diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -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 | 8938 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29836 |
5 files changed, 21066 insertions, 21064 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 629877df..73d7d45c 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2264462 . 3461381193) +(2264462 . 3462551506) (-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 -1909) +(-32 R -1975) ((|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 -1909 UP UPUP -3809) +(-40 -1975 UP UPUP -2317) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4408 |has| (-409 |#2|) (-365)) (-4413 |has| (-409 |#2|) (-365)) (-4407 |has| (-409 |#2|) (-365)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 -1909) +((|HasCategory| (-409 |#2|) (QUOTE (-145))) (|HasCategory| (-409 |#2|) (QUOTE (-147))) (|HasCategory| (-409 |#2|) (QUOTE (-351))) (-2676 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2676 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2676 (-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)))) (-2676 (|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 -1975) ((|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."))) ((-4415 . T) (-4416 . T)) -((-2700 (-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|))))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|))))))) +((-2676 (-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|))))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-850))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1909) +(-54 |Base| R -1975) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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}."))) ((-4415 . T) (-4416 . 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 -3707) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2676 (-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 -3534) ((|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 -3707) +(-62 -3534) ((|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 -3707) +(-63 -3534) ((|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 -3707) +(-64 -3534) ((|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 -3707) +(-65 -3534) ((|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 -3707) +(-66 -3534) ((|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 -3707) +(-67 -3534) ((|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 -3707) +(-68 -3534) ((|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 -3707) +(-69 -3534) ((|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 -3707) +(-70 -3534) ((|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 -3707) +(-71 -3534) ((|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 -3707) +(-72 -3534) ((|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 -3707) +(-73 -3534) ((|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 -3707) +(-74 -3534) ((|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 -3707) +(-77 -3534) ((|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 -3707) +(-78 -3534) ((|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 -3707) +(-79 -3534) ((|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 -3707) +(-80 -3534) ((|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 -3707) +(-81 -3534) ((|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 -3707) +(-82 -3534) ((|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 -3707) +(-83 -3534) ((|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 -3707) +(-84 -3534) ((|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 -3707) +(-85 -3534) ((|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 -3707) +(-86 -3534) ((|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 -3707) +(-87 -3534) ((|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 -3707) +(-88 -3534) ((|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 -3707) +(-89 -3534) ((|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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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 -1909 UP) +(-115 -1975 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}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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"))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4416 . T) (-4415 . 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)))))) +((-2676 (-12 (|HasCategory| (-129) (QUOTE (-850))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1099))) (|HasCategory| (-129) (LIST (QUOTE -310) (QUOTE (-129)))))) (-2676 (-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)))) (-2676 (|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4417 "*") . T)) NIL -(-135 |minix| -3754 S T$) +(-135 |minix| -3910 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -3754 R) +(-136 |minix| -3910 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) ((-4415 . T) (-4405 . T) (-4416 . 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)))))) +((-2676 (-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{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4412 . T)) NIL -(-148 -1909 UP UPUP) +(-148 -1975 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 -1909) +(-158 R -1975) ((|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 (-1200))) (|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 -4411)) (|HasAttribute| |#2| (QUOTE -4414)) (|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})"))) -((-4408 -2700 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4411 |has| |#1| (-6 -4411)) (-4414 |has| |#1| (-6 -4414)) (-1652 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-4408 -2676 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4411 |has| |#1| (-6 -4411)) (-4414 |has| |#1| (-6 -4414)) (-1560 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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}."))) -((-4408 -2700 (|has| |#1| (-558)) (-12 (|has| |#1| (-308)) (|has| |#1| (-909)))) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4411 |has| |#1| (-6 -4411)) (-4414 |has| |#1| (-6 -4414)) (-1652 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-351))) (-2676 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2676 (-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))))) (-2676 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-12 (|HasCategory| |#1| (QUOTE (-1002))) (|HasCategory| |#1| (QUOTE (-1200)))) (|HasCategory| |#1| (QUOTE (-1200))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2676 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 (-1200)))) (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909))) (-2676 (-12 (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-365)))) (-2676 (-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 -4411)) (|HasAttribute| |#1| (QUOTE -4414)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (-12 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -900) (QUOTE (-1175))))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-308))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2676 (-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| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -1909) +(-188 R -1975) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -1909 UP UPUP R) +(-215 -1975 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 -1909 FP) +(-216 -1975 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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -1909) +(-219 R -1975) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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}."))) ((-4412 . T)) NIL -(-224 R -1909) +(-224 R -1975) ((|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}."))) -((-1645 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-1551 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,Y,Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,sy,sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4415 . T) (-4416 . 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 (-4417 "*"))) (|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))) (-2676 (-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 (-4417 "*"))) (|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 -3754 R) +(-237 S -3910 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 -4412)) (|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 -3754 R) +(-238 -3910 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"))) ((-4409 |has| |#2| (-1049)) (-4410 |has| |#2| (-1049)) (-4412 |has| |#2| (-6 -4412)) ((-4417 "*") |has| |#2| (-172)) (-4415 . T)) NIL -(-239 -3754 A B) +(-239 -3910 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 -3754 R) +(-240 -3910 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."))) ((-4409 |has| |#2| (-1049)) (-4410 |has| |#2| (-1049)) (-4412 |has| |#2| (-6 -4412)) ((-4417 "*") |has| |#2| (-172)) (-4415 . 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 -4412)) (|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}"))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -900) (QUOTE (-1175))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1049)))) (-2676 (-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))))) (-2676 (|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)))) (-2676 (|HasAttribute| |#3| (QUOTE -4412)) (-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"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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 -1909) +(-277 R -1975) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-278 R -1909) +(-278 R -1975) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1088,7 +1088,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-290 S R |Mod| -2361 -1485 |exactQuo|) +(-290 S R |Mod| -3007 -4374 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL @@ -1110,21 +1110,21 @@ NIL NIL (-295 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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 -1909 S) +(-298 -1975 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 -1909) +(-299 E -1975) ((|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 -1909) +(-311 -1975) ((|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))}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2700 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2700 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-1175)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (QUOTE (-538)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-1022))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (-2676 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-820))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-850)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-1150))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-381)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -886) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-381))))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -516) (QUOTE (-1175)) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -310) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (LIST (QUOTE -287) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1251) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-308))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-547))) (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-850))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-909))) (|HasCategory| $ (QUOTE (-145)))) (-2676 (|HasCategory| (-1251 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1251 |#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."))) -((-4412 -2700 (-3360 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (-12 (|has| |#1| (-558)) (-2700 (-3360 (|has| |#1| (-1049)) (|has| |#1| (-639 (-566)))) (|has| |#1| (-1049)) (|has| |#1| (-475)))) (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4410 |has| |#1| (-172)) (-4409 |has| |#1| (-172)) ((-4417 "*") |has| |#1| (-558)) (-4408 |has| |#1| (-558)) (-4413 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(-1111)))) (-2676 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1049))) (|HasCategory| |#1| (LIST (QUOTE -639) (QUOTE (-566)))))) (-2676 (|HasCategory| |#1| (QUOTE (-475))) (|HasCategory| |#1| (QUOTE (-1049)))) (-2676 (-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 -1975) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1211,7 +1211,7 @@ NIL (-320 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (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))) (-2676 (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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."))) ((-4416 . T) (-4415 . 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 -1909) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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 -1975) ((|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 -1909) +(-330 -1975) ((|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 -1909 UP UPUP R) +(-336 S -1975 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 -1909 UP UPUP R) +(-337 -1975 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 -1909 UP UPUP R) +(-338 -1975 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 -1909 UP UPUP) +(-343 S -1975 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-365)))) -(-344 -1909 UP UPUP) +(-344 -1975 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4408 |has| (-409 |#2|) (-365)) (-4413 |has| (-409 |#2|) (-365)) (-4407 |has| (-409 |#2|) (-365)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL -(-352 R UP -1909) +(-352 R UP -1975) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-353 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2676 (|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}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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)))) +((-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) -(-358 -1909 GF) +((-2676 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +(-358 -1975 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 -1909 FP FPP) +(-360 -1975 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-361 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2676 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-370)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-145)))) (-362 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1454,7 +1454,7 @@ NIL NIL (-381) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,exponent,\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{pi},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4398 . T) (-4406 . T) (-1645 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-4398 . T) (-4406 . T) (-1551 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 -1909 UP UPUP R) +(-394 -1975 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 -3707 |returnType| -3721 |symbols|) +(-400 -3534 |returnType| -3099 |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 -1909 UP) +(-401 -1975 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1554,7 +1554,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4398)) (|HasAttribute| |#1| (QUOTE -4406))) (-406) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-1645 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-1551 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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."))) ((-4402 -12 (|has| |#1| (-6 -4413)) (|has| |#1| (-454)) (|has| |#1| (-6 -4402))) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 -4413)) (|HasAttribute| |#1| (QUOTE -4402)) (|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))) (-2676 (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828)))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538))))) (|HasCategory| |#1| (QUOTE (-1022))) (|HasCategory| |#1| (QUOTE (-820))) (-2676 (|HasCategory| |#1| (QUOTE (-820))) (|HasCategory| |#1| (QUOTE (-850)))) (-2676 (-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)))) (-2676 (-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))))) (-2676 (|HasCategory| |#1| (LIST (QUOTE -614) (LIST (QUOTE -892) (QUOTE (-566))))) (-12 (|HasCategory| |#1| (QUOTE (-547))) (|HasCategory| |#1| (QUOTE (-828))))) (-2676 (|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 -4413)) (|HasAttribute| |#1| (QUOTE -4402)) (|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)))) (-2676 (-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|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1588,11 +1588,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-415 R -1909 UP A) +(-415 R -1975 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4412 . T)) NIL -(-416 R -1909 UP A |ibasis|) +(-416 R -1975 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."))) ((-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 (-1219))) (-2700 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1219)))) (|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 (-1219))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-1219)))) (|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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4415 . T) (-4405 . T) (-4416 . T)) NIL -(-428 R -1909) +(-428 R -1975) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1648,7 +1648,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4402 -12 (|has| |#1| (-6 -4402)) (|has| |#2| (-6 -4402))) (-4409 . T) (-4410 . T) (-4412 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4402)) (|HasAttribute| |#2| (QUOTE -4402)))) -(-430 R -1909) +(-430 R -1975) ((|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| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4412 -2700 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4410 |has| |#1| (-172)) (-4409 |has| |#1| (-172)) ((-4417 "*") |has| |#1| (-558)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-558)) (-4407 |has| |#1| (-558))) +((-4412 -2676 (|has| |#1| (-1049)) (|has| |#1| (-475))) (-4410 |has| |#1| (-172)) (-4409 |has| |#1| (-172)) ((-4417 "*") |has| |#1| (-558)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-558)) (-4407 |has| |#1| (-558))) NIL -(-433 R -1909) +(-433 R -1975) ((|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 -1909) +(-434 R -1975) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-435 R -1909) +(-435 R -1975) ((|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 -1909 UP) +(-437 R -1975 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 -1909) +(-445 R UP -1975) ((|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"))) (((-4417 "*") |has| |#2| (-172)) (-4408 |has| |#2| (-558)) (-4413 |has| |#2| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (-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| -1909 R) +(-473 |lv| -1975 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."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (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))) (-2676 (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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."))) ((-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#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 (|:| -2334 |#1|) (|:| -2303 |#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 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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)}"))) ((-4416 . T) (-4415 . 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."))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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"))) (((-4417 "*") |has| |#2| (-172)) (-4408 |has| |#2| (-558)) (-4413 |has| |#2| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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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))))) (-2676 (|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 -4412)) (|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}."))) ((-4415 . T) (-4416 . 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 -1909 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2676 (-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 -1975 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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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 -1909 UP |AlExt| |AlPol|) +(-496 -1975 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."))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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 -1909) +(-501 R UP -1975) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1952,7 +1952,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-506 -1909 |Expon| |VarSet| |DPoly|) +(-506 -1975 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}"))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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)))) +((-2676 (|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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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."))) ((-4415 . T) (-4416 . 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 (-4417 "*"))) (|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))) (-2676 (-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 (-4417 "*"))) (|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 -1909 |Par|) +(-534 K -1975 |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 -1909 |Par|) +(-540 K -1975 |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}."))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) -(-553 R -1909) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +(-553 R -1975) ((|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 -1909 UP UPUP R) +(-554 R0 -1975 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."))) -((-1645 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-1551 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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."))) ((-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL -(-559 R -1909) +(-559 R -1975) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -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 -1909 L) +(-562 R -1975 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -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 -1909 UP UPUP R) +(-564 -1975 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 -1909 UP) +(-565 -1975 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 -1909 L) +(-568 R -1975 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -656) (|devaluate| |#2|)))) -(-569 R -1909) +(-569 R -1975) ((|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 -1909 UP) +(-570 -1975 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -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 -1909) +(-572 -1975) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-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."))) -((-1645 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-1551 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-575 R -1909) +(-575 R -1975) ((|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 -1909 UP) +(-576 -1975 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p, ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f, ')} returns \\spad{[ir, s, p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p, foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-577 R -1909) +(-577 R -1975) ((|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 -1909) +(-585 R -1975) ((|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 -1909) +(-586 E -1975) ((|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 -1909) +(-587 -1975) ((|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}."))) ((-4410 . T) (-4409 . 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"))) ((-4416 . T) (-4415 . 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)))))) +((-2676 (-12 (|HasCategory| (-144) (QUOTE (-850))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1099))) (|HasCategory| (-144) (LIST (QUOTE -310) (QUOTE (-144)))))) (-2676 (|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)))) (-2676 (|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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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))) (-2676 (|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 -2725) (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.}"))) ((-4410 |has| |#1| (-558)) (-4409 |has| |#1| (-558)) ((-4417 "*") |has| |#1| (-558)) (-4408 |has| |#1| (-558)) (-4412 . 