NIL) (-184 320877 320988 321147 "CTORCAT-" 321152 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320366 320580 320678 "CTORCALL" 320799 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 319740 319839 319992 "CSTTOOLS" 320263 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315539 316196 316954 "CRFP" 319052 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 315014 315260 315352 "CRCEAST" 315467 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 314061 314246 314474 "CRAPACK" 314818 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313445 313546 313750 "CPMATCH" 313937 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 313170 313198 313304 "CPIMA" 313411 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309518 310190 310909 "COORDSYS" 312505 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308930 309051 309193 "CONTOUR" 309396 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304821 306933 307425 "CONTFRAC" 308470 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304701 304722 304750 "CONDUIT" 304787 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303789 304343 304371 "COMRING" 304376 T COMRING (NIL) -9 NIL 304428 NIL) (-171 302843 303147 303331 "COMPPROP" 303625 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302504 302539 302667 "COMPLPAT" 302802 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292795 302313 302422 "COMPLEX" 302427 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292431 292488 292595 "COMPLEX2" 292732 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 292149 292184 292282 "COMPFACT" 292390 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 276229 286223 286263 "COMPCAT" 287267 NIL COMPCAT (NIL T) -9 NIL 288615 NIL) (-165 265741 268668 272295 "COMPCAT-" 272651 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265470 265498 265601 "COMMUPC" 265707 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 265264 265298 265357 "COMMONOP" 265431 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264820 265015 265102 "COMM" 265197 T COMM (NIL) -8 NIL NIL NIL) (-161 264396 264624 264699 "COMMAAST" 264765 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263645 263839 263867 "COMBOPC" 264205 T COMBOPC (NIL) -9 NIL 264380 NIL) (-159 262541 262751 262993 "COMBINAT" 263435 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258998 259572 260199 "COMBF" 261963 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257756 258114 258349 "COLOR" 258783 T COLOR (NIL) -8 NIL NIL NIL) (-156 257232 257477 257569 "COLONAST" 257684 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256872 256919 257044 "CMPLXRT" 257179 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256320 256572 256671 "CLLCTAST" 256793 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251818 252850 253930 "CLIP" 255260 T CLIP (NIL) -7 NIL NIL NIL) (-152 250164 250924 251163 "CLIF" 251645 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246339 248310 248351 "CLAGG" 249280 NIL CLAGG (NIL T) -9 NIL 249816 NIL) (-150 244761 245218 245801 "CLAGG-" 245806 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244305 244390 244530 "CINTSLPE" 244670 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241806 242277 242825 "CHVAR" 243833 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240980 241534 241562 "CHARZ" 241567 T CHARZ (NIL) -9 NIL 241582 NIL) (-146 240734 240774 240852 "CHARPOL" 240934 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239792 240379 240407 "CHARNZ" 240454 T CHARNZ (NIL) -9 NIL 240510 NIL) (-144 237758 238482 238817 "CHAR" 239477 T CHAR (NIL) -8 NIL NIL NIL) (-143 237484 237545 237573 "CFCAT" 237684 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236729 236840 237022 "CDEN" 237368 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232694 235882 236162 "CCLASS" 236469 T CCLASS (NIL) -8 NIL NIL NIL) (-140 232001 232144 232307 "CATEGORY" 232551 T -10 (NIL) -8 NIL NIL NIL) (-139 231574 231920 231968 "CATCTOR" 231973 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 231025 231277 231375 "CATAST" 231496 T CATAST (NIL) -8 NIL NIL NIL) (-137 230501 230746 230838 "CASEAST" 230953 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225510 226530 227283 "CARTEN" 229804 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224618 224766 224987 "CARTEN2" 225357 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222934 223768 224025 "CARD" 224381 T CARD (NIL) -8 NIL NIL NIL) (-133 222510 222738 222813 "CAPSLAST" 222879 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 222014 222222 222250 "CACHSET" 222382 T CACHSET (NIL) -9 NIL 222460 NIL) (-131 221484 221806 221834 "CABMON" 221884 T CABMON (NIL) -9 NIL 221940 NIL) (-130 220957 221188 221298 "BYTEORD" 221394 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219936 220491 220633 "BYTE" 220796 T BYTE (NIL) -8 NIL NIL 220918) (-128 215286 219441 219613 "BYTEBUF" 219784 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212795 214978 215085 "BTREE" 215212 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 210244 212443 212565 "BTOURN" 212705 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207614 209714 209755 "BTCAT" 209823 NIL BTCAT (NIL T) -9 NIL 209900 NIL) (-124 207281 207361 207510 "BTCAT-" 207515 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202546 206424 206452 "BTAGG" 206674 T BTAGG (NIL) -9 NIL 206835 NIL) (-122 202036 202161 202367 "BTAGG-" 202372 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 199031 201314 201529 "BSTREE" 201853 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 198169 198295 198479 "BRILL" 198887 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194821 196895 196936 "BRAGG" 197585 NIL BRAGG (NIL T) -9 NIL 197843 NIL) (-118 193350 193756 194311 "BRAGG-" 194316 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186579 192696 192880 "BPADICRT" 193198 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184894 186516 186561 "BPADIC" 186566 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184592 184622 184736 "BOUNDZRO" 184858 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179820 181018 181930 "BOP" 183700 T BOP (NIL) -8 NIL NIL NIL) (-113 177601 178005 178480 "BOP1" 179378 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176426 177175 177324 "BOOLEAN" 177472 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175705 176109 176163 "BMODULE" 176168 NIL BMODULE (NIL T T) -9 NIL 176233 NIL) (-110 171506 175503 175576 "BITS" 175652 T BITS (NIL) -8 NIL NIL NIL) (-109 170927 171046 171186 "BINDING" 171386 T BINDING (NIL) -8 NIL NIL NIL) (-108 164934 170524 170672 "BINARY" 170799 T BINARY (NIL) -8 NIL NIL NIL) (-107 162714 164189 164230 "BGAGG" 164490 NIL BGAGG (NIL T) -9 NIL 164627 NIL) (-106 162545 162577 162668 "BGAGG-" 162673 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161616 161929 162134 "BFUNCT" 162360 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 160306 160484 160772 "BEZOUT" 161440 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156775 159158 