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 -1909 FG) +(-600 R -1975 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -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."))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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)."))) -((-4412 -2700 (-3360 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4410 . T) (-4409 . 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|)))) +((-4412 -2676 (-3144 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4410 . T) (-4409 . T)) +((-2676 (|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|)))) (-2676 (-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."))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 |#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 (|:| -2334 (-1157)) (|:| -2303 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 |#1|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 |#1|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 |#1|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 |#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 (|:| -3476 (-1157)) (|:| -2484 |#1|)) (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 |#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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-615 -1909 UP) +(-615 -1975 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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}."))) ((-4409 . T) (-4410 . T) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-848)))) -(-622 R -1909) +(-622 R -1975) ((|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| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-630 R -1909) +(-630 R -1975) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-631 |lv| -1909) +(-631 |lv| -1975) ((|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."))) ((-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2303) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-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 (|:| -2334 (-1157)) (|:| -2303 (-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 (|:| -2334 (-1157)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (QUOTE (-1157))) (LIST (QUOTE |:|) (QUOTE -2484) (QUOTE (-52))))))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-1157) (QUOTE (-850))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-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 (|:| -3476 (-1157)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 (-1157)) (|:| -2484 (-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)."))) -((-4412 -2700 (-3360 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4410 . T) (-4409 . 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|)))) +((-4412 -2676 (-3144 (|has| |#2| (-369 |#1|)) (|has| |#1| (-558))) (-12 (|has| |#2| (-419 |#1|)) (|has| |#1| (-558)))) (-4410 . T) (-4409 . T)) +((-2676 (|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|)))) (-2676 (-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 -((-3348 (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-365)))) +((-3129 (|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4412 . T)) @@ -2507,7 +2507,7 @@ NIL (-644 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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} is the empty list."))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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 -1909 L) +(-652 R -1975 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}."))) ((-4409 . T) (-4410 . T) (-4412 . T)) NIL -(-657 -1909 UP) +(-657 -1975 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 -3328) +(-658 A -3209) ((|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}}"))) ((-4409 . T) (-4410 . T) (-4412 . 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}."))) ((-4416 . T) (-4415 . T)) NIL -(-667 -1909) +(-667 -1975) ((|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 -1909 |Row| |Col| M) +(-668 -1975 |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."))) ((-4412 . T) (-4415 . T) (-4409 . T) (-4410 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4417 "*"))) (|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 (-4417 "*"))) (|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 (-4417 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2676 (-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))) (-2676 (|HasAttribute| |#2| (QUOTE (-4417 "*"))) (|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|))))) +((-2676 (-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))) (-2676 (-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."))) ((-4415 . T) (-4416 . 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 (-4417 "*"))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2676 (-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))) (-2676 (-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 (-4417 "*"))) (|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 -1909 FLAF FLAS) +(-692 S -1975 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"))) -((-4408 . T) (-4413 |has| (-699) (-365)) (-4407 |has| (-699) (-365)) (-1652 . T) (-4414 |has| (-699) (-6 -4414)) (-4411 |has| (-699) (-6 -4411)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 (-1200))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1200)))) (-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 (-1200)))) (|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 -4414)) (|HasAttribute| (-699) (QUOTE -4411)) (-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))))) +((-4408 . T) (-4413 |has| (-699) (-365)) (-4407 |has| (-699) (-365)) (-1560 . T) (-4414 |has| (-699) (-6 -4414)) (-4411 |has| (-699) (-6 -4411)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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))) (-2676 (|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))))) (-2676 (|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 (-1200))) (-12 (|HasCategory| (-699) (QUOTE (-1002))) (|HasCategory| (-699) (QUOTE (-1200)))) (-2676 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365))) (-12 (|HasCategory| (-699) (QUOTE (-351))) (|HasCategory| (-699) (QUOTE (-909))))) (-2676 (-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 (-1200)))) (|HasCategory| (-699) (QUOTE (-1059))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909))) (-2676 (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-365)))) (-2676 (-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 -4414)) (|HasAttribute| (-699) (QUOTE -4411)) (-12 (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-699) (QUOTE (-308))) (|HasCategory| (-699) (QUOTE (-909)))) (|HasCategory| (-699) (QUOTE (-145)))) (-2676 (-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}."))) ((-4416 . 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 -1909 PG) +(-698 OV E -1975 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}"))) -((-1645 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) +((-1551 . T) (-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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 -3218 I) +(-706 S -1316 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| -2361 -1485 |exactQuo|) +(-711 R |Mod| -3007 -4374 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL (-712 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4411 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|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)))) (-2676 (|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))))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4410 |has| |#1| (-172)) (-4409 |has| |#1| (-172)) (-4412 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-715 R |Mod| -2361 -1485 |exactQuo|) +(-715 R |Mod| -3007 -4374 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4412 . T)) NIL @@ -2800,7 +2800,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4410 . T) (-4409 . T)) NIL -(-718 -1909) +(-718 -1975) ((|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]]}."))) ((-4412 . 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 -1909 UP) +(-727 -1975 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."))) (((-4417 "*") |has| |#2| (-172)) (-4408 |has| |#2| (-558)) (-4413 |has| |#2| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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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 -1909) +(-765 -1975) ((|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 -1909) +(-766 P -1975) ((|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 -1909) +(-768 UP -1975) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -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."))) (((-4417 "*") . T)) NIL -(-772 R -1909) +(-772 R -1975) ((|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 -1909 |ExtF| |SUEx| |ExtP| |n|) +(-777 -1975 |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."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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(-566))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-3129 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-566))))) (-3129 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -614) (QUOTE (-1175)))) (-3129 (|HasCategory| |#1| (LIST (QUOTE -992) (QUOTE (-566))))))) (|HasAttribute| |#1| (QUOTE -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-781 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3059,7 +3059,7 @@ NIL (-782 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4411 |has| |#1| (-365)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 (-233))) (|HasAttribute| |#1| (QUOTE -4413)) (|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))) (-2676 (|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)))) (-2676 (|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))))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) (-783 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,r)} \\undocumented"))) NIL @@ -3120,23 +3120,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4409 . T) (-4410 . T) (-4412 . T)) NIL -(-798 -2700 R OS S) +(-798 -2676 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-799 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4409 . T) (-4410 . T) (-4412 . 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|))) (-2676 (|HasCategory| (-999 |#1|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (|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 -1909 L) +(-801 R -1975 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-802 R -1909) +(-802 R -1975) ((|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 -1909) +(-804 R -1975) ((|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 -1909 UP UPUP R) +(-806 -1975 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 -1909 UP L LQ) +(-807 -1975 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 -1909 UP L LQ) +(-809 -1975 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk, Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-810 -1909 UP) +(-810 -1975 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 -1909 L UP A LO) +(-811 -1975 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 -1909 UP) +(-812 -1975 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op, zeros)} returns \\spad{[[p1, L1], [p2, L2], ... , [pk,Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-813 -1909 LO) +(-813 -1975 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 -1909 LODO) +(-814 -1975 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. 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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))))) (-2676 (|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 -4412)) (|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"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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."))) (((-4417 "*") |has| |#2| (-365)) (-4408 |has| |#2| (-365)) (-4413 |has| |#2| (-365)) (-4407 |has| |#2| (-365)) (-4412 . T) (-4410 . T) (-4409 . 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."))) ((-4412 |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))) (-2676 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2676 (|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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4412 |has| |#1| (-848))) -((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2700 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2700 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) +((|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (QUOTE (-21))) (-2676 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-848)))) (|HasCategory| |#1| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (-2676 (|HasCategory| |#1| (QUOTE (-848))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566))))) (|HasCategory| |#1| (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-547)))) (-844) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-845 -3754 S) +(-845 -3910 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| -2912) +(-854 R |sigma| -3560) ((|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."))) ((-4409 . T) (-4410 . T) (-4412 . 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| -2912) +(-855 |x| R |sigma| -3560) ((|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}."))) ((-4409 . T) (-4410 . T) (-4412 . 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)."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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)}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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)))) (-2676 (-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 (-3348 (|HasCategory| |#2| (QUOTE (-1049)))) (-3348 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-3348 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175))))) +((-12 (-3129 (|HasCategory| |#2| (QUOTE (-1049)))) (-3129 (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-1175)))))) (-12 (|HasCategory| |#2| (QUOTE (-1049))) (-3129 (|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 -3218) +(-890 R -1316) ((|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 -1909) +(-896 UP -1975) ((|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))) (-2676 (-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."))) ((-4412 . T)) -((-2700 (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) (|HasCategory| |#1| (QUOTE (-370))) (|HasCategory| |#1| (QUOTE (-850)))) +((-2676 (|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 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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-370)))) -(-911 R0 -1909 UP UPUP R) +(-911 R0 -1975 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(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-918 -1909) +(-918 -1975) ((|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}."))) (((-4417 "*") . T)) NIL -(-922 -1909 P) +(-922 -1975 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-923 |xx| -1909) +(-923 |xx| -1975) ((|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 -1909) +(-929 R -1975) ((|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 -1909) +(-932 S R -1975) ((|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 -1909 -3218) +(-937 R -1975 -1316) ((|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 -3218) +(-938 -1316) ((|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"))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . T)) NIL -(-950 E V R P -1909) +(-950 E V R P -1975) ((|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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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 -1909) +((|HasCategory| |#1| (QUOTE (-909))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-953 E V R P -1975) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-454)))) @@ -3763,12 +3763,12 @@ NIL (-958 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4416 . T) (-4415 . T)) -((-2700 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2700 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -614) (QUOTE (-538)))) (-2676 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099)))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| (-566) (QUOTE (-850))) (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-959) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -1909) +(-960 -1975) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1, a1, p2, a2)} returns \\spad{[c1, c2, q]} such that \\spad{k(a1, a2) = k(a)} where \\spad{a = c1 a1 + c2 a2, and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -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}"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4409 . T) (-4410 . T) (-4412 . 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 -4413))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2676 (|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 -4413))) (-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"))) ((-4412 -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))))) +((-2676 (-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)))) (-2676 (-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)))) (-2676 (-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)))) (-2676 (-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)))) (-2676 (-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 -1909) +(-985 K R UP -1975) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -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.}"))) ((-4408 |has| |#1| (-291)) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (|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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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 -1909 UP UPUP |radicnd| |n|) +(-1003 -1975 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4408 |has| (-409 |#2|) (-365)) (-4413 |has| (-409 |#2|) (-365)) (-4407 |has| (-409 |#2|) (-365)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (|HasCategory| (-409 |#2|) (QUOTE (-365))) (|HasCategory| (-409 |#2|) (QUOTE (-370))) (-2676 (-12 (|HasCategory| (-409 |#2|) (QUOTE (-233))) (|HasCategory| (-409 |#2|) (QUOTE (-365)))) (|HasCategory| (-409 |#2|) (QUOTE (-351)))) (-2676 (-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)))) (-2676 (|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."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|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)))) (-2676 (-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}}"))) ((-4408 . T) (-4413 . T) (-4407 . T) (-4410 . T) (-4409 . T) ((-4417 "*") . T) (-4412 . T)) NIL -(-1013 R -1909) +(-1013 R -1975) ((|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 -1909) +(-1014 R -1975) ((|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 -1909 UP) +(-1015 -1975 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 -1909 UP) +(-1016 -1975 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"))) ((-4408 . T) (-4413 . T) (-4407 . T) (-4410 . T) (-4409 . T) ((-4417 "*") . T) (-4412 . 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 -1909 L) +((-2676 (|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 -1975 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -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 -1909 |Expon| |VarSet| |FPol| |LFPol|) +(-1034 -1975 |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"))) (((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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.}"))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2303) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2484) (QUOTE (-52))))))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) (-1036) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4128,7 +4128,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4412 . T)) NIL -(-1050 |xx| -1909) +(-1050 |xx| -1975) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4147,7 +4147,7 @@ NIL (-1054 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4415 . T) (-4410 . T) (-4409 . 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))) (-2676 (-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)))) (-2676 (|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}"))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2303) (QUOTE (-52))))))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (QUOTE (-1175))) (LIST (QUOTE |:|) (QUOTE -2484) (QUOTE (-52))))))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-52) (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| (-52) (QUOTE (-1099))) (|HasCategory| (-52) (LIST (QUOTE -310) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (QUOTE (-1099))) (|HasCategory| (-1175) (QUOTE (-850))) (|HasCategory| (-52) (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-52) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 (-1175)) (|:| -2484 (-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 -1909) +(-1075 |Base| R -1975) ((|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 -1909) +(-1076 |Base| R -1975) ((|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."))) ((-4408 |has| |#1| (-365)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . 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))) (-2676 (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-351)))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-370))) (-2676 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-365)))) (|HasCategory| |#1| (QUOTE (-351)))) (-2676 (-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)))) (-2676 (|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"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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)}}"))) ((-4415 . T) (-4405 . T) (-4416 . 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|))))) +((-2676 (-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{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}."))) ((-4409 |has| |#3| (-1049)) (-4410 |has| |#3| (-1049)) (-4412 |has| |#3| (-6 -4412)) ((-4417 "*") |has| |#3| (-172)) (-4415 . T)) -((-2700 (-12 (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-365))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-370))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-726))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-793))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-848))) (|HasCategory| |#3| (LIST (QUOTE -310) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1049))) (|HasCategory| |#3| (LIST 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|#3| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#3| (QUOTE (-1099)))) (|HasAttribute| |#3| (QUOTE -4412)) (|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 -1909) +(-1115 R -1975) ((|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."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (|HasCategory| |#1| (QUOTE (-454))) (|HasCategory| |#1| (QUOTE (-909)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-172))) (-2676 (|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)))) (-2676 (|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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4410 . T) (-4409 . T) (-4412 . 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))) (-2676 (|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}"))) ((-4416 . T) (-4415 . T)) NIL -(-1127 UP -1909) +(-1127 UP -1975) ((|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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2700 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))) (-2676 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862)))) (-12 (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -310) (LIST (QUOTE -1139) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1139 |#1| |#2|) (QUOTE (-1099))))) (|HasCategory| (-1139 |#1| |#2|) (LIST (QUOTE -613) (QUOTE (-862))))) (-1141 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4412 . T) (-4404 |has| |#2| (-6 (-4417 "*"))) (-4415 . T) (-4409 . T) (-4410 . T)) -((|HasCategory| |#2| (LIST (QUOTE -900) (QUOTE (-1175)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4417 "*"))) (|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 (-4417 "*"))) (|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 (-4417 "*"))) (|HasCategory| |#2| (LIST (QUOTE -639) (QUOTE (-566)))) (|HasCategory| |#2| (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (LIST (QUOTE -1038) (QUOTE (-566)))) (-2676 (-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))) (-2676 (|HasAttribute| |#2| (QUOTE (-4417 "*"))) (|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}."))) ((-4415 . T) (-4416 . 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))) (-2676 (-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."))) ((-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#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 (|:| -2334 |#1|) (|:| -2303 |#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 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099)))) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-850))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#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."))) ((-4416 . 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))) (-2676 (-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"))) ((-4416 . T) (-4415 . T)) @@ -4559,11 +4559,11 @@ NIL (-1157) NIL ((-4416 . T) (-4415 . 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)))))) +((-2676 (-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."))) ((-4415 . T) (-4416 . 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,a1,...] * r = [a0 * r,a1 * r,...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,a1,...] = [r * a0,r * a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL @@ -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. 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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 -4413)) (|HasCategory| |#1| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-909)))) (-2676 (-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,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (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))) (-2676 (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1173 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1174) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4639,7 +4639,7 @@ NIL (-1177 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-6 -4413)) (-4409 . T) (-4410 . T) (-4412 . 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 -4413))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2676 (|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 -4413))) (-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 @@ -4683,7 +4683,7 @@ NIL (-1188 |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}"))) ((-4415 . T) (-4416 . T)) -((-12 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2334) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2303) (|devaluate| |#2|)))))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2700 (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -310) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3476) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2484) (|devaluate| |#2|)))))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#2| (QUOTE (-1099)))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -614) (QUOTE (-538)))) (-12 (|HasCategory| |#2| (QUOTE (-1099))) (|HasCategory| |#2| (LIST (QUOTE -310) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (QUOTE (-1099))) (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#2| (QUOTE (-1099))) (-2676 (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#2| (LIST (QUOTE -613) (QUOTE (-862)))) (|HasCategory| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (LIST (QUOTE -613) (QUOTE (-862))))) (-1189 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL @@ -4735,7 +4735,7 @@ NIL (-1201 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4416 . T) (-4415 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2700 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) +((-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1099))) (-2676 (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (|HasCategory| |#1| (LIST (QUOTE -613) (QUOTE (-862))))) (-1202 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4744,7 +4744,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1204 R -1909) +(-1204 R -1975) ((|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 @@ -4752,7 +4752,7 @@ 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 -(-1206 R -1909) +(-1206 R -1975) ((|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|))))) @@ -4767,7 +4767,7 @@ NIL (-1209 |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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4410 . T) (-4409 . T) (-4412 . 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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-558)))) (|HasCategory| |#1| (QUOTE (-558))) (|HasCategory| |#1| (QUOTE (-365)))) (-1210 |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 @@ -4780,7 +4780,7 @@ 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))))) -(-1213 -1909) +(-1213 -1975) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) 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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 @@ -4883,7 +4883,7 @@ NIL (-1238 |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}"))) (((-4417 "*") |has| |#2| (-172)) (-4408 |has| |#2| (-558)) (-4411 |has| |#2| (-365)) (-4413 |has| |#2| (-6 -4413)) (-4410 . T) (-4409 . T) (-4412 . 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 -4413)) (|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))) (-2676 (|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)))) (-2676 (|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))))) (-2676 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (|HasCategory| |#2| (QUOTE (-365))) (|HasCategory| |#2| (QUOTE (-454))) (|HasCategory| |#2| (QUOTE (-558))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (|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 -4413)) (|HasCategory| |#2| (QUOTE (-454))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (-2676 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-909)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1239 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 @@ -4899,7 +4899,7 @@ NIL (-1242 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 -1650) (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 -2725) (LIST (|devaluate| |#2|) (QUOTE (-1175)))))) (-1243 |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."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4409 . T) (-4410 . T) (-4412 . T)) @@ -4927,15 +4927,15 @@ NIL (-1249 |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)}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (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))) (-2676 (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566)))))) (-1250 |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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4413 |has| |#1| (-365)) (-4407 |has| |#1| (-365)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (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))) (-2676 (|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))) (-2676 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-365))) (|HasCategory| |#1| (QUOTE (-558)))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -409) (QUOTE (-566)))))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1251 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))}."))) (((-4417 "*") |has| (-1250 |#2| |#3| |#4|) (-172)) (-4408 |has| (-1250 |#2| |#3| |#4|) (-558)) (-4409 . T) (-4410 . T) (-4412 . T)) -((|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-172))) (-2700 (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-558)))) +((|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-172))) (-2676 (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566)))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| (-1250 |#2| |#3| |#4|) (LIST (QUOTE -1038) (QUOTE (-566)))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-365))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-454))) (|HasCategory| (-1250 |#2| |#3| |#4|) (QUOTE (-558)))) (-1252 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4951,7 +4951,7 @@ NIL (-1255 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-1200))) (|HasSignature| |#2| (LIST (QUOTE -3981) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3613) (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 (-1200))) (|HasSignature| |#2| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -4235) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1175))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#2| (QUOTE (-365)))) (-1256 |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."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4409 . T) (-4410 . T) (-4412 . T)) @@ -4959,12 +4959,12 @@ NIL (-1257 |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}."))) (((-4417 "*") |has| |#1| (-172)) (-4408 |has| |#1| (-558)) (-4409 . T) (-4410 . T) (-4412 . 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 -1650) (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 (-1200))) (|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 -3613) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -3981) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -409) (QUOTE (-566))))) (|HasCategory| |#1| (QUOTE (-558))) (-2676 (|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 -2725) (LIST (|devaluate| |#1|) (QUOTE (-1175)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-771))))) (|HasCategory| |#1| (QUOTE (-365))) (-2676 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-566)))) (|HasCategory| |#1| (QUOTE (-959))) (|HasCategory| |#1| (QUOTE (-1200))) (|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 -4235) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1175))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -644) (QUOTE (-1175))) (|devaluate| |#1|))))))) (-1258 |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 -(-1259 -1909 UP L UTS) +(-1259 -1975 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)))) @@ -4991,7 +4991,7 @@ NIL (-1265 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."))) ((-4416 . T) (-4415 . 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|))))) +((-2676 (-12 (|HasCategory| |#1| (QUOTE (-850))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1099))) (|HasCategory| |#1| (LIST (QUOTE -310) (|devaluate| |#1|))))) (-2676 (-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)))) (-2676 (|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|))))) (-1266) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5024,7 +5024,7 @@ 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 -(-1274 K R UP -1909) +(-1274 K R UP -1975) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL @@ -5060,11 +5060,11 @@ 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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4408 |has| |#2| (-6 -4408)) (-4410 . T) (-4409 . T) (-4412 . T)) NIL -(-1283 S -1909) +(-1283 S -1975) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-370))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1284 -1909) +(-1284 -1975) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4407 . T) (-4413 . T) (-4408 . T) ((-4417 "*") . T) (-4409 . T) (-4410 . T) (-4412 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index a895d814..ded6c6e1 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(188047 . 3461381200) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) #0#) |has| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (-310 (-2 (|:| -2334 |#1|) (|:| -2303 |#2|))))) -((((-566)) . T) (($) -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)) +(188047 . 3462551513) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) #0#) |has| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (-310 (-2 (|:| -3476 |#1|) (|:| -2484 |#2|))))) +((((-566)) . T) (($) -2676 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (((-409 (-566))) -2676 (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-1038 (-409 (-566))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-566)) . T)) -((($ $) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((|#2| |#2|) . T) ((#0=(-409 (-566)) #0#) |has| |#2| (-38 (-409 (-566))))) +((($ $) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((|#2| |#2|) . T) ((#0=(-409 (-566)) #0#) |has| |#2| (-38 (-409 (-566))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2|) . T)) -((($) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566))))) +((($) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566))))) (|has| |#1| (-909)) ((((-862)) . T)) ((((-862)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-862)) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) -((($ $) . T) ((#0=(-409 (-566)) #0#) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) -(-2700 (|has| |#1| (-820)) (|has| |#1| (-850))) +(-2676 (|has| |#1| (-21)) (|has| |#1| (-848))) +((($ $) . T) ((#0=(-409 (-566)) #0#) -2676 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1| |#1|) . T)) +(-2676 (|has| |#1| (-820)) (|has| |#1| (-850))) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) ((((-862)) . T)) ((((-862)) . 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T) (($) -2676 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909)))) +((($) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -248,10 +248,10 @@ ((((-169 (-225))) |has| |#1| (-1022)) (((-169 (-381))) |has| |#1| (-1022)) (((-538)) |has| |#1| (-614 (-538))) (((-1171 |#1|)) . T) (((-892 (-566))) |has| |#1| (-614 (-892 (-566)))) (((-892 (-381))) |has| |#1| (-614 (-892 (-381))))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1|) . 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T)) (-12 (|has| |#4| (-233)) (|has| |#4| (-1049))) (-12 (|has| |#3| (-233)) (|has| |#3| (-1049))) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2676 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2676 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-1180)) . T)) @@ -269,14 +269,14 @@ (((|#1|) . T)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) (((|#1|) . T) (((-566)) |has| |#1| (-639 (-566)))) -(((|#2|) . T) (((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) -(((|#1|) . T) (((-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))) . T)) +(((|#2|) . T) (((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))) . 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T)) (|has| |#1| (-558)) (|has| |#1| (-558)) @@ -289,21 +289,21 @@ ((((-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))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (((-1173 |#1| |#2| |#3|)) |has| |#1| (-365)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) . T)) (((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) (($) . 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T)) ((((-409 $) (-409 $)) |has| |#2| (-558)) (($ $) . T) ((|#2| |#2|) . T)) -((((-2 (|:| -2334 (-1157)) (|:| -2303 (-52)))) . T)) +((((-2 (|:| -3476 (-1157)) (|:| -2484 (-52)))) . T)) (((|#1|) . T)) (|has| |#2| (-909)) ((((-1157) (-52)) . T)) ((((-566)) |has| #0=(-409 |#2|) (-639 (-566))) ((#0#) . T)) ((((-538)) . T) (((-225)) . T) (((-381)) . T) (((-892 (-381))) . T)) ((((-862)) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2676 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((|#1|) |has| |#1| (-172))) (((|#1| $) |has| |#1| (-287 |#1| |#1|))) ((((-862)) . T)) @@ -332,15 +332,15 @@ (|has| |#1| (-1099)) ((((-910 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) (((|#1|) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2676 (|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)) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) ((((-1180)) . 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T)) (((|#1| (-971)) . T)) ((((-566)) . T) ((|#2|) . T)) @@ -350,7 +350,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1150)) -((((-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))) . T)) +((((-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))) . T)) (|has| (-1251 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1251 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -362,27 +362,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-566)) |has| |#2| (-639 (-566)))) -((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-818 (-1175))) . T) (($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . T)) +((((-1124 |#1| (-1175))) . T) (((-566)) . T) (((-818 (-1175))) . T) (($) -2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-1175)) . 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T)) -((($) -2700 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-862)) . T)) ((((-862)) . T)) (|has| (-1250 |#2| |#3| |#4|) (-147)) @@ -393,16 +393,16 @@ ((((-862)) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2676 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((|#1|) . T)) ((((-566) |#1|) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2676 (|has| |#1| (-21)) (|has| |#1| (-848))) ((((-862)) |has| |#1| (-1099))) -(-2700 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)) (|has| |#1| (-1111))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-910 |#1|)) . T)) ((((-409 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-566) |#1|))) @@ -413,7 +413,7 @@ ((((-862)) . 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T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($ $) -2676 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) (|has| |#1| (-1099)) (((|#2| (-819 |#1|)) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) @@ -468,20 +468,20 @@ (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) -((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) (((|#2|) . T) ((|#6|) . T)) (|has| |#1| (-365)) ((((-566)) . T) ((|#2|) . T)) -((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . 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T)) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((((-409 (-566))) . T)) (|has| |#1| (-370)) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-566)) . T)) ((((-566)) . T)) (((|#1|) . T) (((-566)) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) ((((-862)) . T)) ((((-862)) . T)) (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) @@ -536,10 +536,10 @@ ((((-566) |#4|) . T)) ((((-566) |#3|) . T)) (((|#1|) . T) (((-566)) |has| |#1| (-639 (-566)))) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((((-1251 |#1| |#2| |#3| |#4|)) . 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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))) +(-2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-172)) (|has| |#1| (-558))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-1265 |#1|) (-1265 |#1|)) . T)) ((((-566) (-144)) . T)) ((($) . T)) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2676 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2676 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-1180)) . T) (((-862)) . T)) ((((-1180)) . T)) ((((-862)) . T)) @@ -980,20 +980,20 @@ (((|#1| (-971)) . T)) (((|#1| |#1|) . T)) ((($) . T)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2676 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2676 (|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))) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((($) . T) (((-566)) . T) (((-870 |#1|)) . T) (((-409 (-566))) . T)) (((|#1|) . T)) (|has| |#2| (-793)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2676 (|has| |#2| (-793)) (|has| |#2| (-848))) (((|#1| |#2|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#2| (-848)) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) (-12 (|has| |#1| (-793)) (|has| |#2| (-793))) -(-2700 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) +(-2676 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-172)) ((|#4|) . T) (((-566)) . T)) (((|#2|) |has| |#2| (-172))) @@ -1005,7 +1005,7 @@ (((|#1|) . T)) ((((-409 (-566))) . T) (($) . T)) (((|#2|) . T) (($) . T) (((-409 (-566))) . T)) -((($) . T) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) ((|#1|) . T)) (|has| |#1| (-828)) ((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) |has| |#1| (-1038 (-566))) ((|#1|) . T)) (|has| |#1| (-1099)) @@ -1016,13 +1016,13 @@ (((|#4|) |has| |#4| (-1099))) (((|#3|) |has| |#3| (-1099))) (|has| |#3| (-370)) -((($) |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))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1257 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +((($) |has| |#1| (-558)) ((|#1|) . T) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-1038 (-409 (-566))))) (((-566)) . T)) +((((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2676 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1257 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) ((((-862)) . T)) ((((-862)) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558)))) +(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2676 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#1| |#1|) |has| |#1| (-172))) (|has| |#2| (-365)) @@ -1030,19 +1030,19 @@ (((|#1|) |has| |#1| (-172))) ((((-409 (-566))) . T) (((-566)) . T)) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) . T)) -((($ $) -2700 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) +((($ $) -2676 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) |has| |#1| (-38 (-409 (-566))))) ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) ((($) . T) (((-566)) . T)) -((($) -2700 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|has| |#1| (-172)) (|has| |#1| (-558))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) ((((-144)) . T)) (((|#1|) . T)) -((($) -2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) +((($) -2676 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) ((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049)))) ((((-144)) . T)) ((((-144)) . T)) ((((-409 (-566))) . #0=(|has| |#2| (-365))) (($) . #0#) ((|#2|) . T) (((-566)) . T)) (((|#1| |#2| |#3|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-558)) (|has| |#1| (-1049))) +(-2676 (|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)) @@ -1052,15 +1052,15 @@ ((((-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))) +(-2676 (|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))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-558)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) @@ -1071,7 +1071,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-848)) -(((|#2| (-240 (-4142 |#1|) (-771)) (-864 |#1|)) . T)) +(((|#2| (-240 (-3991 |#1|) (-771)) (-864 |#1|)) . T)) (|has| |#3| (-848)) (((|#1| (-533 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -1086,20 +1086,20 @@ (|has| |#1| (-145)) ((((-409 (-566))) |has| |#2| (-365)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2700 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2676 (|has| |#1| (-351)) (|has| |#1| (-370))) ((((-1141 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1049))) -(((|#2|) . T) (((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(((|#2|) . T) (((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) +(-2676 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2676 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-699)) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (|has| |#1| (-558)) (((|#1|) . T)) (((|#1|) . T)) @@ -1123,11 +1123,11 @@ (((|#1| (-409 (-566))) . T)) (((|#3|) . T) (((-612 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) -((((-566)) -2700 (|has| |#2| (-172)) (|has| |#2| (-848)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049))) ((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-1099))) (((-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) +((((-566)) -2676 (|has| |#2| (-172)) (|has| |#2| (-848)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-1049))) ((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-1099))) (((-409 (-566))) -12 (|has| |#2| (-1038 (-409 (-566)))) (|has| |#2| (-1099)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) @@ -1135,8 +1135,8 @@ ((((-862)) . T)) ((((-862)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) |has| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (-310 (-2 (|:| -2334 |#1|) (|:| -2303 |#2|))))) -(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))) |has| (-2 (|:| -2334 (-1157)) (|:| -2303 |#1|)) (-310 (-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))))) +(((|#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) (((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) |has| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (-310 (-2 (|:| -3476 |#1|) (|:| -2484 |#2|))))) +(((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099))) (((-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))) |has| (-2 (|:| -3476 (-1157)) (|:| -2484 |#1|)) (-310 (-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))))) ((((-862)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1150,10 +1150,10 @@ ((($) . T) (((-566)) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566)))) ((|#1|) . T)) ((((-566)) . T) (($) . 