159488 "BBTREE" 160009 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156509 156562 156590 "BASTYPE" 156709 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 156361 156390 156463 "BASTYPE-" 156468 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155795 155871 156023 "BALFACT" 156272 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154651 155210 155396 "AUTOMOR" 155640 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 154377 154382 154408 "ATTREG" 154413 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152629 153074 153426 "ATTRBUT" 154043 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 152237 152457 152523 "ATTRAST" 152581 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151773 151886 151912 "ATRIG" 152113 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151582 151623 151710 "ATRIG-" 151715 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 151227 151413 151439 "ASTCAT" 151444 T ASTCAT (NIL) -9 NIL 151474 NIL) (-92 150954 151013 151132 "ASTCAT-" 151137 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 149103 150730 150818 "ASTACK" 150897 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147608 147905 148270 "ASSOCEQ" 148785 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146640 147267 147391 "ASP9" 147515 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 146403 146588 146627 "ASP8" 146632 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 145271 146008 146150 "ASP80" 146292 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 144169 144906 145038 "ASP7" 145170 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 143123 143846 143964 "ASP78" 144082 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 142092 142803 142920 "ASP77" 143037 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 141004 141730 141861 "ASP74" 141992 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139904 140639 140771 "ASP73" 140903 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 139008 139730 139830 "ASP6" 139835 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137952 138685 138803 "ASP55" 138921 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136901 137626 137745 "ASP50" 137864 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135989 136602 136712 "ASP4" 136822 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 135077 135690 135800 "ASP49" 135910 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133861 134616 134784 "ASP42" 134966 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132637 133394 133564 "ASP41" 133748 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131587 132314 132432 "ASP35" 132550 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 131352 131535 131574 "ASP34" 131579 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 131089 131156 131232 "ASP33" 131307 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129982 130724 130856 "ASP31" 130988 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129747 129930 129969 "ASP30" 129974 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129482 129551 129627 "ASP29" 129702 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 129247 129430 129469 "ASP28" 129474 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 129012 129195 129234 "ASP27" 129239 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 128096 128710 128821 "ASP24" 128932 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 127172 127898 128010 "ASP20" 128015 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 126260 126873 126983 "ASP1" 127093 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 125202 125934 126053 "ASP19" 126172 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124939 125006 125082 "ASP12" 125157 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123791 124538 124682 "ASP10" 124826 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121642 123635 123726 "ARRAY2" 123731 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117407 121290 121404 "ARRAY1" 121559 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116439 116612 116833 "ARRAY12" 117230 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110751 112669 112744 "ARR2CAT" 115374 NIL ARR2CAT (NIL T T T) -9 NIL 116132 NIL) (-56 108185 108929 109883 "ARR2CAT-" 109888 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107502 107812 107937 "ARITY" 108078 T ARITY (NIL) -8 NIL NIL NIL) (-54 106278 106430 106729 "APPRULE" 107338 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105929 105977 106096 "APPLYORE" 106224 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105194 105389 "ANY" 105752 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 8b837fe5..1beb7866 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,36 +1,41 @@ -(732389 . 3453610658) +(732389 . 3453749794) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-1247 *3 *2)) (-4 *3 (-1049)) + (-4 *2 (-1224 *3))))) +(((*1 *2 *3 *3) + (-12 (-5 *3 (-644 *7)) (-4 *7 (-1064 *4 *5 *6)) (-4 *4 (-454)) + (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-112)) + (-5 *1 (-988 *4 *5 *6 *7 *8)) (-4 *8 (-1070 *4 *5 *6 *7)))) + ((*1 *2 *3 *3) + (-12 (-5 *3 (-644 *7)) (-4 *7 (-1064 *4 *5 *6)) (-4 *4 (-454)) + (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-112)) + (-5 *1 (-1106 *4 *5 *6 *7 *8)) (-4 *8 (-1070 *4 *5 *6 *7))))) +(((*1 *2 *1) (-12 (-4 *1 (-995 *2)) (-4 *2 (-1214))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-281))))) +(((*1 *2 *3 *3 *4 *3) + (-12 (-5 *3 (-566)) (-5 *4 (-689 (-225))) (-5 *2 (-1035)) + (-5 *1 (-755))))) (((*1 *2 *3) - (-12 (-5 *3 (-644 (-2 (|:| -2122 *4) (|:| -3821 (-566))))) - (-4 *4 (-1099)) (-5 *2 (-1 *4)) (-5 *1 (-1017 *4))))) + (-12 (-5 *2 (-566)) (-5 *1 (-447 *3)) (-4 *3 (-406)) (-4 *3 (-1049))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-112)) (-5 *1 (-1139 *3 *4)) (-4 *3 (-13 (-1099) (-34))) + (-4 *4 (-13 (-1099) (-34)))))) (((*1 *2 *1) - (-12 (-4 *3 (-1049)) (-5 *2 (-1264 *3)) (-5 *1 (-712 *3 *4)) - (-4 *4 (-1240 *3))))) -(((*1 *1 *1) (-12 (-4 *1 (-674 *2)) (-4 *2 (-1214))))) -(((*1 *2 *3 *4 *4 *5 *3 *3 *3 *3 *3) - (-12 (-5 *3 (-566)) (-5 *5 (-689 (-225))) (-5 *4 (-225)) - (-5 *2 (-1035)) (-5 *1 (-752))))) -(((*1 *2 *3 *3 *3 *3 *4 *5 *5 *6 *7 *8 *8 *3) - (-12 (-5 *6 (-644 (-112))) (-5 *7 (-689 (-225))) - (-5 *8 (-689 (-566))) (-5 *3 (-566)) (-5 *4 (-225)) (-5 *5 (-112)) - (-5 *2 (-1035)) (-5 *1 (-754))))) + (-12 (-4 *1 (-1207 *3 *4 *5 *6)) (-4 *3 (-558)) (-4 *4 (-793)) + (-4 *5 (-850)) (-4 *6 (-1064 *3 *4 *5)) (-5 *2 (-112)))) + ((*1 *2 *3 *1) + (-12 (-4 *1 (-1207 *4 *5 *6 *3)) (-4 *4 (-558)) (-4 *5 (-793)) + (-4 *6 (-850)) (-4 *3 (-1064 *4 *5 *6)) (-5 *2 (-112))))) (((*1 *2 *2) - (|partial| -12 (-5 *2 (-1171 *3)) (-4 *3 (-351)) (-5 *1 (-359 *3))))) + (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) + (-4 *2 (-13 (-432 *3) (-1002)))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-644 (-771))) (-5 *3 (-171)) (-5 *1 (-1163 *4 *5)) + (-14 *4 (-921)) (-4 *5 (-1049))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-3 (-409 (-952 *5)) (-1164 (-1175) (-952 *5)))) - (-4 *5 (-454)) (-5 *2 (-644 (-689 (-409 (-952 *5))))) - (-5 *1 (-293 *5)) (-5 *4 (-689 (-409 (-952 *5))))))) -(((*1 *1 *2) - (-12 (-5 *2 (-644 (-566))) (-5 *1 (-1004 *3)) (-14 *3 (-566))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *3 (-1175)) - (-4 *4 (-13 (-454) (-147) (-1038 (-566)) (-639 (-566)))) - (-5 *1 (-559 *4 *2)) (-4 *2 (-13 (-27) (-1199) (-432 *4)))))) -(((*1 *2 *1) (-12 (-4 *1 (-797 *2)) (-4 *2 (-172)))) - ((*1 *2 *1) (-12 (-4 *1 (-997 *2)) (-4 *2 (-172))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *3 (-771)) (-4 *4 (-308)) (-4 *6 (-1240 *4)) - (-5 *2 (-1264 (-644 *6))) (-5 *1 (-457 *4 *6)) (-5 *5 (-644 *6))))) + (-12 (-5 *3 (-644 *5)) (-5 *4 (-921)) (-4 *5 (-850)) + (-5 *2 (-59 (-644 (-672 *5)))) (-5 *1 (-672 *5))))) (((*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)))) @@ -62,14 +67,14 @@ (-12 (-5 *3 (-1175)) (-5 *2 (-245 (-1157))) (-5 *1 (-214 *4)) (-4 *4 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ *3)) (-15 -1651 ((-1269) $)) - (-15 -4296 ((-1269) $))))))) + (-10 -8 (-15 -4386 ((-1157) $ *3)) (-15 -1697 ((-1269) $)) + (-15 -2509 ((-1269) $))))))) ((*1 *1 *1 *2) (-12 (-5 *2 (-989)) (-5 *1 (-214 *3)) (-4 *3 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1651 ((-1269) $)) - (-15 -4296 ((-1269) $))))))) + (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1697 ((-1269) $)) + (-15 -2509 ((-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)))) @@ -156,70 +161,100 @@ (-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) - (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-368 *3 *4)) - (-4 *3 (-369 *4)))) - ((*1 *2) (-12 (-4 *1 (-369 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) -(((*1 *1) (-5 *1 (-1062)))) -(((*1 *2 *1) (-12 (-5 *2 (-644 (-175))) (-5 *1 (-1084))))) -(((*1 *2 *3 *4 *2 *5) - (-12 (-5 *3 (-644 *8)) (-5 *4 (-644 (-892 *6))) - (-5 *5 (-1 (-889 *6 *8) *8 (-892 *6) (-889 *6 *8))) (-4 *6 (-1099)) - (-4 *8 (-13 (-1049) (-614 (-892 *6)) (-1038 *7))) - (-5 *2 (-889 *6 *8)) (-4 *7 (-1049)) (-5 *1 (-941 *6 *7 *8))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1099)) (-4 *6 (-886 *5)) (-5 *2 (-885 *5 *6 (-644 *6))) - (-5 *1 (-887 *5 *6 *4)) (-5 *3 (-644 *6)) (-4 *4 (-614 (-892 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1099)) (-5 *2 (-644 (-295 *3))) (-5 *1 (-887 *5 *3 *4)) - (-4 *3 (-1038 (-1175))) (-4 *3 (-886 *5)) (-4 *4 (-614 (-892 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1099)) (-5 *2 (-644 (-295 (-952 *3)))) - (-5 *1 (-887 *5 *3 *4)) (-4 *3 (-1049)) - (-2326 (-4 *3 (-1038 (-1175)))) (-4 *3 (-886 *5)) - (-4 *4 (-614 (-892 *5))))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1099)) (-5 *2 (-889 *5 *3)) (-5 *1 (-887 *5 *3 *4)) - (-2326 (-4 *3 (-1038 (-1175)))) (-2326 (-4 *3 (-1049))) - (-4 *3 (-886 *5)) (-4 *4 (-614 (-892 *5)))))) -(((*1 *2 *3 *4 *3 *4 *4 *4) - (-12 (-5 *3 (-689 (-225))) (-5 *4 (-566)) (-5 *2 (-1035)) - (-5 *1 (-756))))) -(((*1 *2 *3) - (-12 (|has| *2 (-6 (-4419 "*"))) (-4 *5 (-375 *2)) (-4 *6 (-375 *2)) - (-4 *2 (-1049)) (-5 *1 (-104 *2 *3 *4 *5 *6)) (-4 *3 (-1240 *2)) - (-4 *4 (-687 *2 *5 *6))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-558)) (-5 *1 (-433 *3 *2)) (-4 *2 (-432 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1138)))) -(((*1 *2) - (-12 (-4 *1 (-344 *3 *4 *5)) (-4 *3 (-1218)) (-4 *4 (-1240 *3)) - (-4 *5 (-1240 (-409 *4))) (-5 *2 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evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1155 (-225))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3021 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *2 (-1035)) (-5 *1 (-306))))) + (|partial| -12 (-4 *4 (-1218)) (-4 *5 (-1240 (-409 *2))) + (-4 *2 (-1240 *4)) (-5 *1 (-343 *3 *4 *2 *5)) + (-4 *3 (-344 *4 *2 *5)))) + ((*1 *2) + (|partial| -12 (-4 *1 (-344 *3 *2 *4)) (-4 *3 (-1218)) + (-4 *4 (-1240 (-409 *2))) (-4 *2 (-1240 *3))))) +(((*1 *1) + (-12 (-5 *1 (-136 *2 *3 *4)) (-14 *2 (-566)) (-14 *3 (-771)) + (-4 *4 (-172))))) +(((*1 *2 *3) (-12 (-5 *3 (-1157)) (-5 *2 (-921)) (-5 *1 (-786))))) (((*1 *2 *1) - (-12 (-5 *2 (-862)) (-5 *1 (-1155 *3)) (-4 *3 (-1099)) - (-4 *3 (-1214))))) + (-12 (-4 *1 (-1133 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(-12 (-5 *1 (-159 *2)) (-4 *2 (-547))))) +(((*1 *1 *1) (-4 *1 (-35))) ((*1 *2 *2) (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) (-4 *2 (-13 (-432 *3) (-1002))))) @@ -6371,16 +5647,15 @@ ((*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) - (-12 (-5 *1 (-341 *2 *3 *4)) (-14 *2 (-644 (-1175))) - (-14 *3 (-644 (-1175))) (-4 *4 (-389)))) ((*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 *2 *2) (-12 (-5 *2 (-566)) (-5 *1 (-926))))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-558)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2222 *3))) + (-5 *1 (-969 *4 *3)) (-4 *3 (-1240 *4))))) (((*1 *1 *1 *2 *3) (-12 (-5 *2 (-644 (-1175))) (-5 *3 (-1175)) (-5 *1 (-538)))) ((*1 *2 *3 *2) @@ -6393,51 +5668,51 @@ (-12 (-5 *4 (-644 (-1175))) (-5 *2 (-1175)) (-5 *1 (-704 *3)) (-4 *3 (-614 (-538)))))) (((*1 *2) - (-12 (-4 *1 (-351)) - (-5 *2 (-644 (-2 (|:| -2296 (-566)) (|:| -2518 (-566)))))))) -(((*1 *2 *1) (-12 (-5 *2 (-1269)) (-5 *1 (-822))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-566)) (|has| *1 (-6 -4418)) (-4 *1 (-375 *3)) - (-4 *3 (-1214))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-771)) (-4 *5 (-558)) - (-5 *2 - (-2 (|:| |coef1| *3) (|:| |coef2| *3) (|:| |subResultant| *3))) - (-5 *1 (-969 *5 *3)) (-4 *3 (-1240 *5))))) + (-12 (-4 *3 (-13 (-558) (-1038 (-566)))) (-5 *2 (-1269)) + (-5 *1 (-435 *3 *4)) (-4 *4 (-432 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-566)) (-5 *1 (-926))))) +(((*1 *1 *1) (-12 (-5 *1 (-892 *2)) (-4 *2 (-1099))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-689 *1)) (-4 *1 (-351)) (-5 *2 (-1264 *1)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-689 *1)) (-4 *1 (-145)) (-4 *1 (-909)) + (-5 *2 (-1264 *1))))) (((*1 *1) (-12 (-4 *3 (-1099)) (-5 *1 (-885 *2 *3 *4)) (-4 *2 (-1099)) (-4 *4 (-666 *3)))) ((*1 *1) (-12 (-5 *1 (-889 *2 *3)) (-4 *2 (-1099)) (-4 *3 (-1099))))) -(((*1 *2 *3 *3) - (-12 (-5 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(-13 (-850) + (-10 -8 (-15 -3134 ((-1175) $)) + (-15 -1353 ((-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))))) ((*1 *2 *2) @@ -6446,70 +5721,48 @@ ((*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) - (-12 (-5 *1 (-341 *2 *3 *4)) (-14 *2 (-644 (-1175))) - (-14 *3 (-644 (-1175))) (-4 *4 (-389)))) + ((*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 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) - ((*1 *2 *2 *2) - (-12 (-4 *3 (-558)) (-5 *1 (-433 *3 *2)) (-4 *2 (-432 *3)))) - ((*1 *1 *1 *1) (-4 *1 (-1138)))) -(((*1 *2 *1) 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(-1240 (-409 *5))) (-14 *7 *6)))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-295 (-843 *3))) (-4 *3 (-13 (-27) (-1199) (-432 *5))) - (-4 *5 (-13 (-454) (-1038 (-566)) (-639 (-566)))) - (-5 *2 - (-3 (-843 *3) - (-2 (|:| |leftHandLimit| (-3 (-843 *3) "failed")) - (|:| |rightHandLimit| (-3 (-843 *3) "failed"))) - "failed")) - (-5 *1 (-636 *5 *3)))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-295 *3)) (-5 *5 (-1157)) - (-4 *3 (-13 (-27) (-1199) (-432 *6))) - (-4 *6 (-13 (-454) (-1038 (-566)) (-639 (-566)))) - (-5 *2 (-843 *3)) (-5 *1 (-636 *6 *3)))) - ((*1 *2 *3 *4) - (-12 (-5 *4 (-295 (-843 (-952 *5)))) (-4 *5 (-454)) - (-5 *2 - (-3 (-843 (-409 (-952 *5))) - (-2 (|:| |leftHandLimit| (-3 (-843 (-409 (-952 *5))) "failed")) - (|:| |rightHandLimit| (-3 (-843 (-409 (-952 *5))) "failed"))) - "failed")) - (-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 - (-3 (-843 *3) - (-2 (|:| |leftHandLimit| (-3 (-843 *3) "failed")) - (|:| |rightHandLimit| (-3 (-843 *3) "failed"))) - "failed")) - (-5 *1 (-637 *5)))) - ((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *4 (-295 (-409 (-952 *6)))) (-5 *5 (-1157)) - (-5 *3 (-409 (-952 *6))) (-4 *6 (-454)) (-5 *2 (-843 *3)) - (-5 *1 (-637 *6))))) -(((*1 *1) (-5 *1 (-439)))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-114))))) + (-12 (-5 *3 (-644 (-566))) (-5 *2 (-904 (-566))) (-5 *1 (-917)))) + ((*1 *2) (-12 (-5 *2 (-904 (-566))) (-5 *1 (-917))))) (((*1 *2 *2) (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) (-4 *2 (-13 (-432 *3) (-1002))))) @@ -6519,97 +5772,64 @@ ((*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 *2 *1) (-12 (-4 *1 (-529)) (-5 *2 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(-2 (|:| |radval| (-317 (-566))) (|:| |radmult| (-566)) + (|:| |radvect| (-644 (-689 (-317 (-566)))))))) + (-5 *1 (-1031))))) (((*1 *2 *3) - (-12 (-4 *4 (-850)) (-5 *2 (-1186 (-644 *4))) (-5 *1 (-1185 *4)) - (-5 *3 (-644 *4))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1264 (-317 (-225)))) (-5 *4 (-644 (-1175))) - (-5 *2 (-689 (-317 (-225)))) (-5 *1 (-205)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1099)) (-4 *6 (-900 *5)) (-5 *2 (-689 *6)) - (-5 *1 (-692 *5 *6 *3 *4)) (-4 *3 (-375 *6)) - (-4 *4 (-13 (-375 *5) (-10 -7 (-6 -4417))))))) -(((*1 *2 *2) - (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) - (-4 *2 (-13 (-432 *3) (-1002))))) - ((*1 *2 *2) - (-12 (-4 *3 (-38 (-409 (-566)))) (-4 *4 (-1255 *3)) - (-5 *1 (-279 *3 *4 *2)) (-4 *2 (-1226 *3 *4)))) - ((*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) - (-12 (-5 *1 (-341 *2 *3 *4)) (-14 *2 (-644 (-1175))) - (-14 *3 (-644 (-1175))) (-4 *4 (-389)))) - ((*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)))) + (-12 (-5 *3 |RationalNumber|) (-5 *2 (-1 (-566))) (-5 *1 (-1047))))) +(((*1 *2 *1) (-12 (-4 *1 (-767 *3)) (-4 *3 (-1099)) (-5 *2 (-112))))) +(((*1 *1 *1 *1) (-12 (-5 *1 (-295 *2)) (-4 *2 (-303)) (-4 *2 (-1214)))) + ((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-644 (-612 *1))) (-5 *3 (-644 *1)) (-4 *1 (-303)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-644 (-295 *1))) (-4 *1 (-303)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-295 *1)) (-4 *1 (-303))))) (((*1 *2 *1) (-12 (-5 *2 @@ -6814,7 +5948,7 @@ (-2 (|:| |var| (-1175)) (|:| |arrayIndex| (-644 (-952 (-566)))) (|:| |rand| - (-2 (|:| |ints2Floats?| (-112)) (|:| -1315 (-862)))))) + (-2 (|:| |ints2Floats?| (-112)) (|:| -1316 (-862)))))) (|:| |arrayAssignmentBranch| (-2 (|:| |var| (-1175)) (|:| |rand| (-862)) (|:| |ints2Floats?| (-112)))) @@ -6822,47 +5956,22 @@ (-2 (|:| |switch| (-1174)) (|:| |thenClause| (-331)) (|:| |elseClause| (-331)))) (|:| |returnBranch| - (-2 (|:| -3003 (-112)) - (|:| -2122 - (-2 (|:| |ints2Floats?| (-112)) (|:| -1315 (-862)))))) + (-2 (|:| -4194 (-112)) + (|:| -2212 + (-2 (|:| |ints2Floats?| (-112)) (|:| -1316 (-862)))))) (|:| |blockBranch| (-644 (-331))) (|:| |commentBranch| (-644 (-1157))) (|:| |callBranch| (-1157)) (|:| |forBranch| - (-2 (|:| -3021 (-1091 (-952 (-566)))) - (|:| |span| (-952 (-566))) (|:| -2531 (-331)))) + (-2 (|:| -4344 (-1091 (-952 (-566)))) + (|:| |span| (-952 (-566))) (|:| -2639 (-331)))) (|:| |labelBranch| (-1119)) - (|:| |loopBranch| (-2 (|:| |switch| (-1174)) (|:| -2531 (-331)))) + (|:| |loopBranch| (-2 (|:| |switch| (-1174)) (|:| -2639 (-331)))) (|:| |commonBranch| - (-2 (|:| -2520 (-1175)) (|:| |contents| (-644 (-1175))))) + (-2 (|:| -2628 (-1175)) (|:| |contents| (-644 (-1175))))) (|:| |printBranch| (-644 (-862))))) (-5 *1 (-331))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1 *3 *4)) (-5 *1 (-683 *4 *3)) (-4 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((*1 *2 *2) (-12 (-5 *2 (-921)) (|has| *1 (-6 -4408)) (-4 *1 (-406)))) + ((*1 *2) (-12 (-4 *1 (-406)) (-5 *2 (-921))))) +(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-771)) (-5 *2 (-112))))) +(((*1 *2 *1) (-12 (-5 *2 (-958 (-771))) (-5 *1 (-334))))) +(((*1 *1 *1) + (-12 (-5 *1 (-223 *2 *3)) (-4 *2 (-13 (-1049) (-850))) + (-14 *3 (-644 (-1175)))))) +(((*1 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-365) (-10 -8 (-15 ** ($ $ (-409 (-566))))))) + (-5 *1 (-1127 *3 *2)) (-4 *3 (-1240 *2))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1049)) (-4 *4 (-792)))) @@ -7924,9 +7099,9 @@ (-4 *6 (-365)) (-5 *2 (-587 *6)) (-5 *1 (-586 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3263 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2806 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-365)) (-4 *6 (-365)) - (-5 *2 (-2 (|:| -3263 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2806 *6) (|:| |coeff| *6))) (-5 *1 (-586 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -8045,7 +7220,7 @@ (-4 *8 (-1049)) (-4 *6 (-793)) (-4 *2 (-13 (-1099) - (-10 -8 (-15 -2942 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-771)))))) + (-10 -8 (-15 -3034 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-771)))))) (-5 *1 (-951 *6 *7 *8 *5 *2)) (-4 *5 (-949 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-958 *5)) (-4 *5 (-1214)) @@ -8058,8 +7233,8 @@ (-4 *2 (-949 (-952 *4) *5 *6)) (-4 *5 (-793)) (-4 *6 (-13 (-850) - (-10 -8 (-15 -3035 ((-1175) $)) - (-15 -1351 ((-3 $ "failed") (-1175)))))) + (-10 -8 (-15 -3134 ((-1175) $)) + (-15 -1353 ((-3 $ "failed") (-1175)))))) (-5 *1 (-984 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-558)) (-4 *6 (-558)) @@ -8146,71 +7321,114 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1049)) (-5 *1 (-1287 *3 *4)) (-4 *4 (-846))))) +(((*1 *2 *2) + (-12 (-4 *3 (-558)) (-5 *1 (-277 *3 *2)) + (-4 *2 (-13 (-432 *3) (-1002))))) + ((*1 *2 *2) + (-12 (-4 *3 (-38 (-409 (-566)))) (-4 *4 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+7476,58 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-1287 *2 *3)) (-4 *2 (-365)) (-4 *2 (-1049)) (-4 *3 (-846))))) -(((*1 *2 *3 *3 *3 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-566)) - (-5 *5 (-3 (|:| |fn| (-390)) (|:| |fp| (-64 G)))) (-5 *2 (-1035)) - (-5 *1 (-748))))) +(((*1 *2 *3 *3 *3) + (-12 (-5 *2 (-644 (-566))) (-5 *1 (-1109)) (-5 *3 (-566))))) +(((*1 *1) + (-12 (-4 *1 (-406)) (-2426 (|has| *1 (-6 -4408))) + (-2426 (|has| *1 (-6 -4400))))) + ((*1 *2 *1) (-12 (-4 *1 (-427 *2)) (-4 *2 (-1099)) (-4 *2 (-850)))) + ((*1 *1) (-4 *1 (-844))) ((*1 *1 *1 *1) (-4 *1 (-850))) + ((*1 *2 *1) (-12 (-4 *1 (-968 *2)) (-4 *2 (-850))))) (((*1 *1 *1 *1) (-4 *1 (-661)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-644 (-780 *5 (-864 *6)))) (-5 *4 (-112)) (-4 *5 (-454)) - (-14 *6 (-644 (-1175))) (-5 *2 (-644 (-1046 *5 *6))) - (-5 *1 (-628 *5 *6))))) -(((*1 *1 *2 *3 *1) - (-12 (-5 *2 (-508)) (-5 *3 (-644 (-965))) (-5 *1 (-292))))) -(((*1 *2 *1 *1) - (-12 - (-5 *2 - (-2 (|:| -3055 *3) (|:| |gap| (-771)) (|:| -1818 (-782 *3)) - (|:| -3077 (-782 *3)))) - (-5 *1 (-782 *3)) (-4 *3 (-1049)))) - ((*1 *2 *1 *1 *3) - (-12 (-4 *4 (-1049)) (-4 *5 (-793)) (-4 *3 (-850)) - (-5 *2 - (-2 (|:| -3055 *1) (|:| |gap| (-771)) (|:| -1818 *1) - (|:| -3077 *1))) - (-4 *1 (-1064 *4 *5 *3)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1049)) (-4 *4 (-793)) (-4 *5 (-850)) - (-5 *2 - (-2 (|:| -3055 *1) (|:| |gap| (-771)) (|:| -1818 *1) - (|:| -3077 *1))) - (-4 *1 (-1064 *3 *4 *5))))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) - (|:| -3021 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) + (-12 (-5 *3 (-1264 (-644 (-2 (|:| -2212 *4) (|:| -2168 (-1119)))))) + (-4 *4 (-351)) (-5 *2 (-689 *4)) (-5 *1 (-348 *4))))) +(((*1 *2) + (-12 (-4 *1 (-344 *3 *4 *5)) (-4 *3 (-1218)) (-4 *4 (-1240 *3)) + (-4 *5 (-1240 (-409 *4))) (-5 *2 (-689 (-409 *4)))))) +(((*1 *2 *2 *3) + (-12 (-4 *4 (-454)) (-4 *5 (-793)) (-4 *6 (-850)) + (-4 *2 (-1064 *4 *5 *6)) (-5 *1 (-776 *4 *5 *6 *2 *3)) + (-4 *3 (-1070 *4 *5 *6 *2))))) +(((*1 *1 *1 *1) + (-12 (-4 *1 (-324 *2 *3)) (-4 *2 (-1099)) (-4 *3 (-131)) + (-4 *3 (-792))))) +(((*1 *2 *3) + (-12 (-5 *3 (-2 (|:| -4357 (-409 (-566))) (|:| -4368 (-409 (-566))))) + (-5 *2 (-409 (-566))) (-5 *1 (-1020 *4)) (-4 *4 (-1240 (-566)))))) +(((*1 *2 *3) + (-12 (-4 *4 (-454)) (-5 *2 - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| "There are singularities at both end points") - (|:| |notEvaluated| "End point continuity not yet evaluated"))) - (-5 *1 (-192))))) -(((*1 *1 *1) (-12 (-5 *1 (-174 *2)) (-4 *2 (-308)))) - ((*1 *2 *3) - (-12 (-5 *2 (-1177 (-409 (-566)))) (-5 *1 (-190)) (-5 *3 (-566)))) - ((*1 *1 *1) (-12 (-4 *1 (-674 *2)) (-4 *2 (-1214)))) - ((*1 *1 *1) (-4 *1 (-869 *2))) - ((*1 *1 *1) - (-12 (-4 *1 (-973 *2 *3 *4)) (-4 *2 (-1049)) (-4 *3 (-792)) - (-4 *4 (-850))))) + (-644 + (-2 (|:| |eigval| (-3 (-409 (-952 *4)) (-1164 (-1175) (-952 *4)))) + (|:| |geneigvec| (-644 (-689 (-409 (-952 *4)))))))) + (-5 *1 (-293 *4)) (-5 *3 (-689 (-409 (-952 *4))))))) (((*1 *2 *3) - (-12 (-5 *3 (-921)) + (-12 (-5 *3 (-927)) (-5 *2 - (-3 (-1171 *4) - (-1264 (-644 (-2 (|:| -2122 *4) (|:| -2074 (-1119))))))) - (-5 *1 (-348 *4)) (-4 *4 (-351))))) + (-2 (|:| |brans| (-644 (-644 (-943 (-225))))) + (|:| |xValues| (-1093 (-225))) (|:| |yValues| (-1093 (-225))))) + (-5 *1 (-153)))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-927)) (-5 *4 (-409 (-566))) + (-5 *2 + (-2 (|:| |brans| (-644 (-644 (-943 (-225))))) + (|:| |xValues| (-1093 (-225))) (|:| |yValues| (-1093 (-225))))) + (-5 *1 (-153))))) (((*1 *2 *2 *3) - (-12 (-5 *3 (-1175)) (-4 *4 (-454)) (-4 *4 (-1099)) - (-5 *1 (-575 *4 *2)) (-4 *2 (-285)) (-4 *2 (-432 *4))))) -(((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 (-169 (-225)) (-169 (-225)))) (-5 *4 (-1093 (-225))) - (-5 *2 (-1266)) (-5 *1 (-258))))) + (-12 (-5 *2 (-689 *4)) (-5 *3 (-921)) (-4 *4 (-1049)) + (-5 *1 (-1028 *4)))) + ((*1 *2 *2 *3) + (-12 (-5 *2 (-644 (-689 *4))) (-5 *3 (-921)) (-4 *4 (-1049)) + (-5 *1 (-1028 *4))))) +(((*1 *1 *2) (-12 (-5 *2 (-644 (-862))) (-5 *1 (-862)))) + ((*1 *1 *1) (-5 *1 (-862)))) (((*1 *2) (-12 (-5 *2 (-833 (-566))) (-5 *1 (-536)))) ((*1 *1) (-12 (-5 *1 (-833 *2)) (-4 *2 (-1099))))) (((*1 *1 *1 *1) (-4 *1 (-21))) ((*1 *1 *1) (-4 *1 (-21))) @@ -8330,8 +7536,8 @@ (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1651 ((-1269) $)) - (-15 -4296 ((-1269) $))))))) + (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1697 ((-1269) $)) + (-15 -2509 ((-1269) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-295 *2)) (-4 *2 (-21)) (-4 *2 (-1214)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-295 *2)) (-4 *2 (-21)) (-4 *2 (-1214)))) ((*1 *1 *1 *1) @@ -8351,60 +7557,43 @@ ((*1 *2 *2 *2) (-12 (-5 *2 (-943 (-225))) (-5 *1 (-1210)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1262 *2)) (-4 *2 (-1214)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1262 *2)) (-4 *2 (-1214)) (-4 *2 (-21))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-365)) (-5 *2 (-2 (|:| -1818 *3) (|:| -3077 *3))) - (-5 *1 (-766 *3 *4)) (-4 *3 (-708 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-365)) (-4 *3 (-1049)) - (-5 *2 (-2 (|:| -1818 *1) (|:| -3077 *1))) (-4 *1 (-852 *3)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-99 *5)) (-4 *5 (-365)) (-4 *5 (-1049)) - (-5 *2 (-2 (|:| -1818 *3) (|:| -3077 *3))) (-5 *1 (-853 *5 *3)) - (-4 *3 (-852 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-558)) (-4 *5 (-992 *4)) - (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4))) (-5 *1 (-142 *4 *5 *3)) - (-4 *3 (-375 *5)))) - ((*1 *2 *3) - (-12 (-4 *4 (-558)) (-4 *5 (-992 *4)) - (-5 *2 (-2 (|:| |num| *6) (|:| |den| *4))) - (-5 *1 (-505 *4 *5 *6 *3)) (-4 *6 (-375 *4)) (-4 *3 (-375 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-689 *5)) (-4 *5 (-992 *4)) (-4 *4 (-558)) - (-5 *2 (-2 (|:| |num| (-689 *4)) (|:| |den| *4))) - (-5 *1 (-693 *4 *5)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-13 (-365) (-147) (-1038 (-409 (-566))))) - (-4 *6 (-1240 *5)) - 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(-370) (-614 (-566)))) (-5 *1 (-544 *3 *2)) + (-4 *2 (-1255 *3)))) + ((*1 *2 *2) + (-12 (-5 *2 (-1155 *3)) (-4 *3 (-13 (-558) (-147))) + (-5 *1 (-1151 *3))))) +(((*1 *2 *3 *3) + (-12 (-4 *3 (-1218)) (-4 *5 (-1240 *3)) (-4 *6 (-1240 (-409 *5))) + (-5 *2 (-112)) (-5 *1 (-343 *4 *3 *5 *6)) (-4 *4 (-344 *3 *5 *6)))) + ((*1 *2 *3 *3) + (-12 (-4 *1 (-344 *3 *4 *5)) (-4 *3 (-1218)) (-4 *4 (-1240 *3)) + (-4 *5 (-1240 (-409 *4))) (-5 *2 (-112))))) +(((*1 *2 *3 *2 *4) + (|partial| -12 (-5 *3 (-644 (-612 *2))) (-5 *4 (-1175)) + (-4 *2 (-13 (-27) (-1199) (-432 *5))) + (-4 *5 (-13 (-558) (-1038 (-566)) (-639 (-566)))) + (-5 *1 (-278 *5 *2))))) +(((*1 *2 *2 *1) (-12 (-4 *1 (-255 *2)) (-4 *2 (-1214))))) (((*1 *2) (-12 (-4 *2 (-13 (-432 *3) (-1002))) (-5 *1 (-277 *3 *2)) (-4 *3 (-558)))) @@ -8417,8 +7606,8 @@ (-12 (-5 *1 (-214 *2)) (-4 *2 (-13 (-850) - (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1651 ((-1269) $)) - (-15 -4296 ((-1269) $))))))) + (-10 -8 (-15 -4386 ((-1157) $ (-1175))) (-15 -1697 ((-1269) $)) + (-15 -2509 ((-1269) $))))))) ((*1 *1 *1 *2) (-12 (-5 *1 (-295 *2)) (-4 *2 (-25)) (-4 *2 (-1214)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-295 *2)) (-4 *2 (-25)) (-4 *2 (-1214)))) ((*1 *1 *2 *1) @@ -8441,70 +7630,81 @@ (-12 (-5 *2 (-1155 *3)) (-4 *3 (-1049)) (-5 *1 (-1159 *3)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-943 (-225))) (-5 *1 (-1210)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1262 *2)) (-4 *2 (-1214)) (-4 *2 (-25))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-644 *6)) (-4 *6 (-1064 *3 *4 *5)) (-4 *3 (-454)) - (-4 *3 (-558)) (-4 *4 (-793)) (-4 *5 (-850)) - (-5 *1 (-977 *3 *4 *5 *6))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-1155 *3)) (-4 *3 (-365)) (-4 *3 (-1049)) - (-5 *1 (-1159 *3))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-644 (-1213))) (-5 *3 (-1213)) (-5 *1 (-681))))) -(((*1 *2 *1) (-12 (-5 *2 (-644 (-183))) (-5 *1 (-140))))) -(((*1 *2 *3 *3 *3) - (-12 (-5 *2 (-644 (-566))) (-5 *1 (-1109)) (-5 *3 (-566))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-436)))) +(((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1163 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*2)) (-4 *5 (-308)) - (-4 *6 (-992 *5)) (-4 *2 (-13 (-411 *6 *7) (-1038 *6))) - (-5 *1 (-415 *5 *6 *7 *2)) (-4 *7 (-1240 *6))))) + (-12 (-5 *3 (-689 *4)) (-4 *4 (-365)) (-5 *2 (-1171 *4)) + (-5 *1 (-534 *4 *5 *6)) (-4 *5 (-365)) (-4 *6 (-13 (-365) (-848)))))) (((*1 *2) - (-12 (-4 *3 (-1218)) (-4 *4 (-1240 *3)) (-4 *5 (-1240 (-409 *4))) - (-5 *2 (-1264 *1)) (-4 *1 (-344 *3 *4 *5))))) -(((*1 *2) (-12 (-5 *2 (-921)) (-5 *1 (-1267)))) - ((*1 *2 *2) (-12 (-5 *2 (-921)) (-5 *1 (-1267))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1264 (-644 (-2 (|:| -2122 *4) (|:| -2074 (-1119)))))) - (-4 *4 (-351)) (-5 *2 (-1269)) (-5 *1 (-530 *4))))) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-368 *3 *4)) + (-4 *3 (-369 *4)))) + ((*1 *2) (-12 (-4 *1 (-369 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-1171 *1)) (-4 *1 (-1012))))) +(((*1 *2 *2 *2 *2) + (-12 (-5 *2 (-689 *3)) (-4 *3 (-1049)) (-5 *1 (-690 *3))))) +(((*1 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-438)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-390)) (-5 *1 (-438))))) (((*1 *2 *1) (-12 (-5 *2 (-1124 (-566) (-612 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-992 *2)) (-4 *4 (-1240 *3)) (-4 *2 (-308)) @@ -8520,79 +7720,32 @@ (-12 (-4 *4 (-172)) (-4 *2 (|SubsetCategory| (-726) *4)) (-5 *1 (-662 *3 *4 *2)) (-4 *3 (-717 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-992 *2)) (-4 *2 (-558))))) -(((*1 *1) (-5 *1 (-144))) ((*1 *1 *1) (-5 *1 (-862)))) +(((*1 *2 *1) (-12 (-5 *2 (-1269)) (-5 *1 (-822))))) (((*1 *2 *1) (-12 (-5 *2 (-1117)) (-5 *1 (-218)))) ((*1 *2 *1) (-12 (-5 *2 (-1117)) (-5 *1 (-441)))) ((*1 *2 *1) (-12 (-5 *2 (-1117)) (-5 *1 (-838)))) ((*1 *2 *1) (-12 (-5 *2 (-1117)) (-5 *1 (-1114)))) ((*1 *1 *2 *3) (-12 (-5 *2 (-644 (-1180))) (-5 *3 (-1180)) (-5 *1 (-1117))))) -(((*1 *2 *3 *3 *4 *3 *4 *4 *4 *4 *5) - (-12 (-5 *3 (-225)) (-5 *4 (-566)) - (-5 *5 (-3 (|:| |fn| (-390)) (|:| |fp| (-64 G)))) (-5 *2 (-1035)) - (-5 *1 (-748))))) -(((*1 *1 *1 *2 *2 *2 *2) - (-12 (-5 *2 (-566)) (-4 *1 (-687 *3 *4 *5)) (-4 *3 (-1049)) - (-4 *4 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+(((*1 *2 *3) + (-12 (-5 *2 (-644 (-1171 (-566)))) (-5 *1 (-191)) (-5 *3 (-566))))) +(((*1 *2) (-12 (-5 *2 (-874)) (-5 *1 (-1267)))) + ((*1 *2 *2) (-12 (-5 *2 (-874)) (-5 *1 (-1267))))) +(((*1 *2 *3 *4) + (-12 (-5 *4 (-566)) (-4 *5 (-351)) (-5 *2 (-420 (-1171 (-1171 *5)))) + (-5 *1 (-1212 *5)) (-5 *3 (-1171 (-1171 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-1124 (-566) (-612 (-48)))) (-5 *1 (-48)))) ((*1 *2 *1) (-12 (-4 *3 (-308)) (-4 *4 (-992 *3)) (-4 *5 (-1240 *4)) @@ -8609,19 +7762,15 @@ (-12 (-4 *3 (-172)) (-4 *2 (-717 *3)) (-5 *1 (-662 *2 *3 *4)) (-4 *4 (|SubsetCategory| (-726) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-992 *2)) (-4 *2 (-558))))) +(((*1 *2 *2) + (-12 (-4 *3 (-454)) (-5 *1 (-1205 *3 *2)) + (-4 *2 (-13 (-432 *3) (-1199)))))) (((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4418)) (-4 *1 (-244 *2)) (-4 *2 (-1214)))) - ((*1 *1 *1 *1) (-12 (-4 *1 (-283 *2)) (-4 *2 (-1214)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-283 *2)) (-4 *2 (-1214)))) + (-12 (-4 *1 (-1064 *2 *3 *4)) (-4 *2 (-1049)) (-4 *3 (-793)) + 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(-15 -2512 ($ (-1124 *4 (-612 $)))))))))) +(((*1 *2 *2 *2) (-12 (-5 *2 (-566)) (-5 *1 (-555))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-508)) (-5 *2 (-112)) (-5 *1 (-114))))) +(((*1 *2 *1 *2) + (-12 (|has| *1 (-6 -4418)) (-4 *1 (-1252 *2)) (-4 *2 (-1214))))) +(((*1 *2 *2) (-12 (-5 *2 (-112)) (-5 *1 (-927))))) (((*1 *2 *2 *2) (-12 (-4 *3 (-558)) (-5 *1 (-969 *3 *2)) (-4 *2 (-1240 *3)))) ((*1 *1 *1 *1) @@ -9338,9 +8679,165 @@ (-4 *4 (-850)) (-4 *2 (-558)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1240 *2)) (-4 *2 (-1049)) (-4 *2 (-558))))) +(((*1 *2) + (-12 (-4 *3 (-558)) (-5 *2 (-644 *4)) (-5 *1 (-43 *3 *4)) + (-4 *4 (-419 *3))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-409 (-952 *5))) (-5 *4 (-1175)) + (-4 *5 (-13 (-308) (-147))) (-5 *2 (-644 (-317 *5))) + (-5 *1 (-1128 *5)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-644 (-409 (-952 *5)))) (-5 *4 (-644 (-1175))) + (-4 *5 (-13 (-308) (-147))) (-5 *2 (-644 (-644 (-317 *5)))) + (-5 *1 (-1128 *5))))) +(((*1 *2 *3) + (-12 (-5 *3 (-644 (-566))) (-5 *2 (-644 (-689 (-566)))) + 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(|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (-5 *2 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1155 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4344 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated"))))) + (-5 *1 (-561))))) +(((*1 *2) + (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-368 *3 *4)) + (-4 *3 (-369 *4)))) + ((*1 *2) (-12 (-4 *1 (-369 *3)) 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end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1155 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4344 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-561)))) + ((*1 *2 *1) + (-12 (-4 *1 (-604 *3 *4)) (-4 *3 (-1099)) (-4 *4 (-1214)) + (-5 *2 (-644 *4))))) +(((*1 *2 *1) (-12 (-4 *1 (-1010 *3)) (-4 *3 (-1214)) (-5 *2 (-112)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1163 *3 *4)) (-14 *3 (-921)) + (-4 *4 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(-558))))) (((*1 *2 *3) (-12 (-5 *3 (-1175)) (-4 *4 (-13 (-454) (-1038 (-566)) (-639 (-566)))) (-5 *2 (-52)) @@ -10966,30 +9992,16 @@ (-5 *1 (-461 *7 *3)))) ((*1 *2 *1) (-12 (-4 *1 (-1226 *3 *2)) (-4 *3 (-1049)) (-4 *2 (-1255 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-644 *6)) (-4 *6 (-1064 *3 *4 *5)) (-4 *3 (-558)) - (-4 *4 (-793)) (-4 *5 (-850)) (-5 *1 (-977 *3 *4 *5 *6)))) - ((*1 *2 *3 *3) - (-12 (-4 *4 (-558)) (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-644 *3)) - (-5 *1 (-977 *4 *5 *6 *3)) (-4 *3 (-1064 *4 *5 *6)))) - ((*1 *2 *2 *3) - (-12 (-5 *2 (-644 *3)) (-4 *3 (-1064 *4 *5 *6)) (-4 *4 (-558)) - (-4 *5 (-793)) (-4 *6 (-850)) (-5 *1 (-977 *4 *5 *6 *3)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-644 *6)) (-4 *6 (-1064 *3 *4 *5)) (-4 *3 (-558)) - (-4 *4 (-793)) (-4 *5 (-850)) (-5 *1 (-977 *3 *4 *5 *6)))) - ((*1 *2 *2 *2 *3) - (-12 (-5 *3 (-1 (-644 *7) (-644 *7))) (-5 *2 (-644 *7)) - (-4 *7 (-1064 *4 *5 *6)) (-4 *4 (-558)) (-4 *5 (-793)) - (-4 *6 (-850)) (-5 *1 (-977 *4 *5 *6 *7))))) -(((*1 *2 *3 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(-1099)) (-5 *2 (-1269)) + (-5 *1 (-1215 *4))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -2772 (-644 (-225))))) + (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -2759 (-644 (-225))))) (-5 *2 (-644 (-1175))) (-5 *1 (-268)))) ((*1 *2 *3) (-12 (-5 *3 (-1171 *7)) (-4 *7 (-949 *6 *4 *5)) (-4 *4 (-793)) @@ -11200,7 +10267,7 @@ (-5 *1 (-950 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-365) - (-10 -8 (-15 -2409 ($ *7)) (-15 -2907 (*7 $)) (-15 -2920 (*7 $))))))) + (-10 -8 (-15 -2512 ($ *7)) (-15 -3001 (*7 $)) (-15 -3013 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-973 *3 *4 *5)) (-4 *3 (-1049)) (-4 *4 (-792)) (-4 *5 (-850)) (-5 *2 (-644 *5)))) @@ -11210,51 +10277,43 @@ ((*1 *2 *3) (-12 (-5 *3 (-409 (-952 *4))) (-4 *4 (-558)) (-5 *2 (-644 (-1175))) (-5 *1 (-1043 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-556 *2)) (-4 *2 (-13 (-406) (-1199))))) - ((*1 *1 *1 *1) (-4 *1 (-793)))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *4 *5)) (-4 *4 (-1099)) (-4 *5 (-1099)) - (-4 *6 (-1099)) (-5 *2 (-1 *6 *5)) (-5 *1 (-684 *4 *5 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-921)) (-5 *2 (-1171 *4)) (-5 *1 (-359 *4)) - (-4 *4 (-351))))) + (-12 (-4 *4 (-558)) (-5 *2 (-169 *5)) (-5 *1 (-600 *4 *5 *3)) + (-4 *5 (-13 (-432 *4) (-1002) (-1199))) + (-4 *3 (-13 (-432 (-169 *4)) (-1002) (-1199)))))) +(((*1 *1 *1) (-4 *1 (-547)))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-112) *2)) (-4 *2 (-132)) (-5 *1 (-1083 *2)))) + ((*1 *2 *2 *3) + (-12 (-5 *3 (-1 (-566) *2 *2)) (-4 *2 (-132)) (-5 *1 (-1083 *2))))) +(((*1 *1 *2) + (-12 (-5 *2 (-771)) (-5 *1 (-675 *3)) (-4 *3 (-1049)) + (-4 *3 (-1099))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-983 *2)) (-4 *2 (-1199))))) +(((*1 *2 *1) + (-12 (-4 *1 (-366 *3 *2)) (-4 *3 (-1099)) (-4 *2 (-1099))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1171 *9)) (-5 *4 (-644 *7)) (-4 *7 (-850)) + (-4 *9 (-949 *8 *6 *7)) (-4 *6 (-793)) (-4 *8 (-308)) + (-5 *2 (-644 (-771))) (-5 *1 (-742 *6 *7 *8 *9)) (-5 *5 (-771))))) (((*1 *2 *3) - (-12 (-5 *3 (-689 (-317 (-225)))) + (-12 (-4 *4 (-454)) (-5 *2 - (-2 (|:| |stiffnessFactor| (-381)) (|:| |stabilityFactor| (-381)))) - (-5 *1 (-205))))) -(((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-771)) (-5 *4 (-921)) (-5 *2 (-1269)) (-5 *1 (-1265)))) - ((*1 *2 *1 *3 *3 *4 *4) - (-12 (-5 *3 (-771)) (-5 *4 (-921)) (-5 *2 (-1269)) (-5 *1 (-1266))))) -(((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-943 (-225))) (-5 *4 (-874)) (-5 *5 (-921)) - (-5 *2 (-1269)) (-5 *1 (-470)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-943 (-225))) (-5 *2 (-1269)) (-5 *1 (-470)))) - ((*1 *2 *1 *3 *4 *4 *5) - (-12 (-5 *3 (-644 (-943 (-225)))) (-5 *4 (-874)) (-5 *5 (-921)) - (-5 *2 (-1269)) (-5 *1 (-470))))) -(((*1 *2 *2 *1) (|partial| -12 (-5 *2 (-644 *1)) (-4 *1 (-308))))) -(((*1 *2 *1) (-12 (-4 *1 (-674 *2)) (-4 *2 (-1214))))) -(((*1 *2 *1) - (|partial| -12 (-4 *3 (-454)) (-4 *4 (-850)) (-4 *5 (-793)) - (-5 *2 (-112)) (-5 *1 (-987 *3 *4 *5 *6)) - (-4 *6 (-949 *3 *5 *4)))) - ((*1 *2 *1) - (-12 (-5 *2 (-112)) (-5 *1 (-1139 *3 *4)) (-4 *3 (-13 (-1099) (-34))) - (-4 *4 (-13 (-1099) (-34)))))) -(((*1 *2 *3 *3 *3 *4 *5 *5 *6) - (-12 (-5 *3 (-1 (-225) (-225) (-225))) - (-5 *4 (-3 (-1 (-225) (-225) (-225) (-225)) "undefined")) - (-5 *5 (-1093 (-225))) (-5 *6 (-644 (-264))) (-5 *2 (-1132 (-225))) - (-5 *1 (-697)))) - ((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1 (-943 (-225)) (-225) (-225))) (-5 *4 (-1093 (-225))) - (-5 *5 (-644 (-264))) (-5 *2 (-1132 (-225))) (-5 *1 (-697)))) - ((*1 *2 *2 *3 *4 *4 *5) - (-12 (-5 *2 (-1132 (-225))) (-5 *3 (-1 (-943 (-225)) (-225) (-225))) - (-5 *4 (-1093 (-225))) (-5 *5 (-644 (-264))) (-5 *1 (-697))))) + (-644 + (-2 (|:| |eigval| (-3 (-409 (-952 *4)) (-1164 (-1175) (-952 *4)))) + (|:| |eigmult| (-771)) + (|:| |eigvec| (-644 (-689 (-409 (-952 *4)))))))) + (-5 *1 (-293 *4)) (-5 *3 (-689 (-409 (-952 *4))))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-644 *1)) (-4 *1 (-1064 *4 *5 *6)) (-4 *4 (-1049)) + (-4 *5 (-793)) (-4 *6 (-850)) (-5 *2 (-112)))) + ((*1 *2 *1 *1) + (-12 (-4 *1 (-1064 *3 *4 *5)) (-4 *3 (-1049)) (-4 *4 (-793)) + (-4 *5 (-850)) (-5 *2 (-112)))) + ((*1 *2 *3 *1 *4) + (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *1 (-1207 *5 *6 *7 *3)) + (-4 *5 (-558)) (-4 *6 (-793)) (-4 *7 (-850)) + (-4 *3 (-1064 *5 *6 *7)) (-5 *2 (-112))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1171 (-409 (-1171 *2)))) (-5 *4 (-612 *2)) (-4 *2 (-13 (-432 *5) (-27) (-1199))) @@ -11271,55 +10330,33 @@ (-4 *6 (-1049)) (-4 *2 (-13 (-365) - (-10 -8 (-15 -2409 ($ *7)) (-15 -2907 (*7 $)) (-15 -2920 (*7 $))))) + (-10 -8 (-15 -2512 ($ *7)) (-15 -3001 (*7 $)) (-15 -3013 (*7 $))))) (-5 *1 (-950 *5 *4 *6 *7 *2)) (-4 *7 (-949 *6 *5 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-409 (-1171 (-409 (-952 *5))))) (-5 *4 (-1175)) (-5 *2 (-409 (-952 *5))) (-5 *1 (-1043 *5)) (-4 *5 (-558))))) -(((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-850))))) -(((*1 *2 *2 *2) - (-12 - (-5 *2 - (-644 - (-2 (|:| |lcmfij| *4) (|:| |totdeg| (-771)) (|:| |poli| *6) - (|:| |polj| *6)))) - (-4 *4 (-793)) (-4 *6 (-949 *3 *4 *5)) (-4 *3 (-454)) (-4 *5 (-850)) - (-5 *1 (-451 *3 *4 *5 *6))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-1175)) - (-4 *5 (-13 (-558) (-1038 (-566)) (-639 (-566)))) - (-5 *2 - (-2 (|:| |func| *3) (|:| |kers| (-644 (-612 *3))) - (|:| |vals| (-644 *3)))) - (-5 *1 (-278 *5 *3)) (-4 *3 (-13 (-27) (-1199) (-432 *5)))))) -(((*1 *1 *1 *1 *2) - (-12 (-5 *2 (-1 *3 *3 *3 *3 *3)) (-4 *3 (-1099)) (-5 *1 (-103 *3)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-1 *2 *2 *2)) (-5 *1 (-103 *2)) (-4 *2 (-1099))))) -(((*1 *2 *1) (-12 (-5 *2 (-1269)) (-5 *1 (-822))))) -(((*1 *2 *1) - (-12 (-5 *2 (-644 (-2 (|:| |k| (-1175)) (|:| |c| (-1286 *3))))) - (-5 *1 (-1286 *3)) (-4 *3 (-1049)))) - ((*1 *2 *1) - (-12 (-5 *2 (-644 (-2 (|:| |k| *3) (|:| |c| (-1288 *3 *4))))) - (-5 *1 (-1288 *3 *4)) (-4 *3 (-850)) (-4 *4 (-1049))))) +(((*1 *2 *1) (-12 (-4 *1 (-995 *2)) (-4 *2 (-1214))))) +(((*1 *1 *2) (-12 (-5 *2 (-1119)) (-5 *1 (-821))))) (((*1 *2 *3 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-771)) (|:| |poli| *7) - (|:| |polj| *7))) - (-4 *5 (-793)) (-4 *7 (-949 *4 *5 *6)) (-4 *4 (-454)) (-4 *6 (-850)) - (-5 *2 (-112)) (-5 *1 (-451 *4 *5 *6 *7))))) + (|partial| -12 (-4 *4 (-558)) + (-5 *2 (-2 (|:| -2760 *3) (|:| -1644 *3))) (-5 *1 (-1235 *4 *3)) + (-4 *3 (-1240 *4))))) +(((*1 *2 *3) (-12 (-5 *3 (-1157)) (-5 *2 (-52)) (-5 *1 (-829))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-225)) (-5 *4 (-566)) (-5 *2 (-1035)) (-5 *1 (-758))))) +(((*1 *2 *3) + (-12 (-5 *3 (-566)) (|has| *1 (-6 -4408)) (-4 *1 (-406)) + (-5 *2 (-921))))) (((*1 *1 *2) (-12 (-5 *2 (-644 *3)) (-4 *3 (-1214)) (-4 *1 (-151 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-644 (-2 (|:| -2518 (-771)) (|:| -2320 *4) (|:| |num| *4)))) + (-5 *2 (-644 (-2 (|:| -3250 (-771)) (|:| -2420 *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)) (|:| -4353 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -4354 "void"))) (-5 *3 (-644 (-952 (-566)))) (-5 *4 (-112)) (-5 *1 (-439)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -4353 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-436)) (|:| -4354 "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)))) @@ -11339,24 +10376,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-713 *2 *3 *4)) (-4 *2 (-850)) (-4 *3 (-1099)) (-14 *4 - (-1 (-112) (-2 (|:| -2074 *2) (|:| -2518 *3)) - (-2 (|:| -2074 *2) (|:| -2518 *3)))))) + (-1 (-112) (-2 (|:| -2168 *2) (|:| -3250 *3)) + (-2 (|:| -2168 *2) (|:| -3250 *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 (|:| -1924 (-1175)) (|:| -2713 *4)))) + (-12 (-5 *2 (-644 (-2 (|:| -2010 (-1175)) (|:| -2818 *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) (|:| -2154 *5)))) + (-12 (-5 *3 (-644 (-2 (|:| |val| *4) (|:| -2248 *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) (|:| -2154 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2248 *4))) (-4 *3 (-13 (-1099) (-34))) (-4 *4 (-13 (-1099) (-34))) (-5 *1 (-1139 *3 *4)))) ((*1 *1 *2 *3) @@ -11379,9 +10416,49 @@ (-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 *1 *1) (-12 (-5 *1 (-608 *2)) (-4 *2 (-1099)))) - ((*1 *1 *1) (-5 *1 (-632)))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-983 *2)) (-4 *2 (-1199))))) +(((*1 *2 *1) + (-12 (-5 *2 (-644 (-2 (|:| |integrand| *3) (|:| |intvar| *3)))) + (-5 *1 (-587 *3)) (-4 *3 (-365))))) +(((*1 *1 *2) + (-12 + (-5 *2 + (-644 + (-2 + (|:| -2010 + (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) + (|:| -4344 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -2818 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1155 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4344 + (-3 (|:| |finite| "The range is finite") + (|:| |lowerInfinite| + "The bottom of range is infinite") + (|:| |upperInfinite| "The top of range is infinite") + (|:| |bothInfinite| + "Both top and bottom points are infinite") + (|:| |notEvaluated| "Range not yet evaluated")))))))) + (-5 *1 (-561))))) +(((*1 *2 *3) + (-12 (-4 *4 (-13 (-365) (-10 -8 (-15 ** ($ $ (-409 (-566))))))) + (-5 *2 (-644 *4)) (-5 *1 (-1127 *3 *4)) (-4 *3 (-1240 *4)))) + ((*1 *2 *3 *3 *3 *3 *3) + (-12 (-4 *3 (-13 (-365) (-10 -8 (-15 ** ($ $ (-409 (-566))))))) + (-5 *2 (-644 *3)) (-5 *1 (-1127 *4 *3)) (-4 *4 (-1240 *3))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1049)) (-4 *3 (-792)))) ((*1 *1 *2 *3) @@ -11389,10 +10466,10 @@ (-4 *2 (-365)) (-14 *5 (-993 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-713 *5 *6 *7)) (-4 *5 (-850)) - (-4 *6 (-238 (-2903 *4) (-771))) + (-4 *6 (-238 (-2997 *4) (-771))) (-14 *7 - (-1 (-112) (-2 (|:| -2074 *5) (|:| -2518 *6)) - (-2 (|:| -2074 *5) (|:| -2518 *6)))) + (-1 (-112) (-2 (|:| -2168 *5) (|:| -3250 *6)) + (-2 (|:| -2168 *5) (|:| -3250 *6)))) (-14 *4 (-644 (-1175))) (-4 *2 (-172)) (-5 *1 (-463 *4 *2 *5 *6 *7 *8)) (-4 *8 (-949 *2 *6 (-864 *4))))) ((*1 *1 *2 *3) @@ -11422,92 +10499,100 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-973 *4 *3 *2)) (-4 *4 (-1049)) (-4 *3 (-792)) (-4 *2 (-850))))) -(((*1 *2 *2) (-12 (-5 *2 (-381)) (-5 *1 (-1266)))) - ((*1 *2) (-12 (-5 *2 (-381)) (-5 *1 (-1266))))) -(((*1 *2 *3) - (-12 (-4 *4 (-27)) - (-4 *4 (-13 (-365) (-147) (-1038 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"void"))) + (-14 *3 (-1175)) (-14 *4 (-3 (|:| |fst| (-436)) (|:| -4354 "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)) (|:| -4353 "void"))) + (-14 *4 (-3 (|:| |fst| (-436)) (|:| -4354 "void"))) (-14 *5 (-644 (-1175))) (-14 *6 (-1179)))) ((*1 *1 *2) (-12 (-5 *2 (-332 *4)) (-4 *4 (-13 (-850) (-21))) @@ -11663,14 +10748,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-436)) (-5 *1 (-439)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3119 (-644 (-331))))) + (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3225 (-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)) (|:| -3119 (-644 (-331))))) + (-5 *2 (-2 (|:| |localSymbols| (-1179)) (|:| -3225 (-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)))) @@ -11739,7 +10824,7 @@ (-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 (|:| -3055 *3) (|:| -1878 *4)))) + (-12 (-5 *2 (-644 (-2 (|:| -3157 *3) (|:| -1966 *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) @@ -11748,25 +10833,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) - (|:| -3021 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) + (|:| -4344 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-317 (-225))) - (|:| -3021 (-644 (-1093 (-843 (-225))))) + (|:| -4344 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-769)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-317 (-225))) - (|:| -3021 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) + (|:| -4344 (-644 (-1093 (-843 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-769)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1175)) (|:| |fn| (-317 (-225))) - (|:| -3021 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) + (|:| -4344 (-1093 (-843 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-769)))) ((*1 *2 *3) (-12 (-5 *2 (-774)) (-5 *1 (-773 *3)) (-4 *3 (-1214)))) @@ -11784,23 +10869,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-317 (-225))) (|:| -2772 (-644 (-225))) + (-2 (|:| |fn| (-317 (-225))) (|:| -2759 (-644 (-225))) (|:| |lb| (-644 (-843 (-225)))) (|:| |cf| (-644 (-317 (-225)))) (|:| |ub| (-644 (-843 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-644 (-317 (-225)))) - (|:| -2772 (-644 (-225))))))) + (|:| -2759 (-644 (-225))))))) (-5 *1 (-841)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -2772 (-644 (-225))))) + (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -2759 (-644 (-225))))) (-5 *1 (-841)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-317 (-225))) (|:| -2772 (-644 (-225))) + (-2 (|:| |fn| (-317 (-225))) (|:| -2759 (-644 (-225))) (|:| |lb| (-644 (-843 (-225)))) (|:| |cf| (-644 (-317 (-225)))) (|:| |ub| (-644 (-843 (-225)))))) (-5 *1 (-841)))) @@ -11901,190 +10986,205 @@ ((*1 *1 *2) (-12 (-5 *2 (-664 *3 *4)) (-4 *3 (-850)) (-4 *4 (-172)) (-5 *1 (-1284 *3 *4))))) -(((*1 *2) (-12 (-5 *2 (-566)) (-5 *1 (-699)))) - ((*1 *2 *2) (-12 (-5 *2 (-566)) (-5 *1 (-699))))) -(((*1 *2) (-12 (-5 *2 (-644 (-1157))) (-5 *1 (-1267)))) - ((*1 *2 *2) (-12 (-5 *2 (-644 (-1157))) (-5 *1 (-1267))))) +(((*1 *2 *1) (-12 (-5 *1 (-1209 *2)) (-4 *2 (-974))))) (((*1 *2 *3) - (-12 (-4 *4 (-1049)) - (-4 *2 (-13 (-406) (-1038 *4) (-365) (-1199) (-285))) - (-5 *1 (-445 *4 *3 *2)) (-4 *3 (-1240 *4))))) -(((*1 *2 *3 *3) - (-12 (-5 *2 (-1155 (-644 (-566)))) (-5 *1 (-883)) - (-5 *3 (-644 (-566))))) - ((*1 *2 *3) - (-12 (-5 *2 (-1155 (-644 (-566)))) (-5 *1 (-883)) - (-5 *3 (-644 (-566)))))) -(((*1 *2 *2 *3) - (-12 (-5 *3 (-612 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