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T)) @@ -1545,7 +1545,7 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) ((((-1257 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) #0#) |has| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (-310 (-2 (|:| -2334 |#1|) (|:| -2303 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099))) ((#0=(-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) #0#) |has| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (-310 (-2 (|:| -3476 |#1|) (|:| -2484 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-1099)) (|has| |#1| (-38 (-409 (-566)))) @@ -1557,14 +1557,14 @@ (((|#2|) . T)) (((|#1|) . 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T)) @@ -1590,19 +1590,19 @@ (((|#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (((|#1| |#2|) . T)) ((((-566) (-144)) . T)) -(((#0=(-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) #0#) |has| (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)) (-310 (-2 (|:| -2334 |#1|) (|:| -2303 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((#0=(-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) #0#) |has| (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)) (-310 (-2 (|:| -3476 |#1|) (|:| -2484 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) +((($) -2676 (|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))) +(-2676 (|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)))) +(-2676 (|has| |#1| (-147)) (-12 (|has| |#1| (-365)) (|has| |#2| (-147)))) +(-2676 (|has| |#1| (-145)) (-12 (|has| |#1| (-365)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1157) |#1|) . T)) @@ -1616,24 +1616,24 @@ (((|#3|) . T)) ((((-1257 |#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|) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) @@ -1652,7 +1652,7 @@ ((((-566)) . T)) (|has| |#2| (-147)) (|has| |#1| (-475)) -(-2700 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) +(-2676 (|has| |#1| (-475)) (|has| |#1| (-726)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (|has| |#1| (-365)) ((((-862)) . T)) (|has| |#1| (-38 (-409 (-566)))) @@ -1663,8 +1663,8 @@ (|has| |#1| (-848)) ((((-862)) . T)) (((|#2|) . T)) -((((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1257 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2700 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2700 (|has| |#1| (-365)) (|has| |#1| (-558)))) +((((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2676 (|has| |#1| (-365)) (|has| |#1| (-558))) (((-1257 |#1| |#2| |#3|)) |has| |#1| (-365)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-409 (-566))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2676 (|has| |#1| (-365)) (|has| |#1| (-558)))) ((($) |has| |#1| (-558)) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) (((|#2|) . T) (((-566)) . T) (((-819 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1673,7 +1673,7 @@ ((((-862)) . T)) ((((-862)) . 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T)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2700 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) +(((|#1|) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2676 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((|#1|) . T) (((-566)) |has| |#1| (-1038 (-566))) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566))))) (|has| |#1| (-850)) (|has| |#1| (-850)) @@ -1722,13 +1722,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#1|) |has| |#1| (-172))) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)))) -((($) -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))) -((($) -2700 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(((|#3|) -2676 (|has| |#3| (-172)) (|has| |#3| (-365)))) +((($) -2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +(-2676 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-909))) +((($) -2676 (|has| |#1| (-172)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) . T) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) ((((-566) |#2|) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)))) (|has| |#1| (-351)) (((|#3| |#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) (((|#2|) . T) (((-566)) . T)) @@ -1737,7 +1737,7 @@ (|has| |#1| (-820)) (|has| |#1| (-820)) (((|#1|) . T)) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-848)) (|has| |#1| (-848)) (|has| |#1| (-848)) @@ -1746,14 +1746,14 @@ ((((-566)) . T) (($) . T) (((-409 (-566))) . T)) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) ((((-1175)) |has| |#1| (-900 (-1175))) (((-1081)) . T)) (((|#1|) . T)) (|has| |#1| (-848)) -(((#0=(-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) #0#) |has| (-2 (|:| -2334 (-1157)) (|:| -2303 (-52))) (-310 (-2 (|:| -2334 (-1157)) (|:| -2303 (-52)))))) +(((#0=(-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) #0#) |has| (-2 (|:| -3476 (-1157)) (|:| -2484 (-52))) (-310 (-2 (|:| -3476 (-1157)) (|:| -2484 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) (|has| |#1| (-1099)) ((((-862)) . T) (((-1180)) . T)) @@ -1776,11 +1776,11 @@ (((|#1| (-771) (-1081)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) -2700 (|has| |#1| (-848)) (|has| |#1| (-1038 (-566)))) ((|#1|) . T)) +((((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) (((-566)) -2676 (|has| |#1| (-848)) (|has| |#1| (-1038 (-566)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . 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T)) ((((-566)) . T)) (|has| |#1| (-365)) -(-2700 (-12 (|has| (-1257 |#1| |#2| |#3|) (-147)) (|has| |#1| (-365))) (|has| |#1| (-147))) -(-2700 (-12 (|has| (-1257 |#1| |#2| |#3|) (-145)) (|has| |#1| (-365))) (|has| |#1| (-145))) +(-2676 (-12 (|has| (-1257 |#1| |#2| |#3|) (-147)) (|has| |#1| (-365))) (|has| |#1| (-147))) +(-2676 (-12 (|has| (-1257 |#1| |#2| |#3|) (-145)) (|has| |#1| (-365))) (|has| |#1| (-145))) (|has| |#1| (-365)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2314,25 +2314,25 @@ (|has| |#1| (-1099)) ((((-1141 |#2| |#1|)) . T) ((|#1|) . T) (((-566)) . T)) (((|#1| |#2|) . T)) -((((-566)) . T) ((|#1|) . T) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-1038 (-409 (-566)))))) +((((-566)) . T) ((|#1|) . T) (((-409 (-566))) -2676 (|has| |#1| (-365)) (|has| |#1| (-1038 (-409 (-566)))))) (((|#1|) . T) (((-566)) |has| |#1| (-639 (-566)))) (((|#3|) |has| |#3| (-172))) (((|#2|) . T) (($) . T) (((-566)) . T)) (((|#1|) . T) (($) . T) (((-566)) . 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T)) ((((-566) |#1|) . T)) ((((-1175)) |has| (-409 |#2|) (-900 (-1175)))) -(((|#1|) . T) (($) -2700 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-409 (-566))) |has| |#1| (-365))) +(((|#1|) . T) (($) -2676 (|has| |#1| (-291)) (|has| |#1| (-365))) (((-409 (-566))) |has| |#1| (-365))) ((((-538)) |has| |#2| (-614 (-538)))) ((((-689 |#2|)) . T) (((-862)) . T)) (((|#1|) . T)) @@ -2340,22 +2340,22 @@ (((|#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) ((((-870 |#1|)) . T)) (((|#1|) |has| |#1| (-172))) -(-2700 (|has| |#4| (-793)) (|has| |#4| (-848))) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2676 (|has| |#4| (-793)) (|has| |#4| (-848))) +(-2676 (|has| |#3| (-793)) (|has| |#3| (-848))) (((|#1| |#1|) -12 (|has| |#1| (-310 |#1|)) (|has| |#1| (-1099)))) ((((-862)) . T)) ((((-862)) . T)) (((|#1|) . T)) ((($) . T) (((-566)) . T) ((|#2|) . T)) (((|#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) -(((|#3|) -2700 (|has| |#3| (-172)) (|has| |#3| (-365)))) +(((|#3|) -2676 (|has| |#3| (-172)) (|has| |#3| (-365)))) (((|#2|) |has| |#2| (-1049))) (((|#3|) . T)) (((|#1|) . T)) ((((-409 |#2|)) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)))) (((|#1|) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) (((|#3|) -12 (|has| |#3| (-310 |#3|)) (|has| |#3| (-1099)))) ((((-566) |#1|) . T)) (((|#1|) . T)) @@ -2364,17 +2364,17 @@ ((((-409 (-566))) . T) (($) . T)) ((((-409 (-566))) . T) (($) . T)) ((((-409 (-566))) . T) (($) . T)) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-1219))) +(-2676 (|has| |#1| (-454)) (|has| |#1| (-1219))) ((($) . 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T)) @@ -2465,10 +2465,10 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) ((((-566)) . T) (($) . 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|) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) (((|#1|) . T) (((-409 (-566))) . T) (($) . T)) @@ -2478,10 +2478,10 @@ (((|#1|) . T) (($) . 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)) +((($) -2676 (|has| |#1| (-365)) (|has| |#1| (-351))) (((-409 (-566))) -2676 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) (((|#2|) . T)) ((((-409 (-566))) . T) (((-699)) . T) (($) . T)) -((($) . T) (((-409 (-566))) -2700 (|has| |#1| (-365)) (|has| |#1| (-351))) ((|#1|) . T)) +((($) . T) (((-409 (-566))) -2676 (|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) (($) . T)) @@ -2500,13 +2500,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . 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T)) (((|#1| $) |has| |#1| (-287 |#1| |#1|))) ((((-1251 |#1| |#2| |#3| |#4|)) . T) (((-409 (-566))) . T) (($) . 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))) -2676 (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-365))) (($) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-558))) ((|#1|) . T)) (|has| |#1| (-365)) -((($) |has| |#1| (-848)) (((-566)) -2700 (|has| |#1| (-21)) (|has| |#1| (-848)))) +((($) |has| |#1| (-848)) (((-566)) -2676 (|has| |#1| (-21)) (|has| |#1| (-848)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) @@ -2567,17 +2567,17 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-310 |#2|)) (|has| |#2| (-1099)))) (((|#2| |#3|) . T)) -(-2700 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2676 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((|#1| (-533 |#2|)) . T)) (((|#1| (-771)) . T)) (((|#1| (-533 (-1087 (-1175)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-909)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2676 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-862)) . T)) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)))) -(((|#2|) -2700 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) +(((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)))) +(((|#2|) -2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-1049))) (($) |has| |#2| (-172))) ((($ $) . T) ((#0=(-1250 |#2| |#3| |#4|) #0#) . T) ((#1=(-409 (-566)) #1#) |has| #0# (-38 (-409 (-566))))) ((((-910 |#1|)) . T)) (-12 (|has| |#1| (-365)) (|has| |#2| (-820))) @@ -2585,14 +2585,14 @@ ((((-862)) . T)) ((($) . T)) ((($) . T)) -(-2700 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-308)) (|has| |#1| (-365)) (|has| |#1| (-351)) (|has| |#1| (-558))) (|has| |#1| (-365)) (|has| |#1| (-365)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1250 |#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))) +(-2676 (-12 (|has| |#1| (-308)) (|has| |#1| (-909))) (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) ((((-566)) |has| |#1| (-639 (-566))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-862)) . T)) @@ -2637,28 +2637,28 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) (((|#2|) . 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T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) ((((-862)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-566)) . T)) (((|#1| (-409 (-566))) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-291)) (|has| |#1| (-365))) +(-2676 (|has| |#1| (-291)) (|has| |#1| (-365))) ((((-144)) . T)) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T)) (|has| |#1| (-848)) @@ -2674,7 +2674,7 @@ ((((-862)) . T)) ((((-862)) . T)) ((((-187)) . T) (((-862)) . T)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -2687,7 +2687,7 @@ ((((-862)) . T)) ((((-1157)) . T)) ((((-1175) |#1|) |has| |#1| (-516 (-1175) |#1|)) ((|#1| |#1|) |has| |#1| (-310 |#1|))) -((((-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))) . T)) +((((-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))) . T)) (|has| |#1| (-850)) ((((-862)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) @@ -2699,16 +2699,16 @@ (((|#2|) . T)) ((((-910 |#1|)) . 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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))) +(-2676 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (|has| |#1| (-909)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) (|has| |#1| (-909)) @@ -2725,12 +2725,12 @@ (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566)))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) (|has| |#1| (-820)) (((#0=(-910 |#1|) #0#) . T) (($ $) . T) ((#1=(-409 (-566)) #1#) . T)) ((((-409 |#2|)) . T)) (|has| |#1| (-848)) -((((-1201 |#1|)) . T) (((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-1201 |#1|)) . T) (((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1| |#1|) . T) ((#0=(-409 (-566)) #0#) . T) ((#1=(-566) #1#) . T) (($ $) . T)) ((((-910 |#1|)) . T) (($) . T) (((-409 (-566))) . T)) (((|#2|) |has| |#2| (-1049)) (((-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049)))) @@ -2746,28 +2746,28 @@ (((|#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 (|:| -2334 (-1175)) (|:| -2303 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -2334 (-1175)) (|:| -2303 #0#))) . T)) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) +((((-2 (|:| -3476 (-1175)) (|:| -2484 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3476 (-1175)) (|:| -2484 #0#))) . T)) (|has| |#1| (-351)) ((((-566)) . T)) ((((-862)) . T)) (((|#1|) . T)) (((#0=(-1251 |#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|) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049))) (($) -2676 (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049))) (((-566)) -2676 (|has| |#1| (-21)) (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-900 (-1175))) (|has| |#1| (-1049)))) (((#0=(-1081) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) (((#0=(-409 (-566)) #0#) . T) ((#1=(-699) #1#) . T) (($ $) . T)) ((((-317 |#1|)) . T) (($) . 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|) -2676 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) +(((|#1|) -2676 (|has| |#2| (-369 |#1|)) (|has| |#2| (-419 |#1|)))) (((|#2|) . T)) ((((-409 (-566))) . T) (((-699)) . T) (($) . T)) ((((-581)) . T)) @@ -2792,7 +2792,7 @@ (((|#1|) . T)) ((((-566)) . T)) (((|#2|) . T) (((-409 (-566))) |has| |#1| (-1038 (-409 (-566)))) ((|#1|) . T) (($) . T) (((-566)) . T)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2676 (|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)) ((($) . T)) @@ -2836,7 +2836,7 @@ (|has| |#2| (-1022)) ((($) . T)) (|has| |#1| (-909)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2845,10 +2845,10 @@ (|has| |#1| (-365)) ((((-910 |#1|)) . T)) ((($) . 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)))) +((($) -2676 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) |has| |#1| (-848)) (((-566)) -2676 (|has| |#1| (-21)) (|has| |#1| (-848)))) ((($ $) . T) ((#0=(-409 (-566)) #0#) . T)) -(-2700 (|has| |#1| (-370)) (|has| |#1| (-850))) +(-2676 (|has| |#1| (-370)) (|has| |#1| (-850))) (((|#1|) . T)) ((((-771)) . T)) ((((-862)) . T)) @@ -2859,17 +2859,17 @@ ((((-566)) . T) (($) . T)) ((((-566)) . T) (($) . T)) ((((-771) |#1|) . T)) -(((|#2| (-240 (-4142 |#1|) (-771))) . T)) +(((|#2| (-240 (-3991 |#1|) (-771))) . T)) (((|#1| (-533 |#3|)) . T)) ((((-409 (-566))) . T)) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((((-1157)) . T) (((-862)) . T)) -(((#0=(-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) #0#) |has| (-2 (|:| -2334 (-1175)) (|:| -2303 (-52))) (-310 (-2 (|:| -2334 (-1175)) (|:| -2303 (-52)))))) +(((#0=(-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) #0#) |has| (-2 (|:| -3476 (-1175)) (|:| -2484 (-52))) (-310 (-2 (|:| -3476 (-1175)) (|:| -2484 (-52)))))) ((((-1157)) . T)) (|has| |#1| (-909)) (|has| |#2| (-365)) (((|#1|) . T) (($) . T) (((-566)) . T)) -(-2700 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|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)) @@ -2886,11 +2886,11 @@ (|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))) +(-2676 (|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)) -2676 (-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)) @@ -2902,7 +2902,7 @@ (((|#2|) |has| |#1| (-365))) (((|#2|) |has| |#1| (-365))) ((((-566)) . T) (($) . T)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2932,11 +2932,11 @@ (((|#2|) |has| |#1| (-365))) ((((-381)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-381)))) (((-566)) -12 (|has| |#1| (-365)) (|has| |#2| (-886 (-566))))) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (((|#1|) . T)) ((($) . T) (((-566)) . T) ((|#2|) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) (|has| |#1| (-365)) (((|#3|) . T)) ((((-1157)) . T) (((-508)) . T) (((-225)) . T) (((-566)) . T)) @@ -2944,23 +2944,23 @@ (|has| |#1| (-558)) (((|#4| |#4|) -12 (|has| |#4| (-310 |#4|)) (|has| |#4| (-1099)))) ((((-409 |#2|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) -(-2700 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) (((|#2|) . T)) (((|#2|) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) -((((-2 (|:| -2334 (-1157)) (|:| -2303 |#1|))) . T)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +(-2676 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) +((((-2 (|:| -3476 (-1157)) (|:| -2484 |#1|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (|has| |#1| (-38 (-409 (-566)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-409 (-566)))) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) ((((-1157) |#1|) . T)) (|has| |#1| (-147)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) (|has| |#1| (-147)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-370))) ((($) . T)) (|has| |#1| (-147)) ((((-583 |#1|)) . T)) @@ -2974,7 +2974,7 @@ ((((-409 (-566))) |has| |#2| (-1038 (-566))) (((-566)) |has| |#2| (-1038 (-566))) (((-1175)) |has| |#2| (-1038 (-1175))) ((|#2|) . T)) (((#0=(-409 |#2|) #0#) . T) ((#1=(-409 (-566)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2700 (|has| |#1| (-145)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-145)) (|has| |#1| (-351))) (|has| |#1| (-147)) ((((-862)) . T)) ((($) . T)) @@ -2999,7 +2999,7 @@ ((((-862)) . T)) ((((-910 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3021,7 +3021,7 @@ ((((-566)) . T)) ((((-862)) . T)) ((((-566)) . T)) -(-2700 (|has| |#2| (-793)) (|has| |#2| (-848))) +(-2676 (|has| |#2| (-793)) (|has| |#2| (-848))) ((((-169 (-381))) . T) (((-225)) . T) (((-381)) . T)) ((((-862)) . T)) ((((-862)) . T)) @@ -3033,9 +3033,9 @@ (((|#1|) . T) (($) . T) (((-409 (-566))) . 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T)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)))) +(((|#1|) -2676 (|has| |#1| (-172)) (|has| |#1| (-365)))) (((|#1|) . T)) -(((|#1|) -2700 (|has| |#1| (-172)) (|has| |#1| (-365)) (|has| |#1| (-1049)))) +(((|#1|) -2676 (|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))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) ((((-381)) . T)) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|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))) +(-2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3082,13 +3082,13 @@ (|has| |#2| (-365)) ((((-583 |#1|)) . T) (((-409 (-566))) . T) (($) . T) (((-566)) . T)) ((((-566)) . T) (((-409 (-566))) . T) (($) . T)) -((((-2 (|:| -2334 (-1157)) (|:| -2303 (-52)))) . T)) +((((-2 (|:| -3476 (-1157)) (|:| -2484 (-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))) +(-2676 (|has| |#3| (-793)) (|has| |#3| (-848))) ((((-862)) . 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T)) (((|#2| |#2|) . T) ((#0=(-409 (-566)) #0#) . T) (($ $) . T)) ((((-566)) . T)) @@ -3609,17 +3609,17 @@ ((($) . T) (((-566)) . T) (((-116 |#1|)) . T) (((-409 (-566))) . T)) ((((-862)) . T)) ((((-1257 |#1| |#2| |#3|)) . T)) -((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909)))) +((((-409 (-566))) |has| |#2| (-38 (-409 (-566)))) ((|#2|) |has| |#2| (-172)) (($) -2676 (|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)) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1103)) . T)) ((((-862)) . T)) -((($) -2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|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)) -((($) -2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) +((($) -2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((|#1|) |has| |#1| (-172)) (((-409 (-566))) |has| |#1| (-38 (-409 (-566))))) ((((-1257 |#1| |#2| |#3|)) |has| |#1| (-365))) (|has| |#1| (-365)) ((((-1257 |#1| |#2| |#3|)) . T) (((-1229 |#1| |#2| |#3|)) . T)) @@ -3631,7 +3631,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-699)) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-1180)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1180)) . T)) @@ -3648,13 +3648,13 @@ ((((-1180)) . T)) ((((-1180)) . T)) ((((-1180)) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1180)) . T)) ((((-1180)) . T)) (|has| |#1| (-365)) (|has| |#1| (-365)) -(-2700 (|has| |#1| (-172)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-172)) (|has| |#1| (-558))) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) (((|#1| (-771)) . T)) @@ -3669,16 +3669,16 @@ ((((-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)))) +(-2676 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-365)) (|has| |#2| (-793)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (-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 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2700 (|has| |#2| (-172)) (|has| |#2| (-726)) (|has| |#2| (-848)) (|has| |#2| (-1049))) +(-2676 (|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)))) +(-2676 (-12 (|has| |#1| (-475)) (|has| |#2| (-475))) (-12 (|has| |#1| (-726)) (|has| |#2| (-726)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-365)) @@ -3709,7 +3709,7 @@ (((|#1| |#2|) . T)) ((((-566)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-566)) . T)) -(-2700 (|has| |#1| (-351)) (|has| |#1| (-370))) +(-2676 (|has| |#1| (-351)) (|has| |#1| (-370))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-409 (-566))) . T) (($) . T) (((-566)) . T)) @@ -3721,7 +3721,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-538)) |has| |#1| (-614 (-538)))) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) +((((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-850)) (|has| |#1| (-1099)))) ((($) . T) (((-409 (-566))) . T)) (|has| |#1| (-909)) (|has| |#1| (-909)) @@ -3732,14 +3732,14 @@ (((|#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))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-558))) +(-2676 (|has| |#1| (-21)) (|has| |#1| (-848))) (((|#2|) . T)) -(-2700 (|has| |#1| (-21)) (|has| |#1| (-848))) +(-2676 (|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)) -2676 (-12 (|has| |#1| (-613 (-862))) (|has| |#2| (-613 (-862)))) (-12 (|has| |#1| (-1099)) (|has| |#2| (-1099))))) ((((-409 |#2|) |#3|) . T)) ((((-409 (-566))) . T) (($) . T)) (|has| |#1| (-38 (-409 (-566)))) @@ -3753,19 +3753,19 @@ (((|#1|) . T) (((-409 (-566))) . T) (((-566)) . T) (($) . T)) (((#0=(-566) #0#) . T)) ((($) . T) (((-409 (-566))) . T)) -(-2700 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) -(-2700 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) +(-2676 (|has| |#4| (-172)) (|has| |#4| (-726)) (|has| |#4| (-848)) (|has| |#4| (-1049))) +(-2676 (|has| |#3| (-172)) (|has| |#3| (-726)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((((-862)) . T) (((-1180)) . T)) (|has| |#4| (-793)) -(-2700 (|has| |#4| (-793)) (|has| |#4| (-848))) +(-2676 (|has| |#4| (-793)) (|has| |#4| (-848))) (|has| |#4| (-848)) (|has| |#3| (-793)) ((((-1180)) . T)) -(-2700 (|has| |#3| (-793)) (|has| |#3| (-848))) +(-2676 (|has| |#3| (-793)) (|has| |#3| (-848))) (|has| |#3| (-848)) ((((-566)) . T)) (((|#2|) . T)) -((((-1175)) -2700 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) +((((-1175)) -2676 (-12 (|has| (-1173 |#1| |#2| |#3|) (-900 (-1175))) (|has| |#1| (-365))) (-12 (|has| |#1| (-15 * (|#1| (-566) |#1|))) (|has| |#1| (-900 (-1175)))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-409 (-566)) |#1|))) (|has| |#1| (-900 (-1175))))) ((((-1175)) -12 (|has| |#1| (-15 * (|#1| (-771) |#1|))) (|has| |#1| (-900 (-1175))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3780,11 +3780,11 @@ ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) ((((-1139 |#1| |#2|)) . T)) ((((-1173 |#1| |#2| |#3|)) |has| |#1| (-365))) -(((|#2|) . T) (((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) -((((-2 (|:| -2334 (-1175)) (|:| -2303 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) +((((-2 (|:| -3476 (-1175)) (|:| -2484 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1022)) -(((|#2|) . T) (((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3476 |#1|) (|:| -2484 |#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)) @@ -3801,15 +3801,15 @@ ((((-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)) -2676 (|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) (($) -2676 (|has| |#4| (-172)) (|has| |#4| (-848)) (|has| |#4| (-1049))) ((|#4|) -2676 (|has| |#4| (-172)) (|has| |#4| (-365)) (|has| |#4| (-1049)))) +(((|#2|) . T) (($) -2676 (|has| |#3| (-172)) (|has| |#3| (-848)) (|has| |#3| (-1049))) ((|#3|) -2676 (|has| |#3| (-172)) (|has| |#3| (-365)) (|has| |#3| (-1049)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-365)) @@ -3824,7 +3824,7 @@ ((((-187)) . T) (((-862)) . T)) ((((-862)) . T)) (((|#1|) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) ((((-129)) . T) (((-862)) . T)) ((((-566) |#1|) . T)) ((((-129)) . T)) @@ -3833,13 +3833,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-365)) (|has| |#2| (-287 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) -(-2700 (|has| |#1| (-850)) (|has| |#1| (-1099))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-454)) (|has| |#1| (-909))) +(-2676 (|has| |#1| (-850)) (|has| |#1| (-1099))) ((((-862)) . T)) ((((-862)) . T)) ((((-862)) . T)) (((|#1| (-533 |#2|)) . T)) -((((-2 (|:| -2334 (-1175)) (|:| -2303 (-52)))) . T)) +((((-2 (|:| -3476 (-1175)) (|:| -2484 (-52)))) . T)) ((((-566) (-129)) . T)) (((|#1| (-566)) . T)) (((|#1| (-409 (-566))) . T)) @@ -3854,8 +3854,8 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) -(-2700 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) -(-2700 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) +(-2676 (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) +(-2676 (|has| |#1| (-454)) (|has| |#1| (-558)) (|has| |#1| (-909))) ((($) . T)) (((|#2| (-533 (-864 |#1|))) . T)) ((((-1180)) . T)) @@ -3870,13 +3870,13 @@ ((((-1180)) . T)) ((((-862)) . T) (((-1180)) . T)) ((((-1180)) . T)) -((((-862)) -2700 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) +((((-862)) -2676 (|has| |#1| (-613 (-862))) (|has| |#1| (-1099)))) (((|#1|) . T)) (((|#2| (-771)) . T)) (((|#1| |#2|) . T)) ((((-1157) |#1|) . T)) ((((-409 |#2|)) . T)) -((((-2 (|:| -2334 |#1|) (|:| -2303 |#2|))) . T)) +((((-2 (|:| -3476 |#1|) (|:| -2484 |#2|))) . T)) (|has| |#1| (-558)) (|has| |#1| (-558)) ((($) . T) ((|#2|) . T)) @@ -3887,14 +3887,14 @@ ((((-566)) . T) (($) . T)) (((|#2| $) |has| |#2| (-287 |#2| |#2|))) (((|#1| (-644 |#1|)) |has| |#1| (-848))) -(-2700 (|has| |#1| (-233)) (|has| |#1| (-351))) -(-2700 (|has| |#1| (-365)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-233)) (|has| |#1| (-351))) +(-2676 (|has| |#1| (-365)) (|has| |#1| (-351))) ((((-1261 |#1|)) . T) (((-566)) . T) ((|#2|) . T) (((-409 (-566))) |has| |#2| (-1038 (-409 (-566))))) (|has| |#1| (-1099)) (((|#1|) . T)) -((((-1261 |#1|)) . T) (((-566)) . T) (($) -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)))))) +((((-1261 |#1|)) . T) (((-566)) . T) (($) -2676 (|has| |#2| (-365)) (|has| |#2| (-454)) (|has| |#2| (-558)) (|has| |#2| (-909))) (((-1081)) . T) ((|#2|) . T) (((-409 (-566))) -2676 (|has| |#2| (-38 (-409 (-566)))) (|has| |#2| (-1038 (-409 (-566)))))) ((((-409 (-566))) . T) (($) . 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)) -2676 (|has| (-999 |#1|) (-1038 (-566))) (|has| |#1| (-1038 (-566)))) (((-409 (-566))) -2676 (|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)))) @@ -3910,10 +3910,10 @@ (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1139 |#1| |#2|) #0#) |has| (-1139 |#1| |#2|) (-310 (-1139 |#1| |#2|)))) (((|#1|) . 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. -613) 184104) ((-390 . -102) T) ((-1119 . -143) T) ((-126 . -613) 184036) ((-874 . -1099) T) ((-658 . -413) 184020) ((-714 . -613) 184002) ((-249 . -613) 183969) ((-187 . -613) 183951) ((-162 . -613) 183933) ((-157 . -613) 183915) ((-1280 . -726) T) ((-1101 . -34) T) ((-871 . -795) NIL) ((-871 . -792) NIL) ((-858 . -850) T) ((-731 . -886) NIL) ((-1289 . -131) T) ((-383 . -131) T) ((-892 . -616) 183883) ((-904 . -102) T) ((-731 . -1038) 183759) ((-533 . -131) T) ((-1086 . -413) 183743) ((-1000 . -491) 183727) ((-117 . -402) 183704) ((-1166 . -1215) 183683) ((-782 . -413) 183667) ((-780 . -413) 183651) ((-943 . -34) T) ((-694 . -1150) NIL) ((-252 . -648) 183486) ((-251 . -648) 183308) ((-817 . -920) 183287) ((-456 . -413) 183271) ((-602 . -19) 183255) ((-1145 . -1208) 183224) ((-1166 . -886) NIL) ((-1166 . -884) 183176) ((-602 . -604) 183153) ((-1201 . -613) 183085) ((-1174 . -613) 183067) ((-62 . -397) T) ((-1172 . -1038) 183002) ((-1166 . -1038) 182968) ((-694 . -38) 182918) ((-40 . -646) 182848) ((-476 . -287) 182833) ((-1221 . -613) 182815) ((-731 . -379) 182799) ((-838 . -613) 182781) ((-658 . -1057) T) ((-1249 . -1002) 182747) ((-1228 . -1002) 182713) ((-1087 . -616) 182697) ((-1062 . -1191) 182672) ((-1075 . -616) 182649) ((-872 . -614) 182456) ((-872 . -613) 182438) ((-1188 . -491) 182375) ((-420 . -1022) 182353) ((-48 . -310) 182340) ((-1062 . -107) 182286) ((-481 . -491) 182223) ((-522 . -1215) T) ((-1166 . -340) 182175) ((-1140 . -491) 182146) ((-1166 . -379) 182098) ((-1086 . -1057) T) ((-439 . -102) T) ((-183 . -1099) T) ((-252 . -34) T) ((-251 . -34) T) ((-782 . -1057) T) ((-780 . -1057) T) ((-731 . -900) 182075) ((-456 . -1057) T) ((-59 . -491) 182059) ((-1034 . -1056) 182033) ((-521 . -491) 182017) ((-518 . -491) 182001) ((-499 . -491) 181985) ((-498 . -491) 181969) ((-245 . -516) 181902) ((-1034 . -111) 181869) ((-1173 . -900) 181782) ((-1172 . -900) 181688) ((-1166 . -900) 181521) ((-1125 . -900) 181505) ((-670 . -1111) T) ((-356 . -1150) T) ((-645 . -93) T) ((-323 . -1056) 181487) ((-252 . -791) 181466) ((-252 . -794) 181417) ((-31 . -492) 181398) ((-252 . -793) 181377) ((-251 . -791) 181356) ((-251 . -794) 181307) ((-251 . -793) 181286) ((-31 . -613) 181252) ((-50 . -1057) T) ((-252 . -726) 181162) ((-251 . -726) 181072) ((-1209 . -1099) T) ((-670 . -23) T) ((-583 . -1057) T) ((-520 . -1057) T) ((-381 . -1056) 181037) ((-323 . -111) 181012) ((-73 . -385) T) ((-73 . -397) T) ((-1024 . -38) 180949) ((-694 . -402) 180931) ((-99 . -102) T) ((-711 . -1099) T) ((-1293 . -1051) 180918) ((-1003 . -145) 180890) ((-1003 . -147) 180862) ((-870 . -646) 180834) ((-381 . -111) 180790) ((-320 . -1219) 180769) ((-476 . -1002) 180735) ((-356 . -38) 180700) ((-40 . -372) 180672) ((-873 . -613) 180544) ((-127 . -125) 180528) ((-121 . -125) 180512) ((-836 . -1056) 180482) ((-833 . -21) 180434) ((-827 . -1056) 180418) ((-833 . -25) 180370) ((-320 . -558) 180321) ((-519 . -616) 180302) ((-566 . -828) T) ((-240 . -1215) T) ((-1034 . -616) 180271) 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((-290 . -558) T) ((-621 . -25) T) ((-1195 . -1099) T) ((-711 . -717) 178728) ((-240 . -379) 178697) ((-1004 . -1038) 178657) ((-381 . -1049) T) ((-223 . -1057) T) ((-117 . -231) 178634) ((-59 . -287) 178611) ((-152 . -23) T) ((-518 . -287) 178588) ((-328 . -516) 178521) ((-498 . -287) 178498) ((-381 . -243) T) ((-381 . -233) T) ((-836 . -1049) T) ((-827 . -1049) T) ((-712 . -949) 178467) ((-701 . -850) T) ((-476 . -613) 178449) ((-1251 . -1051) 178354) ((-582 . -646) 178326) ((-566 . -646) 178298) ((-497 . -646) 178248) ((-827 . -233) 178227) ((-134 . -850) T) ((-1251 . -640) 178119) ((-658 . -1099) T) ((-1188 . -604) 178098) ((-552 . -1191) 178077) ((-338 . -1099) T) ((-320 . -365) 178056) ((-409 . -147) 178035) ((-409 . -145) 178014) ((-964 . -1111) 177913) ((-240 . -900) 177845) ((-815 . -1111) 177755) ((-654 . -852) 177739) ((-481 . -604) 177718) ((-552 . -107) 177668) ((-1004 . -379) 177650) ((-1004 . -340) 177632) ((-97 . -1099) T) ((-964 . -23) 177443) ((-479 . -21) T) ((-479 . -25) T) ((-815 . -23) 177313) ((-1175 . -613) 177295) ((-59 . -19) 177279) ((-1175 . -614) 177201) ((-1171 . -726) T) ((-1124 . -726) T) ((-518 . -19) 177185) ((-498 . -19) 177169) ((-59 . -604) 177146) ((-1086 . -1099) T) ((-901 . -102) 177124) ((-854 . -726) T) ((-782 . -1099) T) ((-518 . -604) 177101) ((-498 . -604) 177078) ((-780 . -1099) T) ((-780 . -1064) 177045) ((-463 . -1099) T) ((-456 . -1099) T) ((-587 . -717) 177020) ((-649 . -1099) T) ((-1257 . -47) 176997) ((-1251 . -102) T) ((-1250 . -47) 176967) ((-1229 . -47) 176944) ((-1209 . -172) 176895) ((-1172 . -308) 176874) ((-1166 . -308) 176853) ((-1095 . -616) 176834) ((-1089 . -616) 176815) ((-1079 . -558) 176766) ((-1004 . -900) NIL) ((-1079 . -1219) 176717) ((-670 . -131) T) ((-627 . -1111) T) ((-1072 . -616) 176698) ((-1065 . -616) 176679) ((-1036 . -616) 176660) ((-1019 . -616) 176641) ((-699 . -646) 176591) ((-276 . -1099) T) ((-85 . -443) T) ((-85 . -397) T) ((-714 . -1056) 176561) ((-711 . -172) T) ((-50 . -1099) T) 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((-1229 . -884) 175715) ((-1086 . -717) 175564) ((-1061 . -648) 175551) ((-952 . -648) 175476) ((-782 . -717) 175305) ((-538 . -613) 175287) ((-538 . -614) 175268) ((-780 . -717) 175117) ((-1076 . -102) T) ((-383 . -25) T) ((-623 . -646) 175089) ((-383 . -21) T) ((-483 . -648) 175014) ((-463 . -717) 174985) ((-456 . -717) 174834) ((-987 . -102) T) ((-1229 . -1038) 174800) ((-1188 . -614) NIL) ((-1188 . -613) 174782) ((-737 . -102) T) ((-117 . -646) 174712) ((-605 . -616) 174694) ((-1141 . -1122) 174639) ((-1046 . -1208) 174568) ((-533 . -25) T) ((-901 . -310) 174506) ((-714 . -616) 174460) ((-681 . -93) T) ((-645 . -492) 174441) ((-141 . -102) T) ((-44 . -131) T) ((-676 . -93) T) ((-664 . -613) 174423) ((-345 . -1057) T) ((-290 . -1111) T) ((-645 . -613) 174376) ((-480 . -93) T) ((-357 . -613) 174358) ((-354 . -613) 174340) ((-346 . -613) 174322) ((-265 . -614) 174070) ((-265 . -613) 174052) ((-247 . -613) 174034) ((-247 . -614) 173895) ((-133 . -93) T) ((-138 . -93) T) ((-137 . -93) T) ((-1209 . -516) 173862) ((-1140 . -613) 173844) ((-1119 . -640) 173831) ((-819 . -857) T) ((-819 . -726) T) ((-602 . -289) 173808) ((-583 . -717) 173773) ((-481 . -614) NIL) ((-481 . -613) 173755) ((-520 . -717) 173700) ((-317 . -102) T) ((-314 . -102) T) ((-290 . -23) T) ((-152 . -131) T) ((-1119 . -1051) 173687) ((-910 . -613) 173669) ((-388 . -726) T) ((-872 . -1056) 173621) ((-910 . -614) 173603) ((-872 . -111) 173541) ((-714 . -1049) T) ((-712 . -1241) 173525) ((-694 . -351) NIL) ((-136 . -102) T) ((-114 . -102) T) ((-139 . -102) T) ((-521 . -613) 173457) ((-381 . -795) T) ((-223 . -1099) T) ((-381 . -792) T) ((-225 . -794) T) ((-225 . -791) T) ((-59 . -614) 173418) ((-59 . -613) 173330) ((-225 . -726) T) ((-518 . -614) 173291) ((-518 . -613) 173203) ((-499 . -613) 173135) ((-498 . -614) 173096) ((-498 . -613) 173008) ((-1079 . -365) 172959) ((-40 . -413) 172936) ((-77 . -1215) T) ((-871 . -909) NIL) ((-361 . -330) 172920) ((-361 . -365) T) ((-355 . -330) 172904) ((-355 . -365) T) ((-347 . -330) 172888) ((-347 . -365) T) ((-317 . -285) 172867) ((-108 . -365) T) ((-70 . -1215) T) ((-1229 . -340) 172819) ((-871 . -648) 172764) ((-1229 . -379) 172716) ((-964 . -131) 172571) ((-815 . -131) 172441) ((-958 . -651) 172425) ((-1086 . -172) 172336) ((-958 . -375) 172320) ((-1061 . -794) T) ((-1061 . -791) T) ((-872 . -616) 172218) ((-782 . -172) 172109) ((-780 . -172) 172020) ((-816 . -47) 171982) ((-1061 . -726) T) ((-328 . -491) 171966) ((-952 . -726) T) ((-456 . -172) 171877) ((-245 . -287) 171854) ((-1278 . -310) 171792) ((-1257 . -900) 171705) ((-1250 . -900) 171611) ((-483 . -726) T) ((-1249 . -1056) 171446) ((-1229 . -900) 171279) ((-1228 . -1056) 171087) ((-1209 . -291) 171066) ((-1185 . -1215) T) ((-1182 . -370) T) ((-1181 . -370) T) ((-1145 . -151) 171050) ((-1119 . -102) T) ((-1117 . -1099) T) ((-1079 . -23) T) ((-1079 . -1111) T) ((-1074 . -102) T) ((-927 . -955) T) ((-737 . -310) 170988) ((-75 . -1215) T) ((-664 . -384) 170960) ((-169 . -909) 170913) 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167963) ((-1003 . -404) NIL) ((-670 . -639) 167911) ((-317 . -38) 167821) ((-314 . -38) 167750) ((-69 . -613) 167732) ((-320 . -495) 167698) ((-48 . -646) 167648) ((-1188 . -289) 167627) ((-1223 . -850) T) ((-1112 . -1111) 167537) ((-83 . -1215) T) ((-61 . -613) 167519) ((-481 . -289) 167498) ((-1280 . -1038) 167475) ((-1163 . -1099) T) ((-1112 . -23) 167345) ((-816 . -900) 167281) ((-1238 . -726) T) ((-1101 . -1215) T) ((-476 . -616) 167107) ((-1086 . -291) 167038) ((-966 . -1099) T) ((-893 . -102) T) ((-782 . -291) 166949) ((-328 . -19) 166933) ((-59 . -289) 166910) ((-780 . -291) 166841) ((-855 . -726) T) ((-117 . -848) NIL) ((-518 . -289) 166818) ((-328 . -604) 166795) ((-498 . -289) 166772) ((-456 . -291) 166703) ((-1035 . -310) 166554) ((-681 . -492) 166535) ((-573 . -726) T) ((-676 . -492) 166516) ((-681 . -613) 166466) ((-676 . -613) 166432) ((-662 . -613) 166414) ((-480 . -492) 166395) ((-480 . -613) 166361) ((-245 . -614) 166322) ((-245 . -492) 166299) ((-138 . -492) 166280) ((-137 . -492) 166261) ((-133 . -492) 166242) ((-245 . -613) 166134) ((-213 . -102) T) ((-138 . -613) 166100) ((-137 . -613) 166066) ((-133 . -613) 166032) ((-1146 . -34) T) ((-943 . -1215) T) ((-345 . -717) 165977) ((-670 . -25) T) ((-670 . -21) T) ((-1175 . -616) 165958) ((-476 . -1049) T) ((-635 . -419) 165923) ((-607 . -419) 165888) ((-1119 . -1150) T) ((-712 . -1051) 165711) ((-583 . -291) T) ((-520 . -291) T) ((-1250 . -308) 165690) ((-476 . -233) 165642) ((-476 . -243) 165621) ((-1229 . -308) 165600) ((-712 . -640) 165429) ((-1229 . -1022) NIL) ((-1079 . -131) T) ((-872 . -795) 165408) ((-144 . -102) T) ((-40 . -1099) T) ((-872 . -792) 165387) ((-644 . -1010) 165371) ((-582 . -1057) T) ((-566 . -1057) T) ((-497 . -1057) T) ((-409 . -454) T) ((-361 . -131) T) ((-317 . -402) 165355) ((-314 . -402) 165316) ((-355 . -131) T) ((-347 . -131) T) ((-1180 . -1099) T) ((-1119 . -38) 165303) ((-1093 . -613) 165270) ((-108 . -131) T) ((-954 . -1099) T) ((-921 . -1099) T) ((-771 . -1099) T) 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. -1056) 94814) ((-347 . -717) 94766) ((-341 . -111) 94745) ((-174 . -1056) 94677) ((-217 . -646) 94627) ((-174 . -111) 94538) ((-108 . -717) 94488) ((-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 . -1203) 94466) ((-169 . -1200) 94444) ((-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) 94234) ((-169 . -35) 94212) ((-169 . -95) 94190) ((-654 . -1038) 94086) ((-484 . -1057) 94016) ((-1112 . -1099) 93806) ((-1141 . -34) T) ((-670 . -491) 93790) ((-73 . -1215) T) ((-105 . -613) 93772) ((-1289 . -613) 93754) ((-383 . -613) 93736) ((-341 . -616) 93688) ((-174 . -616) 93605) ((-1214 . -492) 93586) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 140dde60..b3294bde 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3461381191) +(30 . 3462551504) (4418 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -479,663 +479,665 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |multinomial| |identity| |error| |outputBinaryFile| - |generalizedContinuumHypothesisAssumed| |expextendedint| |sub| - |e02adf| |f01ref| |sup| |position| |nullary| |assert| |rightUnits| - |flatten| |listLoops| |d02cjf| |f04adf| |besselY| |nthCoef| |OMread| - |distFact| |f02xef| |vconcat| |solid?| |outputFloating| - |noncommutativeJordanAlgebra?| |loopPoints| |measure2Result| |varList| - |iisinh| |addMatchRestricted| |number?| |rotate| |s17aef| - |expenseOfEvaluationIF| |jacobi| |setfirst!| |PDESolve| |stopTable!| - |pdf2ef| |mkPrim| |sparsityIF| |s19abf| |zero| |retractable?| - |getMultiplicationTable| |sizeMultiplication| - |exprHasLogarithmicWeights| |leftQuotient| |goto| |removeCoshSq| - |outputGeneral| |index| |pade| |SturmHabichtMultiple| |iflist2Result| - |clipPointsDefault| |complexRoots| |regime| |singleFactorBound| - |makeEq| |And| |list?| |leftTrace| |cSech| |cAsinh| |in?| - |lieAlgebra?| |hostPlatform| |mappingAst| |Or| |hasHi| |secIfCan| - |bits| |quadraticNorm| |bumptab1| |leastMonomial| |nthFractionalTerm| - |pushNewContour| |Not| |arity| |pair| |elements| |pair?| |denomLODE| - |doubleRank| |elliptic| |simpleBounds?| |string?| |lazy?| |value| - |readUInt8!| |unrankImproperPartitions0| |more?| |writeInt8!| - |linkToFortran| |inputOutputBinaryFile| |zag| |d01fcf| |pushdown| - |expandPower| |cycleElt| |sizePascalTriangle| |superscript| - |outerProduct| |setFieldInfo| |delete| |bezoutResultant| - |homogeneous?| |d01gaf| |cyclic?| |capacity| - |integralMatrixAtInfinity| |integralLastSubResultant| |packageCall| - |cLog| |s14abf| |iiperm| |fill!| |BumInSepFFE| |lfunc| UTS2UP |cCot| - |mainDefiningPolynomial| ** |fixedPoints| |isImplies| |groebSolve| - |tableau| |continue| |gramschmidt| |binarySearchTree| - |radicalEigenvectors| |completeEval| |minordet| |critpOrder| |norm| - |s17akf| |reduceByQuasiMonic| |bumptab| |getConstant| |s13adf| - |quoted?| |drawComplex| |binaryTree| |fglmIfCan| - |basisOfCommutingElements| |pop!| |palgint0| |alternatingGroup| - |possiblyNewVariety?| |s21bdf| |clip| |plus| |swap| |float?| - |outputAsScript| |commonDenominator| |linearDependence| |droot| - |countable?| |setProperty!| |leastPower| |numberOfComputedEntries| - |semiSubResultantGcdEuclidean1| |imagE| |LiePolyIfCan| |cond| - |uniform| |contract| |Is| |setEmpty!| |trigs| |vedf2vef| - |completeEchelonBasis| |reflect| |powerAssociative?| |isAnd| - |divisors| |internalDecompose| |quadraticForm| |flexible?| |tanIfCan| - GF2FG |schema| |ptree| |merge| |redmat| |OMgetSymbol| - |resetVariableOrder| |removeSuperfluousQuasiComponents| |denominator| - |generalizedEigenvectors| |computeBasis| |tubePoints| - |nextLatticePermutation| |rename!| |ran| |curryLeft| - |extendedIntegrate| |sin2csc| |identitySquareMatrix| |reverse!| - |oblateSpheroidal| |LazardQuotient2| |primintegrate| - |minimalPolynomial| |divideExponents| |solveLinearlyOverQ| |wrregime| - |write!| |binomial| |An| |noKaratsuba| |OMreadFile| |intPatternMatch| - |d03eef| |lazyPseudoQuotient| |imports| |xCoord| |contractSolve| |sum| - |convergents| |graphState| |constantKernel| |style| |bsolve| - |flagFactor| |iidprod| |sts2stst| |discreteLog| |f02adf| |id| - |branchIfCan| |node| |conjug| |nil?| |clearDenominator| |predicates| - |jordanAdmissible?| |createZechTable| |mainForm| |nor| - |infiniteProduct| |absolutelyIrreducible?| |float| |controlPanel| - |rightQuotient| |stoseInvertibleSetsqfreg| |create3Space| - |functionIsFracPolynomial?| |decreasePrecision| |logical?| |totalLex| - |fortranCarriageReturn| |table| |subResultantGcdEuclidean| |supersub| - |dioSolve| |diagonals| |parabolic| |qfactor| |search| |constantLeft| - |d02ejf| |polygamma| |extractClosed| |new| |expPot| |one?| - |radicalRoots| |lp| |cAcot| |stFunc1| |content| |incrementKthElement| - |ipow| |tab1| |complexNormalize| |iipow| |quasiComponent| - |generalPosition| |factorials| |iibinom| |exprToUPS| |mergeDifference| - |symmetricTensors| |OMputApp| |getGoodPrime| |ode1| |infinite?| - |antiCommutative?| |zerosOf| |nextSublist| |nthExpon| |collect| |qqq| - |mapExpon| |expint| |d03edf| |rst| |readable?| |explicitEntries?| - |cPower| |cycleSplit!| |primPartElseUnitCanonical| |possiblyInfinite?| - |mathieu23| |high| |atrapezoidal| |iiasech| |meatAxe| - |resultantReduit| |solveRetract| |nil| UP2UTS |squareFree| |putGraph| - |companionBlocks| |preprocess| |acotIfCan| |mapDown!| |sizeLess?| - |makeGraphImage| |arbitrary| |subHeight| GE |spherical| - |computeCycleEntry| |leftExactQuotient| |bubbleSort!| |rightUnit| - |f02aaf| |makeYoungTableau| |eq?| |intensity| GT |weight| - |exteriorDifferential| |characteristicSerie| |terms| |leftRank| - |antiCommutator| |mkcomm| |fractRagits| |simplifyExp| |approximate| LE - |entries| |mainVariables| |lineColorDefault| |coerce| |ref| |complex| - |printingInfo?| |quadratic?| |f04arf| |multiEuclidean| - |integralCoordinates| |log| |equation| LT |cap| |rational| - |jordanAlgebra?| |construct| |readInt16!| |bottom!| |nthRootIfCan| - |geometric| |genericRightDiscriminant| |addPoint| |e01sef| |hex| - |readIfCan!| |clearTheIFTable| |univariate?| |FormatArabic| |monomRDE| - |modularGcdPrimitive| |trim| |rewriteIdealWithRemainder| - |insertBottom!| |close!| |finite?| |var2StepsDefault| |ip4Address| - |sinh2csch| |extendIfCan| |viewport3D| |genericLeftTraceForm| - |members| |scale| |conjugates| |leftUnits| |complex?| |inRadical?| - |cyclotomicDecomposition| |complexLimit| |formula| |symmetric?| - |iroot| |selectNonFiniteRoutines| |transpose| |roughBase?| |hexDigit| - |lighting| |cardinality| |setTopPredicate| |dictionary| - |sturmVariationsOf| |empty| |curve?| |makeResult| |meshFun2Var| - |multiple?| |createLowComplexityNormalBasis| |lazyGintegrate| - |leftRankPolynomial| |doubleResultant| |constantCoefficientRicDE| - |rotatex| |reverse| |c02aff| |mathieu22| |extendedSubResultantGcd| - |checkForZero| |updatD| |tanQ| |mainSquareFreePart| - |symmetricDifference| |s17ajf| |OMgetEndAtp| |critB| |relativeApprox| - |debug3D| |nextColeman| |nrows| |hdmpToDmp| |rightTraceMatrix| - |closedCurve?| |elementary| |f04mcf| |linearAssociatedOrder| - |indicialEquationAtInfinity| |complexZeros| |coefChoose| |ncols| - |fortranLiteral| |mapGen| |e01sbf| |power!| |whitePoint| - |processTemplate| |crest| |eigenvector| |deriv| |exponential| - |permutation| |moreAlgebraic?| |nextPrime| |increasePrecision| - |bombieriNorm| |stoseSquareFreePart| |balancedBinaryTree| - |rationalPoints| |horizConcat| |log2| |saturate| - |numericalIntegration| |solveid| |rationalFunction| |leftFactorIfCan| - |invertible?| |positiveSolve| |simplifyPower| |internalSubPolSet?| - |outputForm| |setelt| |squareFreePart| |presub| |push| - |functionIsContinuousAtEndPoints| |e04fdf| |init| |intChoose| |lllp| - |getRef| |e01baf| |OMlistCDs| |iisech| |gcdPolynomial| |tower| - |gbasis| |torsion?| |mainPrimitivePart| |mergeFactors| |weierstrass| - |ksec| |subresultantVector| |internalSubQuasiComponent?| |copy| - |f04jgf| |swapColumns!| |internalZeroSetSplit| |putColorInfo| - |multisect| |Ci| |primeFactor| |subQuasiComponent?| |nonSingularModel| - |charClass| |zeroSetSplitIntoTriangularSystems| |linGenPos| - |screenResolution| |nonLinearPart| |function| |makeprod| |external?| - |toseSquareFreePart| |lyndon| |checkPrecision| |retractIfCan| |point| - |reduceBasisAtInfinity| |tanintegrate| |leftTraceMatrix| |OMputBVar| - |notelem| |createMultiplicationTable| |shallowCopy| |autoCoerce| |tab| - |torsionIfCan| |indicialEquation| |rootDirectory| |optional?| - |composites| |remove| |eval| |unknownEndian| |maxRowIndex| |aCubic| - |createNormalElement| |s20acf| |linearAssociatedExp| |integralBasis| - |intcompBasis| |removeConstantTerm| |solve| |eulerPhi| |series| - |LyndonWordsList1| |changeWeightLevel| |forLoop| - |nextNormalPrimitivePoly| |last| |basisOfRightNucleus| |ideal| - |wholeRagits| |quasiRegular?| |unitNormal| |simpson| |jacobiIdentity?| - |definingEquations| |assoc| |duplicates?| |zeroDimensional?| |remove!| - |factor1| |parabolicCylindrical| |cyclicEntries| - |leadingCoefficientRicDE| |options| |polyPart| |implies| |s17def| - |rules| |stoseIntegralLastSubResultant| |usingTable?| |LiePoly| - |postfix| |movedPoints| |fortranDouble| |stripCommentsAndBlanks| - |level| |RemainderList| |clearFortranOutputStack| |testModulus| |min| - |solveLinearPolynomialEquationByFractions| |expandLog| |argument| - |belong?| |isTerm| |symmetricSquare| |map| |normal01| |userOrdered?| - |d01aqf| |subSet| |eq| |string| |extensionDegree| |const| |palgLODE0| - |OMmakeConn| |insertMatch| |sign| |iter| F |df2st| |complete| - |integralMatrix| |prefix| |extractBottom!| |subscriptedVariables| - |traverse| |f01qcf| |fortranCompilerName| |unknown| |bivariate?| - |normalizedAssociate| |conditionP| |twoFactor| |lift| |lex| - |tracePowMod| |iteratedInitials| |repeating| |coth2tanh| |operators| - |lcm| |GospersMethod| |showTheFTable| |generate| |getOperands| - |reduce| |sqfree| |htrigs| |simplifyLog| |concat!| |OMgetEndObject| - |multiplyExponents| |printStatement| |points| |convert| |makeSin| - |monicRightDivide| |deref| |prologue| |comment| |append| - |variationOfParameters| |prinb| |linearlyDependent?| |incrementBy| - |s13aaf| |exprHasAlgebraicWeight| |expintegrate| |airyAi| |someBasis| - |rightDivide| |gcd| |OMopenFile| |symmetricProduct| |initTable!| - |interval| |expand| |tanNa| |leadingBasisTerm| - |semiResultantReduitEuclidean| |returns| |ReduceOrder| |false| - |setPredicates| |frobenius| |karatsubaDivide| |quasiMonic?| - |filterWhile| |e01bff| |intersect| |unaryFunction| |nextItem| |exp| - |realRoots| |distance| |lfextlimint| |root?| |cyclotomic| - |filterUntil| |rightMult| |quasiAlgebraicSet| |hasTopPredicate?| - |transcendentalDecompose| |nilFactor| |midpoint| |cCos| |select| - |cross| |solveLinearPolynomialEquation| |stopMusserTrials| - |divideIfCan!| |c06ebf| |lquo| |cubic| |branchPoint?| - |currentCategoryFrame| |s17ahf| |semiResultantEuclideannaif| - |OMputError| |ParCondList| |e04gcf| |halfExtendedResultant1| - |changeBase| EQ |real?| |univariatePolynomial| |multMonom| - |discriminant| |vark| |trigs2explogs| |cAcosh| - |semiDiscriminantEuclidean| |drawCurves| |seriesSolve| |karatsubaOnce| - |splitNodeOf!| |imagk| |orbit| |hash| |lyndonIfCan| |e02ajf| - |singularitiesOf| |indices| |fracPart| |localReal?| - |OMencodingUnknown| |count| |prem| |subResultantsChain| |nthr| - |credPol| |f04faf| |mapUnivariateIfCan| |atanhIfCan| |mpsode| - |collectUnder| |OMgetVariable| |sinIfCan| |mainValue| |OMputEndError| - |factorSquareFreeByRecursion| |viewport2D| |clearTheFTable| - |changeThreshhold| |binaryTournament| |constantOperator| - |eisensteinIrreducible?| |minGbasis| |numerator| |makeRecord| - |dmp2rfi| |byte| |mix| |rewriteIdealWithQuasiMonicGenerators| - |symmetricGroup| |cyclicEqual?| |divisorCascade| |definingPolynomial| - |lfintegrate| |rational?| |epilogue| |headReduce| |subPolSet?| - |colorDef| |quotient| |perfectNthPower?| |algebraicVariables| |addiag| - |monomialIntegrate| |characteristicPolynomial| |Vectorise| - |graphCurves| |baseRDE| |UpTriBddDenomInv| |OMgetAtp| |zCoord| - |vertConcat| |category| |subresultantSequence| |minPol| |cschIfCan| - |pointLists| |quotientByP| |createNormalPoly| |commaSeparate| - |algDsolve| |charthRoot| |knownInfBasis| |mantissa| |domain| |create| - |plus!| |mathieu11| |HermiteIntegrate| |setTex!| |normalize| - |factorSquareFreePolynomial| |iilog| |unmakeSUP| |child?| |package| - |viewZoomDefault| |sechIfCan| |delay| |moebius| |c06gqf| |build| - |removeZero| |groebnerIdeal| |thetaCoord| |cyclic| - |intermediateResultsIF| |quasiMonicPolynomials| |extractIndex| - |showAllElements| |lazyIrreducibleFactors| |LyndonBasis| - |currentSubProgram| |c06ekf| |cycleRagits| |returnType!| - |screenResolution3D| |setleft!| |rectangularMatrix| |getProperty| - |quotedOperators| |int| |lepol| |product| |ratPoly| |fTable| - |irreducibleFactors| |iiacos| |e02bdf| |generalTwoFactor| |e02def| - |stronglyReduce| |systemCommand| |height| |f04maf| - |removeRoughlyRedundantFactorsInPol| |octon| |viewWriteAvailable| - |minset| |fi2df| |genericLeftNorm| |getBadValues| |symbolTable| - |generalizedInverse| |dihedralGroup| |sayLength| |solveInField| - |binding| |chebyshevU| |rationalIfCan| |inrootof| |brillhartTrials| - |gderiv| |iomode| |viewDeltaXDefault| |algSplitSimple| |subNode?| - |adaptive?| |isTimes| |rightRecip| |pushFortranOutputStack| - |UnVectorise| |minrank| |oddintegers| |selectFiniteRoutines| |polygon| - |distribute| |updatF| |normal| |antisymmetricTensors| |fortranTypeOf| - |printCode| |findConstructor| |popFortranOutputStack| |odd?| - |truncate| |lazyPquo| |besselI| |binomThmExpt| |mathieu12| |anticoord| - |hcrf| |rename| |fortranReal| |npcoef| |rischDEsys| |outputAsFortran| - |reorder| |reducedSystem| |block| |semiIndiceSubResultantEuclidean| - |palgint| |setMaxPoints3D| |clearCache| |digit?| |numberOfFactors| - |iiatanh| |selectPDERoutines| |diag| |plenaryPower| |minPoly| - |trapezoidal| |constDsolve| |unitsColorDefault| |row| |factorAndSplit| - |e02baf| |setsubMatrix!| |satisfy?| |ptFunc| |myDegree| - |validExponential| |evenInfiniteProduct| |encodingDirectory| - |inverseColeman| |arg1| |structuralConstants| |startPolynomial| - |halfExtendedSubResultantGcd2| |d01alf| |OMreadStr| - |pointColorPalette| |OMreceive| |f2df| |listOfLists| |arg2| - |complexElementary| |rootOf| |lexGroebner| |nodeOf?| |basisOfCentroid| - |leadingExponent| |infinityNorm| |errorInfo| |setOfMinN| - |recoverAfterFail| |yCoord| |stoseInvertible?| |resultantEuclidean| - |bounds| |addmod| |d02bbf| |selectPolynomials| |conditions| - |realEigenvectors| |rangePascalTriangle| |dimension| |property| - |rationalPoint?| |resetBadValues| |complementaryBasis| |backOldPos| - |acosIfCan| |match| |iiacsch| |sqfrFactor| |resultantnaif| |legendre| - |replaceKthElement| |isList| |tail| |generators| |integral| - |moebiusMu| |iisec| |failed| |outlineRender| |rootRadius| |getMeasure| - |mapCoef| |diagonalProduct| |viewPosDefault| |powern| |directory| - |units| |tanhIfCan| |typeList| |pascalTriangle| |measure| - |selectMultiDimensionalRoutines| |unit?| |pureLex| |normalDeriv| - |sncndn| |numericalOptimization| |front| |addPointLast| |entry| - |critBonD| |nodes| |slex| |divide| |universe| |stopTableInvSet!| - |copyInto!| |viewPhiDefault| |representationType| |leftUnit| - |stoseInvertible?reg| |vector| |deepExpand| |adaptive3D?| |unexpand| - |redpps| |viewpoint| |showFortranOutputStack| |positiveRemainder| - |complexExpand| |differentiate| |errorKind| |mr| |isConnected?| - |hostByteOrder| |isobaric?| |ramified?| |hMonic| |invmultisect| - |maxint| |key| |taylorQuoByVar| |code| |hconcat| |root| - |binaryFunction| |even?| |decimal| |constantIfCan| - |trailingCoefficient| |reducedDiscriminant| |cosh2sech| |palgRDE0| - |lazyPrem| |color| |updateStatus!| |filename| |listOfMonoms| |stFunc2| - |viewSizeDefault| |nativeModuleExtension| |iiGamma| - |createPrimitivePoly| |factorsOfDegree| |algebraicSort| |qelt| - |acschIfCan| |reduction| |setLegalFortranSourceExtensions| - |dimensions| |Ei| |clipParametric| |graeffe| |qsetelt| |logpart| - |interactiveEnv| |substring?| |explogs2trigs| - |selectSumOfSquaresRoutines| |linear| |OMputEndObject| |parse| - |isExpt| |cylindrical| |d02gbf| |rarrow| |Nul| |xRange| |f01rdf| - |messagePrint| |exactQuotient!| |interReduce| |goodPoint| |s18aef| - |yRange| |atoms| |showScalarValues| |suffix?| |iisin| |precision| - |mainExpression| |f02awf| |polynomial| |rootsOf| - |createNormalPrimitivePoly| |mapBivariate| |multiset| |zRange| - |direction| |inverseIntegralMatrix| |box| |leftZero| |OMencodingXML| - |stoseInternalLastSubResultant| |exprToGenUPS| |map!| |leftLcm| - |hermiteH| |exactQuotient| |prefix?| |OMputInteger| |drawStyle| - |f02wef| |qsetelt!| |patternMatchTimes| |difference| - |lastSubResultantEuclidean| |square?| |prime?| |d01bbf| |evaluate| - |getExplanations| |floor| |prepareDecompose| |branchPointAtInfinity?| - |leftRegularRepresentation| |factors| |newLine| |edf2fi| |escape| - |constantToUnaryFunction| |dAndcExp| |polCase| - |algebraicCoefficients?| |setRealSteps| |heap| |interpret| - |generalInfiniteProduct| |pquo| |bandedJacobian| |genericRightTrace| - |pole?| |elColumn2!| |writable?| |opeval| |s17acf| |mapExponents| - |cscIfCan| |topPredicate| |position!| |wronskianMatrix| - |limitedIntegrate| |f04asf| |radicalEigenvector| |finiteBasis| - |solveLinear| |children| |identityMatrix| |acsch| |infix?| |order| - |expintfldpoly| |att2Result| |coerceListOfPairs| |csch2sinh| - |sequences| |pointColorDefault| |mask| |e01bhf| |cosIfCan| |signature| - |d02kef| |palginfieldint| |primextendedint| |restorePrecision| - |numberOfComposites| |endSubProgram| |nsqfree| - |integralDerivationMatrix| |internalIntegrate| - |createPrimitiveElement| |e02dcf| |rischDE| |semicolonSeparate| - |deleteRoutine!| |polyRicDE| |singularAtInfinity?| |aLinear| |redPo| - |associatedSystem| |graphImage| |nothing| |omError| |routines| - |outputAsTex| |numer| |OMUnknownCD?| |getOrder| |symbol?| |logGamma| - |laplacian| |any| |algebraicDecompose| |denom| |singular?| |leftNorm| - |pow| |shallowExpand| |lllip| |hessian| |normalizedDivide| |rk4f| - |innerint| |directSum| |superHeight| |outputSpacing| |pushuconst| - |derivative| |rightRankPolynomial| |complexEigenvalues| - |selectIntegrationRoutines| |scanOneDimSubspaces| - |associatorDependence| |chineseRemainder| |pi| |generator| |is?| - |basisOfLeftNucloid| |youngGroup| |df2mf| |ramifiedAtInfinity?| - |maxPoints| |mainContent| |delete!| |lo| |pointColor| |matrix| - |infinity| |rightFactorCandidate| |parametric?| |numeric| |sPol| - |realEigenvalues| |FormatRoman| |inGroundField?| |localAbs| |gethi| - |radical| |supRittWu?| |OMsetEncoding| |coerceImages| |width| - |augment| |totalGroebner| |hdmpToP| |sylvesterMatrix| |light| - |writeBytes!| |incr| |paren| |internalLastSubResultant| - |viewDeltaYDefault| |copies| |parseString| |numFunEvals| |printHeader| - |selectAndPolynomials| |multiplyCoefficients| |insertTop!| |hi| - |kernel| |f02agf| |selectODEIVPRoutines| |wholeRadix| |close| - |compiledFunction| |dmpToHdmp| |readByte!| |roughUnitIdeal?| |pdf2df| - |deepestInitial| |OMputSymbol| |stiffnessAndStabilityOfODEIF| |draw| - |degreeSubResultant| |var1StepsDefault| |pushup| - |showTheRoutinesTable| |categories| |e04dgf| |polyred| |nthExponent| - |figureUnits| |setClipValue| |over| |localIntegralBasis| |digits| - |display| |mindeg| |rootPower| |deepCopy| BY |numberOfMonomials| - |OMUnknownSymbol?| |primintfldpoly| |roughBasicSet| |nullary?| - |triangularSystems| |ocf2ocdf| |whileLoop| |center| - |removeRedundantFactorsInPols| |bitLength| |exponential1| |fibonacci| - |isOpen?| |showIntensityFunctions| |readLineIfCan!| - |fortranDoubleComplex| |mainCoefficients| |char| |enumerate| |cycle| - |diagonalMatrix| |rowEchelonLocal| |airyBi| |super| |shufflein| - |monomRDEsys| |lintgcd| |interpolate| |radicalOfLeftTraceForm| - |inHallBasis?| |makeObject| |tableForDiscreteLogarithm| |normalized?| - |showAll?| |graphStates| |generic?| |optional| |bigEndian| - |reciprocalPolynomial| |pdct| |invertibleSet| |palgextint0| - |nextPartition| |ratpart| |coef| |musserTrials| - |standardBasisOfCyclicSubmodule| |getDatabase| |Beta| |swap!| - |before?| |rootKerSimp| |primextintfrac| |polygon?| |coleman| - |zeroDimPrimary?| |input| |addMatch| |round| |unit| |denomRicDE| - |adjoint| |cyclePartition| |ellipticCylindrical| |reverseLex| - |anfactor| |setCondition!| |fullPartialFraction| |coefficients| - |library| |s19aaf| |subMatrix| |tanAn| |setValue!| |Hausdorff| |cAsin| - |asinhIfCan| |iiasin| |ridHack1| |index?| |lhs| NOT |OMgetEndBVar| - |enterInCache| |mainKernel| |polyRDE| |signAround| |setlast!| |find| - |d01amf| |tubePointsDefault| |mesh| |rhs| OR |resetNew| |coordinates| - |subscript| |algintegrate| |signatureAst| |deleteProperty!| - |exponents| |exprHasWeightCosWXorSinWX| |leadingIdeal| - |numberOfVariables| |stoseLastSubResultant| |numberOfNormalPoly| - |lifting| AND |length| |mainMonomial| |denominators| |cos2sec| - |freeOf?| |f02ajf| |antisymmetric?| |e01sff| SEGMENT |palgextint| |sh| - |internalIntegrate0| |e02zaf| |normFactors| |scripts| |set| |expr| - |bothWays| |probablyZeroDim?| |coshIfCan| - |purelyAlgebraicLeadingMonomial?| |generateIrredPoly| |reduceLODE| - |palglimint0| |s19acf| |kind| |setnext!| |integerIfCan| |clikeUniv| - |s01eaf| |makingStats?| |basisOfMiddleNucleus| - |setAttributeButtonStep| |listYoungTableaus| |c05nbf| |extractPoint| - |xn| |depth| |op| |charpol| |drawComplexVectorField| - |extendedResultant| |varselect| |removeSquaresIfCan| |basisOfNucleus| - |permanent| |leftDivide| |merge!| |nextNormalPoly| |checkRur| |cSinh| - |factorGroebnerBasis| |iicos| |atom?| |cAtan| |collectQuasiMonic| - |sorted?| |initializeGroupForWordProblem| |heapSort| |complexSolve| - |domainTemplate| |headAst| |zeroDimPrime?| |elRow2!| |fractRadix| - |variable| |rquo| |mkIntegral| |cycleTail| |bipolar| |power| |binary| - |mainMonomials| |outputFixed| |llprop| |realElementary| |conjugate| - |iterators| |stronglyReduced?| |perfectSquare?| |setMinPoints3D| - |patternVariable| |stoseInvertible?sqfreg| |writeUInt8!| - |RittWuCompare| |reducedContinuedFraction| |changeName| |OMputString| - |transform| |e02ddf| |specialTrigs| |f02aef| |normalizeIfCan| - |characteristicSet| |lfextendedint| |makeViewport3D| |bfKeys| |ode| - |assign| |primitiveElement| |squareMatrix| |contains?| |consnewpol| - |predicate| |solve1| |asecIfCan| |nand| |idealSimplify| - |totalDifferential| |c06gbf| |getCode| |union| |linear?| * |concat| - |mindegTerm| |thenBranch| |minus!| |yellow| |scan| - |shanksDiscLogAlgorithm| |lexico| |functorData| |isOr| |iiatan| |mat| - |coefficient| |lazyVariations| |unrankImproperPartitions1| - |chebyshevT| |ord| |pushucoef| |polynomialZeros| |safeFloor| - |rootOfIrreduciblePoly| |pointPlot| |setLength!| |explicitlyEmpty?| - |tensorProduct| |show| |generalizedContinuumHypothesisAssumed?| - |pushdterm| |s15adf| |genericLeftTrace| |iterationVar| - |expenseOfEvaluation| |getZechTable| |adaptive| |OMgetApp| - |curveColorPalette| |declare| |groebnerFactorize| |output| = - |findCycle| |trace2PowMod| |expressIdealMember| |roughSubIdeal?| - |diagonal| |appendPoint| |complexEigenvectors| |optAttributes| - |laguerre| |var2Steps| |eof?| |innerSolve| |trace| |computeInt| - |cycleLength| |tryFunctionalDecomposition?| |compose| |rangeIsFinite| - |makeTerm| |read!| |endOfFile?| |kmax| |s20adf| < |plot| |toScale| - |rightAlternative?| |ffactor| |exptMod| |setref| |minColIndex| |space| - |innerSolve1| |factorFraction| |d01akf| > |goodnessOfFit| - |closeComponent| |integerBound| |insertionSort!| |quickSort| - |characteristic| |cAcsch| |delta| |imagK| |addBadValue| <= - |stosePrepareSubResAlgo| |meshPar2Var| |semiResultantEuclidean1| |obj| - |currentEnv| |createPrimitiveNormalPoly| |lambert| |linSolve| - |headRemainder| |maxdeg| |testDim| |coth2trigh| >= |extend| |e01daf| - |internalAugment| |parameters| |cache| |iicot| |trivialIdeal?| - |cyclotomicFactorization| |antiAssociative?| |rspace| |atanIfCan| - |orthonormalBasis| |refine| |sin?| |B1solve| |numberOfDivisors| - |linears| |edf2efi| |setScreenResolution| |rur| |createThreeSpace| - |bezoutDiscriminant| |modifyPoint| |s17adf| |vectorise| |properties| - |rightDiscriminant| |minimumExponent| |transcendent?| |makeCrit| - |f01maf| |sequence| |f04mbf| |abelianGroup| |roman| + - |differentialVariables| |Lazard2| |extract!| |translate| |duplicates| - |rewriteSetByReducingWithParticularGenerators| - |semiLastSubResultantEuclidean| |eyeDistance| |functionIsOscillatory| - |f01qdf| |isEquiv| |partitions| - |bipolarCylindrical| - |OMsupportsSymbol?| |pr2dmp| |nlde| |computeCycleLength| |ParCond| - |linearPart| |rightNorm| |useSingleFactorBound| |li| |headReduced?| - |karatsuba| / |f02aff| |patternMatch| |d02gaf| |prepareSubResAlgo| - |c05adf| |currentScope| |edf2ef| |setProperties| |permutations| - |noLinearFactor?| |nextPrimitiveNormalPoly| |bernoulliB| - |argumentList!| |infRittWu?| |realSolve| |groebgen| - |univariatePolynomials| |SturmHabichtSequence| |open| |beauzamyBound| - |certainlySubVariety?| |dimensionOfIrreducibleRepresentation| - |componentUpperBound| |corrPoly| |numFunEvals3D| |setProperties!| - |sdf2lst| |powerSum| |complexIntegrate| |minPoints| |toroidal| - |numberOfCycles| |iitanh| |getSyntaxFormsFromFile| - |wordsForStrongGenerators| |listBranches| |call| |leadingTerm| |elem?| - |euler| |printInfo!| |degreeSubResultantEuclidean| - |associatedEquations| |prinpolINFO| |separateDegrees| |module| - |s17dgf| |stoseInvertibleSetreg| |nthFlag| |lazyPseudoRemainder| - |invertIfCan| |fintegrate| |internal?| |iExquo| |identification| - |meshPar1Var| |rightZero| |useEisensteinCriterion| |double| |rightLcm| - |lazyPseudoDivide| |f07adf| |rk4a| |vspace| |operations| |rotatey| - |latex| |quasiRegular| |s13acf| |contours| |fortran| |readBytes!| - |seed| |approximants| |presuper| |e04mbf| |inverseLaplace| - |squareFreePolynomial| |exportedOperators| |subNodeOf?| |cAcoth| - |bumprow| |setPoly| |LazardQuotient| |euclideanSize| |laplace| |digit| - |gcdcofactprim| |cyclicGroup| |printStats!| |neglist| |lazyIntegrate| - |numberOfImproperPartitions| |constant?| |kovacic| |permutationGroup| - |shrinkable| |pointSizeDefault| |makeSeries| |maxIndex| |test| - |var1Steps| |makeop| |rootSimp| |resultant| |stirling1| |nary?| - |recolor| |minIndex| |rotatez| |OMserve| |eigenvalues| |operation| - |factorset| |palgLODE| |iprint| |mainVariable| |dot| - |squareFreeLexTriangular| |OMcloseConn| |s21baf| |dmpToP| |scopes| - |genericRightMinimalPolynomial| |lprop| |sech2cosh| |cCoth| - |limitPlus| |padicFraction| |randomR| |besselJ| |declare!| |unary?| - |normal?| |poisson| |integer?| |dihedral| |removeZeroes| - |prolateSpheroidal| |sumOfSquares| |f2st| |integralBasisAtInfinity| - |choosemon| |matrixGcd| |createGenericMatrix| |topFortranOutputStack| - |increment| |integralRepresents| |zeroOf| |ldf2vmf| |removeSinSq| - |extractTop!| |setMaxPoints| |cTanh| |c06gsf| |doubleComplex?| |untab| - |iifact| |setMinPoints| |s18aff| |pseudoQuotient| |getProperties| - |boundOfCauchy| |condition| |partialFraction| |primitivePart| - |splitDenominator| |separant| |completeHensel| |primitivePart!| - |match?| |components| |evenlambert| |tryFunctionalDecomposition| - |wholePart| |indiceSubResultant| |mesh?| |alternative?| |extendedint| - |true| |rowEch| |leftPower| |bag| |principalAncestors| |e02dff| - |divideIfCan| |removeRoughlyRedundantFactorsInPols| |equiv| |s17aff| - |taylorRep| |nextPrimitivePoly| |sumSquares| |script| |sumOfDivisors| - |ScanFloatIgnoreSpaces| |regularRepresentation| |exprex| - |chainSubResultants| |represents| |factorList| |OMgetObject| - |nullSpace| |readLine!| |segment| |curryRight| |newTypeLists| - |rightOne| |s21bbf| |radicalEigenvalues| |medialSet| - |removeRedundantFactorsInContents| |besselK| |schwerpunkt| |e01bgf| - |bfEntry| |gradient| |point?| |debug| - |solveLinearPolynomialEquationByRecursion| |rightTrace| |iiacsc| - |triangular?| |retract| |quoByVar| |setright!| |tex| |cRationalPower| - D |back| |monomial?| |henselFact| |normDeriv2| |clipBoolean| - |irreducibleFactor| |s18def| |monicDivide| |polar| |BasicMethod| - |fortranCharacter| |revert| |limit| |tanh2coth| |strongGenerators| - |typeLists| |dfRange| |rewriteSetWithReduction| |f02abf| - |extractIfCan| |factorial| |OMputAttr| |s17agf| |unitVector| - |constantRight| |sturmSequence| |dimensionsOf| |singRicDE| - |setErrorBound| |purelyTranscendental?| |powmod| |findBinding| - |OMgetString| |inspect| |getGraph| |stirling2| |transcendenceDegree| - |pleskenSplit| |pack!| |alternating| |numberOfChildren| |character?| - |removeRoughlyRedundantFactorsInContents| |hypergeometric0F1| - |colorFunction| |imagi| |OMputFloat| |c02agf| |asimpson| |tRange| - |fixedDivisor| |parametersOf| |primeFrobenius| |rightExtendedGcd| - |hitherPlane| |range| |mapMatrixIfCan| |idealiserMatrix| |pastel| - |resetAttributeButtons| |selectOptimizationRoutines| |shiftRoots| - |nthRoot| |OMReadError?| |setvalue!| |degreePartition| |normalDenom| - |leftAlternative?| |complexNumericIfCan| |dualSignature| |mulmod| - |cSec| |idealiser| |sort| |prefixRagits| |simplify| |every?| - |lflimitedint| |coerceP| |compile| |setStatus!| - |halfExtendedResultant2| |definingInequation| |c06gcf| |crushedSet| - |OMclose| |OMencodingSGML| |OMputEndAtp| |partition| |iisqrt2| |cAcsc| - |c06frf| |print| |whatInfinity| |isOp| |sortConstraints| - |LagrangeInterpolation| |sn| |stoseInvertibleSet| |rootPoly| - |firstUncouplingMatrix| |radPoly| |resolve| |newSubProgram| - |isQuotient| |perfectSqrt| |aQuartic| |hyperelliptic| |mainVariable?| - |diff| |OMconnInDevice| |dequeue| |lastSubResultant| |upperCase?| - |symbolIfCan| |subResultantGcd| |null| |inR?| |split!| |ratDenom| - |cartesian| |curveColor| |random| |nextsubResultant2| |leaves| - |determinant| |commutative?| |factorSFBRlcUnit| |resize| |not| - |defineProperty| |LowTriBddDenomInv| |times| |janko2| |getButtonValue| - |shiftRight| |isMult| |d02bhf| |attributeData| |bitTruth| |cAcos| - |and| |makeSUP| |eulerE| |shiftLeft| |d01apf| |Frobenius| |SFunction| - |sec2cos| |or| |factorPolynomial| |roughEqualIdeals?| - |subResultantChain| |printTypes| |OMgetAttr| |iiacosh| |reindex| - |iiacot| |cAsec| |separate| |genericLeftMinimalPolynomial| |f02bbf| - |subset?| |xor| |reduced?| |setImagSteps| |biRank| |mkAnswer| - |primlimitedint| |exponent| |setScreenResolution3D| - |lazyPremWithDefault| |keys| |central?| |listexp| |romberg| |frst| - |case| |e02ahf| |log10| |monom| |monomials| |d01ajf| |closed?| - |s21bcf| |expandTrigProducts| |relationsIdeal| |pomopo!| |lyndon?| - |column| |divergence| |Zero| |hasSolution?| |bitand| |iitan| |iiasec| - |ListOfTerms| |zoom| |setColumn!| |pile| |outputMeasure| |component| - |infieldIntegrate| |OMgetError| |c06fqf| |One| |pointData| |bitior| - |dark| |harmonic| |realZeros| |lfinfieldint| |stopTableGcd!| |d01asf| - |algebraicOf| |OMputVariable| |badNum| |simpsono| |common| |insert| - |OMParseError?| |sinhIfCan| |selectfirst| |decomposeFunc| |cycles| - |univariatePolynomialsGcds| |leftDiscriminant| |OMgetEndError| - |f01brf| |monic?| |lagrange| |fprindINFO| |uniform01| |curve| - |sinhcosh| |upperCase| |viewDefaults| |initial| |unparse| |slash| - |returnTypeOf| |viewThetaDefault| |s19adf| |iiexp| |iidsum| - |factorSquareFree| |brillhartIrreducible?| |leftOne| - |partialQuotients| |bit?| |bandedHessian| |qualifier| |mathieu24| - |elliptic?| |padicallyExpand| |fillPascalTriangle| |univcase| |shift| - |head| |f07fdf| |list| |isNot| |wordInStrongGenerators| |scripted?| - |elt| |symbolTableOf| |byteBuffer| |rank| |any?| |readUInt16!| - |separateFactors| |unprotectedRemoveRedundantFactors| |car| |expt| - |lazyResidueClass| |toseInvertible?| |complexForm| |shellSort| - |d01gbf| |splitSquarefree| |createRandomElement| |basisOfLeftNucleus| - |resultantEuclideannaif| |cdr| |select!| |mdeg| |multiEuclideanTree| - |completeSmith| |showTheSymbolTable| |fullDisplay| |e02daf| |ode2| - |genericPosition| |cCsch| |setDifference| |applyRules| - |euclideanGroebner| |f02fjf| |rightRemainder| |compound?| |cn| - |f07fef| |generalizedEigenvector| |subspace| |entry?| - |primPartElseUnitCanonical!| |setIntersection| |middle| - |initiallyReduce| |commutator| |infix| |oddlambert| - |genericLeftDiscriminant| |totalfract| |connectTo| - |stiffnessAndStabilityFactor| |resultantReduitEuclidean| |setUnion| - |makeFR| |rroot| |midpoints| |positive?| |s14baf| |radicalSimplify| - |numerators| |squareFreeFactors| |dequeue!| |numberOfComponents| - |apply| |nullity| |hermite| |buildSyntax| |composite| |asechIfCan| - |fixedPoint| |e02bbf| |left| |imagI| |kroneckerDelta| |rightGcd| |po| - |oddInfiniteProduct| |dflist| |removeSinhSq| |equality| |randomLC| - |lists| |member?| |right| |logIfCan| |subtractIfCan| |leftRecip| - |size| |leftMinimalPolynomial| |psolve| |minRowIndex| |autoReduced?| - |OMgetType| |monomialIntPoly| |useSingleFactorBound?| - |pseudoRemainder| |countRealRootsMultiple| |showClipRegion| - |overlabel| |child| |Aleph| |radix| |tan2cot| |setButtonValue| |cSin| - |approxSqrt| |tree| |d02raf| |semiDegreeSubResultantEuclidean| Y - |extendedEuclidean| |bitCoef| |getlo| |linearAssociatedLog| - |physicalLength| LODO2FUN |raisePolynomial| |c06eaf| |iisqrt3| - |pmintegrate| |first| |cotIfCan| |lastSubResultantElseSplit| - |integralAtInfinity?| |hclf| |palglimint| |primaryDecomp| |writeByte!| - |setAdaptive| |integrate| |rubiksGroup| |diagonal?| |rest| - |constantOpIfCan| |symFunc| |integral?| |SturmHabichtCoefficients| - |cTan| |rootBound| |irreducibleRepresentation| |wordInGenerators| - |region| |exQuo| |permutationRepresentation| |showSummary| - |substitute| |setLabelValue| |quatern| |sort!| |leadingSupport| - |e02gaf| |d03faf| |c05pbf| |factorByRecursion| |chvar| |deepestTail| - |removeDuplicates| |iiasinh| |leftExtendedGcd| |s15aef| |magnitude| - |integers| |outputList| |numberOfHues| |repeatUntilLoop| |asinIfCan| - |critMonD1| |fortranLinkerArgs| |exponentialOrder| |result| - |showAttributes| |split| |cAsech| |maxColIndex| |e02aef| |parents| - |OMconnectTCP| |powers| |stFuncN| |conditionsForIdempotents| - |hasPredicate?| |dom| |just| |axes| |indiceSubResultantEuclidean| - |setPrologue!| |overbar| |gcdprim| |tubePlot| |OMwrite| - |doublyTransitive?| |s17dhf| |datalist| |leader| |makeSketch| - |associates?| |reset| |innerEigenvectors| |iFTable| |complement| - |critM| |qPot| |symbol| |writeLine!| |bivariatePolynomials| - |mightHaveRoots| |df2fi| |f01mcf| |pToDmp| |countRealRoots| - |safetyMargin| |highCommonTerms| |expression| - |rewriteIdealWithHeadRemainder| |laurentIfCan| |distdfact| |randnum| - |createLowComplexityTable| |blankSeparate| |write| |groebner| |birth| - |compactFraction| |name| |iicsc| |critMTonD1| |integer| |conical| - |newReduc| |save| |laguerreL| |cycleEntry| |maxrank| - |initiallyReduced?| |ODESolve| |normalise| |body| |arguments| - |rootNormalize| |removeDuplicates!| |ScanRoman| |LyndonCoordinates| - |subTriSet?| |leastAffineMultiple| |low| |linearDependenceOverZ| - |sylvesterSequence| |title| |infLex?| |lambda| |lowerCase!| - |alphabetic| |ranges| |shuffle| |gcdcofact| |squareFreePrim| - |removeCosSq| |getVariableOrder| |reopen!| |fortranLogical| - |firstNumer| |showTheIFTable| |acscIfCan| |KrullNumber| - |symmetricRemainder| |infieldint| |alphanumeric| |useNagFunctions| - |mvar| |monicModulo| |dim| |ldf2lst| |externalList| - |rightExactQuotient| |empty?| |submod| |physicalLength!| |e| - |modularGcd| |removeRedundantFactors| |exprToXXP| |complexNumeric| - |invertibleElseSplit?| |genericRightTraceForm| |basicSet| |dn| - |unitNormalize| |weighted| |eigenvectors| |top| |bringDown| |maxrow| - |overlap| |extractSplittingLeaf| |bytes| |extractProperty| |exists?| - |basis| |label| |setStatus| |modTree| |getPickedPoints| |wreath| - |kernels| |PollardSmallFactor| |port| |laurentRep| |trunc| - |maximumExponent| |lazyEvaluate| |twist| |makeFloatFunction| |e02bcf| - |operator| |computePowers| |OMsupportsCD?| |qroot| |Gamma| - |lSpaceBasis| |categoryFrame| |normalForm| |e02akf| |lifting1| |t| - |cExp| |modulus| |cup| |iiabs| |OMgetEndApp| |rightMinimalPolynomial| - |aromberg| |numberOfIrreduciblePoly| |basisOfRightNucloid| - |univariate| |prindINFO| |sumOfKthPowerDivisors| - |semiSubResultantGcdEuclidean2| |rCoord| |rationalPower| - |createMultiplicationMatrix| |setRow!| |problemPoints| - |mainCharacterization| |OMgetBVar| |monicDecomposeIfCan| |totalDegree| - |minPoints3D| |palgintegrate| |rdHack1| |collectUpper| |arrayStack| - |prime| |interpretString| |Si| |changeMeasure| |abs| |setrest!| - |maxPoints3D| |perspective| |constructor| |discriminantEuclidean| - |ricDsolve| |factor| |iicosh| |withPredicates| |f02bjf| |csc2sin| - |df2ef| |totolex| |axesColorDefault| |green| |commutativeEquality| - |sqrt| |repSq| |startTableInvSet!| |option| |createIrreduciblePoly| - |alphabetic?| |failed?| |seriesToOutputForm| |cyclicSubmodule| |real| - |nthFactor| |OMconnOutDevice| |setleaves!| |toseInvertibleSet| - |s18dcf| |iCompose| |scalarMatrix| |rotate!| |size?| |imag| - |evaluateInverse| |internalInfRittWu?| |trapezoidalo| |smith| |e04jaf| - |lowerPolynomial| |argumentListOf| |e04naf| |directProduct| |cCsc| - |combineFeatureCompatibility| |leftGcd| |minimumDegree| |acothIfCan| - |max| |nonQsign| |normalElement| |numberOfFractionalTerms| |e04ucf| - |supDimElseRittWu?| |second| |showArrayValues| |check| |rightTrim| - |leaf?| |coerceS| |readUInt32!| |null?| |numericIfCan| |increase| - |node?| |brace| |third| |generic| |nextSubsetGray| |coordinate| - |leftTrim| |hue| |listRepresentation| |radicalSolve| - |leftScalarTimes!| |OMputAtp| |destruct| |bindings| |LyndonWordsList| - |rombergo| |linearPolynomials| |copy!| |factorsOfCyclicGroupSize| - |graphs| |getMatch| |comparison| |ef2edf| - |halfExtendedSubResultantGcd1| |squareTop| |argscript| |f04qaf| |prod| - |OMencodingBinary| |status| |shade| |curry| |imaginary| |upperCase!| - |parent| |jacobian| |subCase?| |setprevious!| |option?| |makeMulti| - |selectsecond| |oneDimensionalArray| |double?| |uncouplingMatrices| - |open?| |palgRDE| |OMputBind| |parts| |approxNthRoot| |ratDsolve| - |rdregime| |setAdaptive3D| |inverseIntegralMatrixAtInfinity| - |monomial| |pseudoDivide| |erf| |generalSqFr| |morphism| |f04axf| - |stack| |weights| |f02axf| |connect| |tanSum| |derivationCoordinates| - |OMopenString| |multivariate| |optimize| |surface| |prinshINFO| - |rightScalarTimes!| |key?| |splitConstant| |cyclicCopy| - |diophantineSystem| |variables| |largest| |initials| |modifyPointData| - |extension| |cothIfCan| |sincos| |rationalApproximation| - |doubleFloatFormat| |monicRightFactorIfCan| |irreducible?| |invmod| - |dilog| |baseRDEsys| |makeCos| |makeUnit| |relerror| |pattern| |quote| - |phiCoord| |isPlus| |pmComplexintegrate| |s14aaf| |chiSquare| |sin| - |OMunhandledSymbol| RF2UTS |modularFactor| |partialNumerators| - |coerceL| |genus| |trueEqual| |prevPrime| |zero?| |cos| - |lookupFunction| |rightCharacteristicPolynomial| |comp| |accuracyIF| - |e04ycf| |f01qef| |cCosh| |leviCivitaSymbol| - |isAbsolutelyIrreducible?| |times!| |tan| |useEisensteinCriterion?| - |tValues| |reducedQPowers| |f02akf| |doubleDisc| |setchildren!| - |principal?| |plusInfinity| |rowEchelon| |taylor| |normInvertible?| - |cot| |getMultiplicationMatrix| |completeHermite| |message| - |triangulate| |finiteBound| |imagj| |decrease| |zeroDim?| - |minusInfinity| |laurent| |negative?| |sec| |generalLambert| - |associator| |bat| |dec| |OMputEndAttr| |bernoulli| |setEpilogue!| - |next| |elseBranch| |lowerCase?| |firstSubsetGray| |OMgetInteger| - |puiseux| |gensym| |csc| |pol| |rem| |inc| |toseLastSubResultant| - |polarCoordinates| |OMbindTCP| |calcRanges| |inputBinaryFile| |d01anf| - |fixedPointExquo| |upDateBranches| |asin| |quo| |tube| |quartic| - |setelt!| |startTable!| |e02bef| |changeNameToObjf| |inv| |showRegion| - |iiacoth| |acos| |flexibleArray| |enqueue!| |setOrder| |SturmHabicht| - |tan2trig| |cyclicParents| |has?| |ground?| |matrixDimensions| - |allRootsOf| |div| |atan| |purelyAlgebraic?| |setVariableOrder| - |alphanumeric?| |getStream| |mapUnivariate| |monicCompleteDecompose| - |type| |rk4qc| |ground| |safeCeiling| |explimitedint| - |tubeRadiusDefault| |cons| |acot| |startTableGcd!| |exquo| - |ScanArabic| |badValues| |decompose| |paraboloidal| - |indicialEquations| |nextIrreduciblePoly| |compdegd| ~= - |leadingMonomial| |se2rfi| |asec| |selectOrPolynomials| |aQuadratic| - |basisOfLeftAnnihilator| |variable?| |part?| |divisor| |OMputEndBind| - |rk4| |leftFactor| |leadingCoefficient| |clearTheSymbolTable| - |continuedFraction| |acsc| |zeroSetSplit| |#| |iicsch| |gcdPrimitive| - |sample| |mapUp!| |optpair| |linearMatrix| |setFormula!| - |primitiveMonomials| |rule| F2FG |sinh| |lexTriangular| ~ |moduleSum| - |leftCharacteristicPolynomial| |fortranComplex| |exp1| |host| |csubst| - |reductum| |rowEchLocal| |cosh| |insert!| |getCurve| |readInt8!| - |perfectNthRoot| |cot2trig| |subst| |recur| |limitedint| - |dominantTerm| |e01bef| |tanh| |systemSizeIF| |symmetricPower| - |mapdiv| |primitive?| |redPol| |OMsend| |hexDigit?| |/\\| |source| - |recip| |coth| |clipSurface| |f07aef| |push!| |reify| |scaleRoots| - |algint| |quadratic| |setPosition| |tubeRadius| |elRow1!| |c06fpf| - |sech| |\\/| |pToHdmp| |stop| |linearlyDependentOverZ?| |associative?| - |orbits| |algebraic?| |balancedFactorisation| |hasoln| |splitLinear| - |csch| |summation| |cot2tan| |void| |drawToScale| |froot| |digamma| - |univariateSolve| |skewSFunction| |s17dcf| |firstDenom| |asinh| - |particularSolution| |rightFactorIfCan| |lowerCase| |c06fuf| - |setClosed| |f04atf| |minimize| |OMputEndApp| |mapSolve| |acosh| - |reseed| |enterPointData| |partialDenominators| |rightRank| |e01saf| - |imagJ| |objects| |inf| |bivariateSLPEBR| |target| |atanh| - |viewWriteDefault| |setProperty| |getOperator| |ignore?| |reducedForm| - |numberOfOperations| |element?| |base| |loadNativeModule| |HenselLift| - |inverse| |acoth| |startStats!| |leadingIndex| |plotPolar| |say| - |OMputEndBVar| |btwFact| |OMgetBind| - |removeIrreducibleRedundantFactors| |lieAdmissible?| |tablePow| - |asech| |fmecg| |traceMatrix| |makeViewport2D| |rightPower| |ddFact| - |c06ecf| |fortranInteger| |s18adf| |OMputObject| |fixPredicate| - |getIdentifier| |acoshIfCan| |inconsistent?| |f01bsf| |taylorIfCan| - |isPower| |makeVariable| |unitCanonical| |multiple| - |explicitlyFinite?| |edf2df| |OMlistSymbols| |weakBiRank| - |listConjugateBases| |addPoint2| |bezoutMatrix| |ravel| |applyQuote| - |ScanFloatIgnoreSpacesIfCan| |principalIdeal| |overset?| |mirror| - |degree| |expIfCan| |rootProduct| |insertRoot!| |fortranLiteralLine| - |closedCurve| |qinterval| |coord| |OMgetFloat| - |semiResultantEuclidean2| |primlimintfrac| |reshape| |zeroMatrix| - |UP2ifCan| |changeVar| |clipWithRanges| |zeroVector| |s17dlf| - |OMgetEndAttr| |padecf| |coercePreimagesImages| |cfirst| |repeating?| - |legendreP| |clearTable!| |iicoth| |fractionFreeGauss!| - |basisOfCenter| |nextsousResultant2| |moduloP| |ruleset| - |removeSuperfluousCases| |coHeight| |blue| |basisOfRightAnnihilator| - |mapmult| |numberOfPrimitivePoly| |queue| |bright| |bracket| |primes| - |scalarTypeOf| |aspFilename| |solid| |OMgetEndBind| |monicLeftDivide| - |localUnquote| |matrixConcat3D| |cAtanh| |tanh2trigh| - |rightRegularRepresentation| |areEquivalent?| |compBound| |lookup| - FG2F |printInfo| |socf2socdf| |unravel| |rootSplit| |littleEndian| - |Lazard| |suchThat| |replace| |update| |f01rcf| |swapRows!| |hspace| - |previous| |callForm?| |bat1| |rischNormalize| |remainder| - |yCoordinates| |ceiling| |virtualDegree| |leftMult| |triangSolve| - |zeroSquareMatrix| |top!| |eigenMatrix| |normalizeAtInfinity| |red| - |outputArgs| |factorOfDegree| |fractionPart| |euclideanNormalForm| - |groebner?| |genericRightNorm| |e02agf| |cosSinInfo| |move| |constant| - |s18acf| |leftRemainder| |unvectorise| |critT| |readInt32!| - |chiSquare1| |less?| |nil| |infinite| |arbitraryExponent| - |approximate| |complex| |shallowMutable| |canonical| |noetherian| - |central| |partiallyOrderedSet| |arbitraryPrecision| - |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| - |additiveValuation| |unitsKnown| |canonicalUnitNormal| - |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| - |commutative|)
\ No newline at end of file + |Record| |Union| |elements| |open?| |iisech| |setLabelValue| |delete| + |light| |insertRoot!| |lambda| |resetVariableOrder| |debug| + |optAttributes| |palgRDE| |pair?| |gcdPolynomial| |writeBytes!| + |quatern| |fortranLiteralLine| |removeSuperfluousQuasiComponents| D + |OMgetObject| |delay| |OMputBind| |laguerre| |gbasis| |operation| + |sort!| |paren| |closedCurve| |denominator| |moebius| |nullSpace| + |var2Steps| |approxNthRoot| |outputGeneral| |torsion?| + |leadingSupport| |internalLastSubResultant| |qinterval| + |generalizedEigenvectors| |c06gqf| |readLine!| |eof?| |d02cjf| + |ratDsolve| |init| |pade| |mainPrimitivePart| |coord| |computeBasis| + |build| |curryRight| |innerSolve| |f04adf| |rdregime| |mergeFactors| + |dAndcExp| |showTheSymbolTable| |OMgetFloat| |tubePoints| + |newTypeLists| |removeZero| |computeInt| |setAdaptive3D| |weierstrass| + |fullDisplay| |polCase| |semiResultantEuclidean2| + |nextLatticePermutation| |rightOne| |groebnerIdeal| + |inverseIntegralMatrixAtInfinity| |cycleLength| |ksec| |e02daf| + |algebraicCoefficients?| |primlimintfrac| |rename!| |s21bbf| + |thetaCoord| |subresultantVector| |setRealSteps| |ode2| |char| + |zeroMatrix| |ran| |call| |cyclic| |radicalEigenvalues| + |palgintegrate| |leftDivide| |internalSubQuasiComponent?| + |genericPosition| |heap| |UP2ifCan| |curryLeft| + |intermediateResultsIF| |medialSet| |merge!| |rdHack1| |cAsinh| + |f04jgf| |cCsch| |generalInfiniteProduct| |changeVar| + |extendedIntegrate| |print| |quasiMonicPolynomials| + |removeRedundantFactorsInContents| |nextNormalPoly| |collectUpper| + |in?| |swapColumns!| |applyRules| |pquo| |resolve| |sin2csc| |besselK| + |extractIndex| |arrayStack| |checkRur| |internalZeroSetSplit| + |euclideanGroebner| |bandedJacobian| |mapdiv| |test| |schwerpunkt| + |identitySquareMatrix| ** |rules| |showAllElements| |cSinh| |prime| + |putColorInfo| |genericRightTrace| |f02fjf| |primitive?| |reverse!| + |e01bgf| |lazyIrreducibleFactors| |factorGroebnerBasis| + |interpretString| |multisect| |rightRemainder| |pole?| |redPol| + |bfEntry| |oblateSpheroidal| |level| |iicos| |LyndonBasis| |Si| + |float| |Ci| |eq| |elColumn2!| |compound?| |OMsend| |LazardQuotient2| + |gradient| |currentSubProgram| |changeMeasure| |atom?| |primeFactor| + |iter| |writable?| |f07fef| |hexDigit?| |primintegrate| |c06ekf| + |point?| |cAtan| |abs| |subQuasiComponent?| |generalizedEigenvector| + |opeval| |prefix| |recip| |minimalPolynomial| + |solveLinearPolynomialEquationByRecursion| |cycleRagits| + |collectQuasiMonic| |setrest!| |nonSingularModel| |s17acf| |subspace| + |clipSurface| |divideExponents| |rightTrace| |returnType!| |sorted?| + |maxPoints3D| |charClass| |mapExponents| |entry?| |f07aef| |iiacsc| + |solveLinearlyOverQ| |mantissa| |screenResolution3D| + |initializeGroupForWordProblem| |perspective| + |exprHasLogarithmicWeights| |zeroSetSplitIntoTriangularSystems| + |cscIfCan| |primPartElseUnitCanonical!| |push!| |setleft!| |wrregime| + |heapSort| |triangular?| |discriminantEuclidean| |varList| |insert| + |linGenPos| |leftQuotient| |topPredicate| |middle| |reify| |comment| + |write!| |nil| |rectangularMatrix| |quoByVar| |complexSolve| + |ricDsolve| |parts| |screenResolution| |position!| |initiallyReduce| + |scaleRoots| |setright!| |binomial| |iicosh| |getProperty| + |domainTemplate| GE |nonLinearPart| |exp| |commutator| + |wronskianMatrix| |algint| |headAst| |An| |cRationalPower| + |quotedOperators| |withPredicates| GT |makeprod| |limitedIntegrate| + |infix| |quadratic| |lepol| |noKaratsuba| |approximate| + |zeroDimPrime?| |back| |f02bjf| LE |external?| |f04asf| |oddlambert| + |setPosition| |complex| |elRow2!| |monomial?| |OMreadFile| |log| + |product| LT |csc2sin| |toseSquareFreePart| |genericLeftDiscriminant| + |radicalEigenvector| |tubeRadius| |intPatternMatch| |ratPoly| + |henselFact| |df2ef| |fractRadix| |lyndon| |finiteBasis| |totalfract| + |elRow1!| |d03eef| |fTable| |normDeriv2| |totolex| |rquo| + |reduceBasisAtInfinity| |solveLinear| |connectTo| |c06fpf| + |lazyPseudoQuotient| |clipBoolean| |irreducibleFactors| |mkIntegral| + |axesColorDefault| |tanintegrate| |stiffnessAndStabilityFactor| + |children| |pToHdmp| |iiacos| |imports| |irreducibleFactor| |green| + |cycleTail| |clearCache| |besselY| |leftTraceMatrix| |identityMatrix| + |resultantReduitEuclidean| |linearlyDependentOverZ?| |xCoord| |e02bdf| + |s18def| |bipolar| |commutativeEquality| |nthCoef| |left| |OMputBVar| + |makeFR| |order| |continue| |associative?| |contractSolve| + |generalTwoFactor| |monicDivide| |repSq| |power| |right| |notelem| + |expintfldpoly| |rroot| |orbits| |convergents| |polar| |e02def| + |binary| |startTableInvSet!| |createMultiplicationTable| |att2Result| + |midpoints| |algebraic?| |BasicMethod| |graphState| |isQuotient| + |stronglyReduce| |createIrreduciblePoly| |mainMonomials| |shallowCopy| + |coerceListOfPairs| |positive?| |balancedFactorisation| + |fortranCharacter| |constantKernel| |f04maf| |length| |alphabetic?| + |outputFixed| |cond| |tab| |s14baf| |csch2sinh| |hasoln| |style| + |scripts| |removeRoughlyRedundantFactorsInPol| |revert| |failed?| + |llprop| |torsionIfCan| |sequences| |radicalSimplify| |splitLinear| + |makeEq| |bsolve| |limit| |octon| |realElementary| + |seriesToOutputForm| |indicialEquation| |numerators| + |pointColorDefault| |summation| |flagFactor| |list?| |tanh2coth| + |viewWriteAvailable| |conjugate| |cyclicSubmodule| |makeObject| + |rootDirectory| |e01bhf| |squareFreeFactors| |cot2tan| |iidprod| + |height| |strongGenerators| |minset| |nthFactor| |stronglyReduced?| + |cosIfCan| |optional?| |dequeue!| |coef| |drawToScale| |fi2df| + |sts2stst| |perfectSquare?| |typeLists| |systemCommand| + |OMconnOutDevice| |composites| |d02kef| |numberOfComponents| |subst| + |froot| |dom| |discreteLog| |dfRange| |genericLeftNorm| |setleaves!| + |setMinPoints3D| |unknownEndian| |palginfieldint| |nullity| |digamma| + |function| |f02adf| |getBadValues| |rewriteSetWithReduction| + |patternVariable| |toseInvertibleSet| |symbol| |node| |maxRowIndex| + |primextendedint| |hermite| |univariateSolve| |generalizedInverse| + |branchIfCan| |f02abf| |s18dcf| |normal| |stoseInvertible?sqfreg| + |expression| |aCubic| |restorePrecision| |buildSyntax| |skewSFunction| + |iCompose| |dihedralGroup| |conjug| |remove| |extractIfCan| + |writeUInt8!| |eval| |integer| |createNormalElement| + |numberOfComposites| |composite| |s17dcf| |nil?| |factorial| + |sayLength| |RittWuCompare| |scalarMatrix| |s20acf| |asechIfCan| + |endSubProgram| |digit?| |firstDenom| |solveInField| + |clearDenominator| |title| |OMputAttr| |last| + |reducedContinuedFraction| |rotate!| |linearAssociatedExp| + |fixedPoint| |nsqfree| |particularSolution| |objects| |assoc| + |predicates| |binding| |s17agf| |size?| |changeName| |integralBasis| + |integralDerivationMatrix| |e02bbf| |base| |rightFactorIfCan| + |jordanAdmissible?| |chebyshevU| |unitVector| |OMputString| + |evaluateInverse| |intcompBasis| |internalIntegrate| |imagI| + |lowerCase| |e| |createZechTable| |constantRight| |rationalIfCan| + |transform| |internalInfRittWu?| |removeConstantTerm| |kroneckerDelta| + |createPrimitiveElement| |c06fuf| |mainForm| |inrootof| + |sturmSequence| |e02ddf| |trapezoidalo| |solve| |e02dcf| |rightGcd| + |label| |setClosed| |brillhartTrials| |dimensionsOf| |specialTrigs| + |smith| |eulerPhi| |po| |rischDE| |tail| |f04atf| |cCot| |parents| + |singRicDE| |gderiv| |e04jaf| |f02aef| |LyndonWordsList1| + |semicolonSeparate| |oddInfiniteProduct| |minimize| + |mainDefiningPolynomial| |setErrorBound| |iomode| |lowerPolynomial| + |normalizeIfCan| |changeWeightLevel| |dflist| |deleteRoutine!| + |OMputEndApp| |fixedPoints| |directory| |lcm| |purelyTranscendental?| + |viewDeltaXDefault| |argumentListOf| |characteristicSet| |polyRicDE| + |removeSinhSq| |mapSolve| |isImplies| |algSplitSimple| |powmod| + |lfextendedint| |e04naf| |tanQ| |equality| |singularAtInfinity?| + |reseed| |groebSolve| |cCsc| |findBinding| |subNode?| |append| + |makeViewport3D| |mainSquareFreePart| |randomLC| |unknown| |aLinear| + |enterPointData| |tableau| |bfKeys| |OMgetString| |adaptive?| + |combineFeatureCompatibility| |gcd| |constructor| + |symmetricDifference| |redPo| |member?| |partialDenominators| + |gramschmidt| |leftGcd| |false| |ode| |s17ajf| |rightRank| + |associatedSystem| |logIfCan| |previous| |option| |binarySearchTree| + |f2st| |viewport2D| |assign| |minimumDegree| |OMgetEndAtp| + |subtractIfCan| |graphImage| |e01saf| |radicalEigenvectors| + |integralBasisAtInfinity| |clearTheFTable| |primitiveElement| + |acothIfCan| |critB| |leftRecip| |omError| |imagJ| |completeEval| + |choosemon| |reverse| |changeThreshhold| |squareMatrix| |nonQsign| + |relativeApprox| |inf| |binaryTournament| |minordet| |matrixGcd| + |result| |normalElement| |contains?| |substring?| |debug3D| + |rightTrim| |clipParametric| |univariatePolynomialsGcds| + |bivariateSLPEBR| |critpOrder| |constantOperator| + |createGenericMatrix| |consnewpol| |numberOfFractionalTerms| |hash| + |nextColeman| |leftTrim| |graeffe| |leftDiscriminant| |leastMonomial| + |viewWriteDefault| |norm| |topFortranOutputStack| + |eisensteinIrreducible?| |solve1| |e04ucf| |suffix?| |count| + |hdmpToDmp| |logpart| |OMgetEndError| |setProperty| + |nthFractionalTerm| |s17akf| |minGbasis| |increment| + |rightTraceMatrix| |interactiveEnv| |f01brf| |getOperator| + |reduceByQuasiMonic| |integralRepresents| |numerator| |basicSet| + |setlast!| F |prefix?| |closedCurve?| |explogs2trigs| |monic?| + |ignore?| |zeroOf| |bumptab| |find| |dmp2rfi| |dn| |write| + |elementary| |selectSumOfSquaresRoutines| |lagrange| |reducedForm| + |getConstant| |ldf2vmf| |save| |mix| |unitNormalize| |d01amf| |f04mcf| + |fprindINFO| |OMputEndObject| |s13adf| + |rewriteIdealWithQuasiMonicGenerators| |removeSinSq| |weighted| + |tubePointsDefault| |linearAssociatedOrder| |isExpt| |uniform01| + |alphanumeric?| |quoted?| |extractTop!| |symmetricGroup| + |eigenvectors| |mesh| |indicialEquationAtInfinity| |cylindrical| + |curve| |getStream| |drawComplex| |bringDown| |setMaxPoints| + |cyclicEqual?| |retractIfCan| |resetNew| |complexZeros| |d02gbf| + |sinhcosh| |mapUnivariate| |pattern| |binaryTree| |divisorCascade| + |cTanh| |coordinates| |maxrow| |coefChoose| EQ |rarrow| |upperCase| + |monicCompleteDecompose| |fglmIfCan| |c06gsf| |definingPolynomial| + |overlap| |subscript| |fortranLiteral| |Nul| |viewDefaults| |rk4qc| + |basisOfCommutingElements| |doubleComplex?| |lfintegrate| + |algintegrate| |extractSplittingLeaf| |mapGen| |unparse| |f01rdf| + |safeCeiling| |pop!| |rational?| |untab| |bytes| |signatureAst| + |e01sbf| |slash| |messagePrint| |explimitedint| |message| |palgint0| + |iifact| |epilogue| |deleteProperty!| |extractProperty| |power!| + |exactQuotient!| |returnTypeOf| |tubeRadiusDefault| |infix?| + |alternatingGroup| |setMinPoints| |headReduce| |exponents| |exists?| + |whitePoint| |interReduce| |viewThetaDefault| |startTableGcd!| |mask| + |possiblyNewVariety?| |s18aff| |subPolSet?| + |exprHasWeightCosWXorSinWX| |basis| |processTemplate| |goodPoint| + |s19adf| |ScanArabic| |leadingIdeal| |s21bdf| |pseudoQuotient| + |colorDef| |setStatus| |map| |crest| |iiexp| |s18aef| |badValues| + |clip| |getProperties| |quotient| |modTree| |numberOfVariables| + |eigenvector| |iidsum| |atoms| |decompose| |swap| |perfectNthPower?| + |boundOfCauchy| |stoseLastSubResultant| |getPickedPoints| |cons| + |deriv| |showScalarValues| |factorSquareFree| |paraboloidal| |float?| + |partialFraction| |algebraicVariables| |mr| |wreath| + |numberOfNormalPoly| |exponential| |brillhartIrreducible?| |iisin| + |indicialEquations| |outputAsScript| |addiag| |primitivePart| + |PollardSmallFactor| |lifting| |category| |permutation| |leftOne| + |mainExpression| |nextIrreduciblePoly| |monomialIntegrate| + |commonDenominator| |mainMonomial| |splitDenominator| |laurentRep| + |convert| |domain| |outerProduct| |moreAlgebraic?| |partialQuotients| + |f02awf| |compdegd| |separant| |linearDependence| |categories| + |characteristicPolynomial| |denominators| |trunc| |package| + |nextPrime| |rootsOf| |bit?| |se2rfi| |droot| |completeHensel| + |Vectorise| |maximumExponent| |cos2sec| |increasePrecision| + |createNormalPrimitivePoly| |bandedHessian| |selectOrPolynomials| + |countable?| |primitivePart!| |graphCurves| |freeOf?| |lazyEvaluate| + |mappingAst| |source| |bombieriNorm| |mapBivariate| |qualifier| + |aQuadratic| |failed| |setProperty!| |baseRDE| |components| |twist| + |f02ajf| |hasHi| |stoseSquareFreePart| |multiset| |mathieu24| + |basisOfLeftAnnihilator| |leastPower| |UpTriBddDenomInv| |evenlambert| + |makeFloatFunction| |antisymmetric?| |balancedBinaryTree| |elliptic?| + |direction| |variable?| |numberOfComputedEntries| + |tryFunctionalDecomposition| |OMgetAtp| |e01sff| |e02bcf| + |rationalPoints| |inverseIntegralMatrix| |padicallyExpand| |part?| + |semiSubResultantGcdEuclidean1| |zCoord| |wholePart| |palgextint| + |computePowers| |horizConcat| |leftZero| |fillPascalTriangle| + |divisor| |imagE| |vertConcat| |indiceSubResultant| |OMsupportsCD?| + |sh| |target| |log2| |univcase| |OMencodingXML| |OMputEndBind| + |LiePolyIfCan| |subresultantSequence| |mesh?| |internalIntegrate0| + |qroot| |secIfCan| |saturate| |head| |stoseInternalLastSubResultant| + |rk4| |uniform| |alternative?| |minPol| |e02zaf| |Gamma| |bits| + |numericalIntegration| |exprToGenUPS| |f07fdf| |leftFactor| |contract| + |extendedint| |cschIfCan| |lSpaceBasis| |normFactors| |solveid| + |leftLcm| |isNot| |clearTheSymbolTable| |Is| |pointLists| |rowEch| + |categoryFrame| |bothWays| |rationalFunction| |hermiteH| + |wordInStrongGenerators| |continuedFraction| |setEmpty!| |leftPower| + |quotientByP| |probablyZeroDim?| |normalForm| |depth| |ravel| + |leftFactorIfCan| |exactQuotient| |scripted?| |zeroSetSplit| |trigs| + |bag| |createNormalPoly| |e02akf| |coshIfCan| |reshape| |invertible?| + |OMputInteger| |symbolTableOf| |iicsch| |vedf2vef| + |principalAncestors| |commaSeparate| |lifting1| + |purelyAlgebraicLeadingMonomial?| |positiveSolve| |byteBuffer| + |drawStyle| |gcdPrimitive| |completeEchelonBasis| |e02dff| |algDsolve| + |generateIrredPoly| |cExp| |simplifyPower| |any?| |f02wef| |sample| + |reflect| |charthRoot| |divideIfCan| |reduceLODE| |modulus| + |internalSubPolSet?| |readUInt16!| |patternMatchTimes| |mapUp!| |next| + |powerAssociative?| |knownInfBasis| + |removeRoughlyRedundantFactorsInPols| |cup| |palglimint0| |formula| + |outputForm| |separateFactors| |difference| |optpair| |isAnd| |equiv| + |create| |iiabs| |s19acf| |squareFreePart| |update| + |lastSubResultantEuclidean| |unprotectedRemoveRedundantFactors| + |linearMatrix| |divisors| |plus!| |s17aff| |setnext!| |OMgetEndApp| + |presub| |expt| |square?| |setFormula!| |internalDecompose| + |mathieu11| |taylorRep| |rightMinimalPolynomial| |integerIfCan| |push| + |declare| |lazyResidueClass| |prime?| |parameters| F2FG + |quadraticForm| |nextPrimitivePoly| |HermiteIntegrate| |aromberg| + |clikeUniv| |nrows| |functionIsContinuousAtEndPoints| |d01bbf| + |toseInvertible?| |lexTriangular| |flexible?| |sumSquares| |setTex!| + |numberOfIrreduciblePoly| |s01eaf| |ncols| |e04fdf| |evaluate| + |complexForm| |moduleSum| |sumOfDivisors| |normalize| + |basisOfRightNucloid| |makingStats?| |intChoose| |position| + |shellSort| |getExplanations| |leftCharacteristicPolynomial| + |ScanFloatIgnoreSpaces| |factorSquareFreePolynomial| + |basisOfMiddleNucleus| |prindINFO| |lieAlgebra?| |lllp| |d01gbf| + |floor| |fortranComplex| |iilog| |regularRepresentation| + |setAttributeButtonStep| |sumOfKthPowerDivisors| |getRef| + |splitSquarefree| |hostPlatform| |prepareDecompose| |simpleBounds?| + |exp1| |arg1| |exprex| |unmakeSUP| |semiSubResultantGcdEuclidean2| + |listYoungTableaus| |branchPointAtInfinity?| |createRandomElement| + |host| |string?| |arg2| |chainSubResultants| |child?| |c05nbf| + |rCoord| |genericRightDiscriminant| 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|totalDegree| + |display| |monomRDE| |addPointLast| |separate| |limitedint| |digit| + |cross| |permanent| |minPoints3D| |modularGcdPrimitive| |critBonD| + |genericLeftMinimalPolynomial| |dominantTerm| |gcdcofactprim| + |solveLinearPolynomialEquation| |trim| |f02bbf| |nodes| |e01bef| + |stopMusserTrials| |fortran| |cyclicGroup| |createLowComplexityTable| + |shufflein| |rewriteIdealWithRemainder| |subset?| |slex| + |systemSizeIF| |divideIfCan!| |printStats!| |blankSeparate| + |monomRDEsys| |insertBottom!| |divide| |reduced?| |symmetricPower| + |neglist| |c06ebf| |lintgcd| |groebner| |input| |close!| + |setImagSteps| |universe| |lift| |lazyIntegrate| |lquo| |interpolate| + |birth| |library| |finite?| |biRank| |stopTableInvSet!| + |useEisensteinCriterion?| |suchThat| |reduce| + |numberOfImproperPartitions| |cubic| |radicalOfLeftTraceForm| + |compactFraction| |var2StepsDefault| |copyInto!| |mkAnswer| |tValues| + |branchPoint?| |constant?| |iicsc| |inHallBasis?| |ip4Address| + |primlimitedint| |viewPhiDefault| |reducedQPowers| |kovacic| + |currentCategoryFrame| |tableForDiscreteLogarithm| |critMTonD1| + |sinh2csch| |representationType| |exponent| |f02akf| |s17ahf| + |permutationGroup| |conical| |normalized?| |zeroSquareMatrix| |set| + |extendIfCan| |leftUnit| |setScreenResolution3D| |numeric| + |doubleDisc| |kind| BY |shrinkable| |semiResultantEuclideannaif| + |newReduc| |showAll?| |top!| |id| |viewport3D| |lazyPremWithDefault| + |stoseInvertible?reg| |radical| |setchildren!| |OMputError| + |pointSizeDefault| |op| |laguerreL| |graphStates| |condition| + |eigenMatrix| |genericLeftTraceForm| |central?| |deepExpand| + |principal?| |makeSeries| |ParCondList| |generic?| |cycleEntry| + |normalizeAtInfinity| |members| |table| |listexp| |adaptive3D?| + |rowEchelon| |maxIndex| |e04gcf| |bigEndian| |maxrank| |readUInt8!| + |red| |search| |scale| |new| |romberg| |unexpand| |normInvertible?| + |obj| |var1Steps| |halfExtendedResultant1| |script| + |reciprocalPolynomial| |initiallyReduced?| |outputArgs| |conjugates| + |frst| |redpps| |getMultiplicationMatrix| |makeop| |changeBase| + |cache| |ODESolve| |pdct| |factorOfDegree| |leftUnits| |e02ahf| + |signature| |matrix| |viewpoint| |completeHermite| |rootSimp| |real?| + |normalise| |invertibleSet| |fractionPart| |complex?| NOT + |showFortranOutputStack| |monomials| |triangulate| |rootNormalize| + |resultant| |univariatePolynomial| |tex| |palgextint0| |union| + |euclideanNormalForm| |inRadical?| OR |positiveRemainder| |d01ajf| + |finiteBound| |byte| |stirling1| |multMonom| |removeDuplicates!| + |nextPartition| |groebner?| |cyclotomicDecomposition| AND + |complexExpand| |closed?| |imagj| |numer| |nary?| |discriminant| + |ratpart| |ScanRoman| |genericRightNorm| |show| |complexLimit| + |s21bcf| |errorKind| |decrease| |denom| |recolor| |vark| + |musserTrials| |LyndonCoordinates| |e02agf| |symmetric?| + |isConnected?| |expandTrigProducts| |zeroDim?| |trigs2explogs| + |minIndex| |standardBasisOfCyclicSubmodule| |subTriSet?| |cosSinInfo| + |trace| |iroot| |relationsIdeal| |hostByteOrder| |negative?| |pi| + |generator| |shift| |coerce| |rotatez| |cAcosh| |leastAffineMultiple| + |getDatabase| |move| |isobaric?| |selectNonFiniteRoutines| |lo| + |pomopo!| |generalLambert| |infinity| |center| |construct| |OMserve| + |semiDiscriminantEuclidean| |low| |Beta| |s18acf| |transpose| + |ramified?| |lyndon?| |associator| |eigenvalues| |drawCurves| |swap!| + |linearDependenceOverZ| |leftRemainder| |roughBase?| |incr| |hMonic| + |column| |bat| |int| |seriesSolve| |compile| |factorset| + |sylvesterSequence| |before?| |unvectorise| |hexDigit| |hi| + |divergence| |invmultisect| |kernel| |OMputEndAttr| |palgLODE| + |karatsubaOnce| |rootKerSimp| |infLex?| |critT| |lighting| + |hasSolution?| |maxint| |draw| |bernoulli| |iprint| |splitNodeOf!| + |primextintfrac| |lowerCase!| |readInt32!| |cardinality| * |iitan| + |taylorQuoByVar| |setEpilogue!| |imagk| |mainVariable| |alphabetic| + |polygon?| |currentEnv| |chiSquare1| |setTopPredicate| |iiasec| + |hconcat| |elseBranch| |leaves| |orbit| |dot| |ranges| |coleman| + |less?| |dictionary| |root| |ListOfTerms| |lowerCase?| + |squareFreeLexTriangular| |lyndonIfCan| |zeroDimPrimary?| |shuffle| + |binaryFunction| |sturmVariationsOf| = |zoom| |firstSubsetGray| + |e02ajf| |OMcloseConn| |gcdcofact| |addMatch| |empty| |setColumn!| + |even?| |OMgetInteger| |singularitiesOf| |s21baf| |squareFreePrim| + |round| |decimal| |curve?| |pile| < |gensym| |lazy?| |keys| |indices| + |dmpToP| |unit| |removeCosSq| |outputMeasure| |makeResult| + |constantIfCan| > |pol| |symbolTable| |scopes| |fracPart| |denomRicDE| + |getVariableOrder| |component| |meshFun2Var| |trailingCoefficient| <= + |toseLastSubResultant| |setelt| |localReal?| + |genericRightMinimalPolynomial| |reopen!| |adjoint| |infieldIntegrate| + |multiple?| >= |reducedDiscriminant| |polarCoordinates| + |pushFortranOutputStack| |OMencodingUnknown| |lprop| |fortranLogical| + |cyclePartition| |createLowComplexityNormalBasis| |OMgetError| + |cosh2sech| |popFortranOutputStack| |OMbindTCP| |copy| |prem| + |sech2cosh| |ellipticCylindrical| |firstNumer| |lazyGintegrate| + |palgRDE0| |c06fqf| |calcRanges| |outputAsFortran| |expr| |initial| + |cCoth| |subResultantsChain| |showTheIFTable| |reverseLex| + |leftRankPolynomial| |lazyPrem| |pointData| + |inputBinaryFile| |nthr| + |limitPlus| |anfactor| |acscIfCan| |doubleResultant| |color| - |dark| + |d01anf| |autoCoerce| |credPol| |padicFraction| |setCondition!| + |KrullNumber| |harmonic| |constantCoefficientRicDE| |updateStatus!| / + |fixedPointExquo| |f04faf| |randomR| |fullPartialFraction| + |symmetricRemainder| |rotatex| |showSummary| |listOfMonoms| + |realZeros| |output| |upDateBranches| |variable| |mapUnivariateIfCan| + |besselJ| |infieldint| |coefficients| |c02aff| |lfinfieldint| + |stFunc2| |tube| |iterators| |unary?| |atanhIfCan| |alphanumeric| + |s19aaf| |cn| |showAttributes| |mathieu22| |stopTableGcd!| + |viewSizeDefault| |quartic| |normal?| |mpsode| |useNagFunctions| + |subMatrix| |extendedSubResultantGcd| |d01asf| |nativeModuleExtension| + |setelt!| |collectUnder| |poisson| |mvar| |tanAn| |checkForZero| + |iiGamma| |algebraicOf| |startTable!| |OMgetVariable| |integer?| + |monicModulo| |setValue!| |updatD| |createPrimitivePoly| + |OMputVariable| |e02bef| |dihedral| |ldf2lst| |sinIfCan| |qelt| |true| + |Hausdorff| |factorsOfDegree| |badNum| |changeNameToObjf| |qsetelt| + |mainValue| |removeZeroes| |cAsin| |externalList| |cPower| |simpsono| + |algebraicSort| |showRegion| |prolateSpheroidal| |OMputEndError| + |xRange| |rightExactQuotient| |asinhIfCan| |cycleSplit!| + |OMParseError?| |acschIfCan| |iiacoth| |vector| |sumOfSquares| + |iiasin| |factorSquareFreeByRecursion| |yRange| |empty?| + |primPartElseUnitCanonical| |precision| |reduction| |sinhIfCan| + |flexibleArray| |differentiate| |point| |submod| |zRange| |ridHack1| + |possiblyInfinite?| |box| |setLegalFortranSourceExtensions| + |selectfirst| |enqueue!| |dimensionOfIrreducibleRepresentation| + |conditionP| |map!| |physicalLength!| |index?| |mathieu23| + |decomposeFunc| |dimensions| |setOrder| |componentUpperBound| + |twoFactor| |qsetelt!| |modularGcd| |OMgetEndBVar| |high| |Ei| + |cycles| |SturmHabicht| |corrPoly| |lex| |series| + |removeRedundantFactors| |enterInCache| |atrapezoidal| |tan2trig| + |tracePowMod| |numFunEvals3D| |mainKernel| |exprToXXP| |iiasech| + |pointColorPalette| |c06frf| |cyclicParents| |setProperties!| |goto| + |iteratedInitials| |polyRDE| |invertibleElseSplit?| |meatAxe| + |OMreceive| |whatInfinity| |has?| |sdf2lst| |repeating| |removeCoshSq| + |genericRightTraceForm| |signAround| |reset| |resultantReduit| |f2df| + |isOp| |matrixDimensions| |powerSum| |double| |coth2tanh| |min| + |acsch| |solveRetract| |sortConstraints| |listOfLists| |allRootsOf| + |operators| |complexIntegrate| |e02gaf| |translate| + |viewDeltaYDefault| UP2UTS |LagrangeInterpolation| |complexElementary| + |purelyAlgebraic?| |GospersMethod| |minPoints| |copies| |d03faf| + |squareFree| |rootOf| |stoseInvertibleSet| |setVariableOrder| + |toroidal| |arguments| |open| |showTheFTable| |parseString| |c05pbf| + |putGraph| |rootPoly| |lexGroebner| |numberOfCycles| |getOperands| + |factorByRecursion| |numFunEvals| |tryFunctionalDecomposition?| + |companionBlocks| |firstUncouplingMatrix| |nodeOf?| + |inputOutputBinaryFile| |pseudoDivide| |null| |iitanh| |sqfree| + |chvar| |printHeader| |basisOfCentroid| |any| |preprocess| |radPoly| + |compose| |generalSqFr| |zag| |not| |getSyntaxFormsFromFile| |htrigs| + |selectAndPolynomials| |deepestTail| |OMread| |morphism| |acotIfCan| + |leadingExponent| |newSubProgram| |rangeIsFinite| |d01fcf| + |operations| |SturmHabichtMultiple| |wordsForStrongGenerators| |and| + |declare!| |simplifyLog| |iiasinh| |multiplyCoefficients| |distFact| + |mapDown!| |infinityNorm| |perfectSqrt| |makeTerm| |f04axf| |pushdown| + |iflist2Result| |or| |listBranches| |concat!| |insertTop!| + |leftExtendedGcd| |clipWithRanges| |f02xef| |weights| |sizeLess?| + |errorInfo| |aQuartic| |read!| |expandPower| |zeroVector| |xor| + |leadingTerm| |OMgetEndObject| |f02agf| |s15aef| |interpret| |vconcat| + |cycleElt| |makeGraphImage| |hyperelliptic| |setOfMinN| |f02axf| + |endOfFile?| |log10| |case| |elem?| |multiplyExponents| + |selectODEIVPRoutines| |magnitude| |solid?| |s17dlf| |arbitrary| + |sizePascalTriangle| |mainVariable?| |recoverAfterFail| |kmax| + |connect| |generate| |printStatement| |Zero| |euler| |wholeRadix| + |integers| |bitand| |outputFloating| |OMgetEndAttr| |s20adf| + |subHeight| |diff| |yCoord| |tanSum| |superscript| |numberOfHues| + |One| |printInfo!| |points| |compiledFunction| |bitior| + |noncommutativeJordanAlgebra?| |padecf| |spherical| |setFieldInfo| + |OMconnInDevice| |stoseInvertible?| |derivationCoordinates| |plot| + |incrementBy| |makeSin| |degreeSubResultantEuclidean| + |repeatUntilLoop| |dmpToHdmp| |coercePreimagesImages| |loopPoints| + |bezoutResultant| |computeCycleEntry| |dequeue| |resultantEuclidean| + |toScale| |OMopenString| |expand| |associatedEquations| + |monicRightDivide| |segment| |readByte!| |asinIfCan| |measure2Result| + |cfirst| |homogeneous?| |leftExactQuotient| |lastSubResultant| + |bounds| |rightAlternative?| |surface| |filterWhile| |prinpolINFO| + |deref| |critMonD1| |roughUnitIdeal?| |iisinh| |repeating?| + |upperCase?| |bubbleSort!| |ffactor| |addmod| |prinshINFO| |d01gaf| + |super| |filterUntil| |separateDegrees| |prologue| |pdf2df| + |fortranLinkerArgs| |legendreP| |addMatchRestricted| |rightUnit| + |symbolIfCan| |rightScalarTimes!| |d02bbf| |exptMod| |cyclic?| + |select| |elt| |module| |variationOfParameters| |exponentialOrder| + |deepestInitial| |number?| |clearTable!| |capacity| |f02aaf| + |selectPolynomials| |subResultantGcd| |key?| |setref| |prinb| |s17dgf| + |OMputSymbol| |split| |iicoth| |rotate| |integralMatrixAtInfinity| + |makeYoungTableau| |realEigenvectors| |inR?| |splitConstant| + |minColIndex| |linearlyDependent?| |stoseInvertibleSetreg| + |stiffnessAndStabilityOfODEIF| |cAsech| |fractionFreeGauss!| |s17aef| + |eq?| |space| |rangePascalTriangle| |split!| + |integralLastSubResultant| |cyclicCopy| |nthFlag| |s13aaf| + |degreeSubResultant| |maxColIndex| |basisOfCenter| + |expenseOfEvaluationIF| |ratDenom| |intensity| |packageCall| + |dimension| |innerSolve1| |diophantineSystem| |exprHasAlgebraicWeight| + |lazyPseudoRemainder| |e02aef| |var1StepsDefault| |jacobi| + |nextsousResultant2| |cartesian| |weight| |rationalPoint?| |cLog| + |factorFraction| |largest| |retract| |expintegrate| |invertIfCan| + |OMconnectTCP| |pushup| |moduloP| |setfirst!| |exteriorDifferential| + |curveColor| |d01akf| |resetBadValues| |s14abf| |initials| + |makeRecord| |powers| |airyAi| |fintegrate| |showTheRoutinesTable| + |removeSuperfluousCases| |status| |PDESolve| |iiperm| + |complementaryBasis| |characteristicSerie| |nextsubResultant2| + |goodnessOfFit| |sort| |modifyPointData| |someBasis| |internal?| + |e04dgf| |stFuncN| |coHeight| |stopTable!| |property| |extension| + |terms| |backOldPos| |determinant| |fill!| |closeComponent| |iExquo| + |rightDivide| |conditionsForIdempotents| |polyred| |pdf2ef| |blue| + |leftRank| |integerBound| |commutative?| |erf| |acosIfCan| + |BumInSepFFE| |cothIfCan| |identification| |OMopenFile| |nthExponent| + |hasPredicate?| |basisOfRightAnnihilator| |mkPrim| |iiacsch| + |leftTrace| |lfunc| |antiCommutator| |factorSFBRlcUnit| Y + |insertionSort!| |sincos| |mkcomm| |symmetricProduct| |meshPar1Var| + |figureUnits| |just| |sparsityIF| |mapmult| |cSech| |units| + |quickSort| |rationalApproximation| |sqfrFactor| |resize| UTS2UP + |random| |rightZero| |initTable!| |setClipValue| |axes| + |numberOfPrimitivePoly| |s19abf| |dilog| |fractRagits| |resultantnaif| + |defineProperty| |doubleFloatFormat| |characteristic| + |useEisensteinCriterion| |interval| |over| + |indiceSubResultantEuclidean| |queue| |retractable?| |cAcsch| + |simplifyExp| |legendre| |LowTriBddDenomInv| |sin| + |monicRightFactorIfCan| |rightLcm| |tanNa| |setPrologue!| + |localIntegralBasis| |getMultiplicationTable| |bracket| |irreducible?| + |entries| |plus| |janko2| |replaceKthElement| |imagK| |cos| + |predicate| |leadingBasisTerm| |lazyPseudoDivide| |overbar| |digits| + |sizeMultiplication| |primes| |getButtonValue| |mainVariables| + |invmod| |isList| |addBadValue| |tan| |key| |f07adf| + |semiResultantReduitEuclidean| |gcdprim| |mindeg| |scalarTypeOf| + |code| |generators| |lineColorDefault| |shiftRight| |baseRDEsys| + |stosePrepareSubResAlgo| |cot| |clipPointsDefault| |returns| |rk4a| + |rootPower| |tubePlot| |aspFilename| |makeCos| |ref| |isMult| + |integral| |meshPar2Var| |sec| |complexRoots| |lhs| |filename| + |vspace| |ReduceOrder| |OMwrite| |deepCopy| |solid| |moebiusMu| + |makeUnit| |printingInfo?| |d02bhf| |times| |semiResultantEuclidean1| + |csc| |rhs| |rotatey| |inc| |setPredicates| |doublyTransitive?| + |numberOfMonomials| |OMgetEndBind| |quadratic?| |iisec| + |attributeData| |createPrimitiveNormalPoly| |relerror| |asin| + |frobenius| |parse| |s17dhf| |latex| |OMUnknownSymbol?| |name| + |monicLeftDivide| |bitTruth| |f04arf| |outlineRender| |quote| |acos| + |lambert| |makeSketch| |karatsubaDivide| |quasiRegular| + |primintfldpoly| |body| |localUnquote| |rootRadius| |multiEuclidean| + |cAcos| |linSolve| |phiCoord| |atan| |s13acf| |quasiMonic?| + |associates?| |roughBasicSet| |matrixConcat3D| |integralCoordinates| + |delta| |monom| |getMeasure| |makeSUP| |isPlus| |headRemainder| |acot| + |e01bff| |contours| |nullary?| |innerEigenvectors| |cAtanh| |cap| + |mapCoef| |pmComplexintegrate| |eulerE| |asec| |maxdeg| |readBytes!| + |intersect| |iFTable| |triangularSystems| |tanh2trigh| |testDim| + |rule| |rational| |diagonalProduct| |shiftLeft| |s14aaf| |acsc| + |unaryFunction| |seed| |ocf2ocdf| |complement| + |rightRegularRepresentation| |common| |jordanAlgebra?| |d01apf| + |viewPosDefault| |chiSquare| |sinh| |coth2trigh| |approximants| + |nextItem| |whileLoop| |critM| |areEquivalent?| |readInt16!| |powern| + |Frobenius| |OMunhandledSymbol| |cosh| |extend| |realRoots| |qPot| + |presuper| |port| |removeRedundantFactorsInPols| |compBound| + |SFunction| |bottom!| |e01daf| |tanhIfCan| |tanh| RF2UTS |e04mbf| + |distance| |bitLength| |writeLine!| |lookup| |modularFactor| + |nthRootIfCan| |typeList| |sec2cos| |internalAugment| |coth| + |lfextlimint| |inverseLaplace| |bivariatePolynomials| |exponential1| + |t| |list| FG2F |partialNumerators| |geometric| |pascalTriangle| + |factorPolynomial| |iicot| |sech| |fibonacci| |squareFreePolynomial| + |root?| |car| |mightHaveRoots| |socf2socdf| |coerceL| |measure| + |roughEqualIdeals?| |trivialIdeal?| |csch| |exportedOperators| |df2fi| + |cyclotomic| |cdr| |isOpen?| |unravel| |nor| |cyclotomicFactorization| + |selectMultiDimensionalRoutines| |subResultantChain| |genus| |asinh| + |setDifference| |rightMult| |subNodeOf?| |f01mcf| + |showIntensityFunctions| |rootSplit| |infiniteProduct| + |antiAssociative?| |unit?| |printTypes| |trueEqual| |acosh| |cAcoth| + |setIntersection| |quasiAlgebraicSet| |pToDmp| |readLineIfCan!| + |littleEndian| |absolutelyIrreducible?| |nothing| |rspace| |OMgetAttr| + |pureLex| |prevPrime| |atanh| |fortranDoubleComplex| |setUnion| + |countRealRoots| |Lazard| |controlPanel| |iiacosh| |normalDeriv| + |atanIfCan| |zero?| |acoth| |forLoop| |createThreeSpace| + |safetyMargin| |apply| |mainCoefficients| |say| |replace| + |rightQuotient| |reindex| |sncndn| |lookupFunction| |orthonormalBasis| + |asech| |bezoutDiscriminant| |nextNormalPrimitivePoly| + |highCommonTerms| |enumerate| |f01rcf| |stoseInvertibleSetsqfreg| + |iiacot| |numericalOptimization| |rightCharacteristicPolynomial| + |refine| |basisOfRightNucleus| |modifyPoint| |size| |cycle| + |rewriteIdealWithHeadRemainder| |swapRows!| |create3Space| + |outputList| |accuracyIF| |zero| |sin?| |multiple| |ideal| |s17adf| + |diagonalMatrix| |laurentIfCan| |hspace| |functionIsFracPolynomial?| + |inspect| |isTimes| |applyQuote| |e04ycf| |B1solve| |width| |tree| + |wholeRagits| |vectorise| |distdfact| |rowEchelonLocal| |callForm?| + |decreasePrecision| |rightRecip| |getGraph| |And| |numberOfDivisors| + |f01qef| |leader| |rightDiscriminant| |quasiRegular?| |first| + |randnum| |airyBi| |bat1| |logical?| |stirling2| |UnVectorise| |Or| + |cCosh| |linears| |unitNormal| |minimumExponent| |rest| + |rischNormalize| |totalLex| |minrank| |transcendenceDegree| + |leviCivitaSymbol| |Not| |edf2efi| |ruleset| |simpson| |transcendent?| + |leftMinimalPolynomial| |routines| |substitute| |remainder| + |printInfo| |fortranCarriageReturn| |pleskenSplit| |oddintegers| + |setScreenResolution| |isAbsolutelyIrreducible?| |jacobiIdentity?| + |makeCrit| |psolve| |outputAsTex| |removeDuplicates| |yCoordinates| + |subResultantGcdEuclidean| |pack!| |selectFiniteRoutines| |times!| + |rur| |f01maf| |definingEquations| |OMUnknownCD?| |minRowIndex| + |ceiling| |alternating| |supersub| |checkPrecision| |polygon| + |sequence| |duplicates?| |autoReduced?| |getOrder| |virtualDegree| + |optimize| |dioSolve| |distribute| |numberOfChildren| |asecIfCan| + |supDimElseRittWu?| |zeroDimensional?| |f04mbf| |optional| |OMgetType| + |symbol?| |leftMult| |diagonals| |character?| |updatF| |nand| + |showArrayValues| |abelianGroup| |remove!| |logGamma| + |monomialIntPoly| |triangSolve| |parabolic| + |removeRoughlyRedundantFactorsInContents| |antisymmetricTensors| + |idealSimplify| |check| |constant| |factor1| |roman| + |useSingleFactorBound?| |laplacian| |stack| |totalDifferential| + |qfactor| |hypergeometric0F1| |fortranTypeOf| |tower| |leaf?| + |parabolicCylindrical| |differentialVariables| |algebraicDecompose| + |pseudoRemainder| |numberOfOperations| |constantLeft| |colorFunction| + |printCode| |coerceS| |c06gbf| |Lazard2| |cyclicEntries| |singular?| + |countRealRootsMultiple| |element?| |flatten| |d02ejf| + |findConstructor| |imagi| |getCode| |readUInt32!| |extract!| + |leftNorm| |leadingCoefficientRicDE| |plusInfinity| |showClipRegion| + |HenselLift| |polygamma| |OMputFloat| |odd?| |linear?| |null?| + |polyPart| |duplicates| |pow| |minusInfinity| |overlabel| |inverse| + |c02agf| |extractClosed| SEGMENT |numericIfCan| |truncate| + |mindegTerm| |dim| |equation| |implies| + |rewriteSetByReducingWithParticularGenerators| |shallowExpand| |child| + |startStats!| |increase| |expPot| |rem| |asimpson| |lazyPquo| + |thenBranch| |complexNumeric| |s17def| |semiLastSubResultantEuclidean| + |Aleph| |lllip| |leadingIndex| |top| |one?| |quo| |tRange| |besselI| + |minus!| |node?| |max| |stoseIntegralLastSubResultant| |eyeDistance| + |hessian| |radix| |plotPolar| |yellow| |radicalRoots| |binomThmExpt| + |fixedDivisor| |kernels| |generic| |functionIsOscillatory| + |usingTable?| |normalizedDivide| |tan2cot| |OMputEndBVar| + |nextSubsetGray| |cAcot| |div| |mathieu12| |parametersOf| |operator| + |scan| |setButtonValue| |LiePoly| |f01qdf| |type| |rk4f| |btwFact| + |exquo| |stFunc1| |primeFrobenius| |anticoord| + |shanksDiscLogAlgorithm| |coordinate| |postfix| |isEquiv| |innerint| + |cSin| |OMgetBind| |lexico| ~= |content| |hcrf| |rightExtendedGcd| + |hue| |univariate| |partitions| |movedPoints| |approxSqrt| |directSum| + |removeIrreducibleRedundantFactors| |sn| |incrementKthElement| |#| + |rename| |hitherPlane| |functorData| |listRepresentation| + |bipolarCylindrical| |fortranDouble| |d02raf| |superHeight| + |lieAdmissible?| |ipow| ~ |range| |fortranReal| |isOr| |radicalSolve| + |concat| |OMsupportsSymbol?| |stripCommentsAndBlanks| |outputSpacing| + |semiDegreeSubResultantEuclidean| |tablePow| |iiatan| |tab1| + |mapMatrixIfCan| |npcoef| |leftScalarTimes!| |factor| |pr2dmp| + |RemainderList| |extendedEuclidean| |pushuconst| |fmecg| |mat| + |complexNormalize| |idealiserMatrix| |rischDEsys| |OMputAtp| |sqrt| + |clearFortranOutputStack| |nlde| |derivative| |bitCoef| |traceMatrix| + |iipow| |bindings| |/\\| |reorder| |pastel| |real| |coefficient| + |computeCycleLength| |testModulus| |getlo| |rightRankPolynomial| + |makeViewport2D| |resetAttributeButtons| |\\/| |quasiComponent| + |reducedSystem| |LyndonWordsList| |lazyVariations| |imag| + |solveLinearPolynomialEquationByFractions| |ParCond| + |linearAssociatedLog| |complexEigenvalues| |rightPower| + |directProduct| |generalPosition| |block| |selectOptimizationRoutines| + |rombergo| |unrankImproperPartitions1| |linearPart| |expandLog| + |physicalLength| |selectIntegrationRoutines| |ddFact| |factorials| + |shiftRoots| |chebyshevT| |semiIndiceSubResultantEuclidean| + |linearPolynomials| |second| |rightNorm| |argument| + |scanOneDimSubspaces| LODO2FUN |c06ecf| |ord| |iibinom| |palgint| + |copy!| |denomLODE| |nthRoot| |brace| |third| |ptree| + |useSingleFactorBound| |belong?| |raisePolynomial| + |associatorDependence| |fortranInteger| |factorsOfCyclicGroupSize| + |exprToUPS| |OMReadError?| |setMaxPoints3D| |pushucoef| |destruct| + |isTerm| |headReduced?| |chineseRemainder| |c06eaf| |s18adf| |void| + |doubleRank| |mergeDifference| |numberOfFactors| |setvalue!| + |polynomialZeros| |graphs| |symmetricSquare| |karatsuba| |iisqrt3| + |is?| |OMputObject| |iiatanh| |symmetricTensors| |elliptic| + |degreePartition| |safeFloor| |getMatch| |f02aff| |normal01| + |basisOfLeftNucloid| |pmintegrate| |fixPredicate| |comparison| + |OMputApp| |normalDenom| |selectPDERoutines| |rootOfIrreduciblePoly| + |sum| |patternMatch| |userOrdered?| |youngGroup| |cotIfCan| + |getIdentifier| |ef2edf| |getGoodPrime| |leftAlternative?| |diag| + |pointPlot| |monomial| |d01aqf| |d02gaf| |df2mf| + |lastSubResultantElseSplit| |acoshIfCan| |setLength!| |rank| |ode1| + |plenaryPower| |complexNumericIfCan| |multivariate| + |halfExtendedSubResultantGcd1| |prepareSubResAlgo| |subSet| + |unrankImproperPartitions0| |options| |integralAtInfinity?| + |ramifiedAtInfinity?| |inconsistent?| |dualSignature| |infinite?| + |minPoly| |explicitlyEmpty?| |squareTop| |variables| |c05adf| |more?| + |extensionDegree| |hclf| |maxPoints| |f01bsf| |antiCommutative?| + |mulmod| |trapezoidal| |tensorProduct| |argscript| |const| + |writeInt8!| |currentScope| |palglimint| |mainContent| |lp| + |taylorIfCan| |zerosOf| |cSec| |constDsolve| + |generalizedContinuumHypothesisAssumed?| |f04qaf| |delete!| |edf2ef| + |linkToFortran| |palgLODE0| |string| |primaryDecomp| |bright| + |isPower| |nextSublist| |idealiser| |unitsColorDefault| |pushdterm| + |prod| |setProperties| |comp| |OMmakeConn| |pointColor| |writeByte!| + |makeVariable| |multinomial| |nthExpon| |prefixRagits| |row| |s15adf| + |OMencodingBinary| |permutations| |insertMatch| |rightFactorCandidate| + |setAdaptive| |unitCanonical| |identity| |loadNativeModule| + |factorAndSplit| |collect| |genericLeftTrace| |simplify| |shade| + |taylor| |noLinearFactor?| |sign| |parametric?| |integrate| + |explicitlyFinite?| |every?| |iterationVar| |lists| |qqq| |curry| + |e02baf| |outputBinaryFile| |laurent| |df2st| + |nextPrimitiveNormalPoly| |sPol| |rubiksGroup| |edf2df| + |generalizedContinuumHypothesisAssumed| |imaginary| |mapExpon| + |lflimitedint| |setsubMatrix!| |expenseOfEvaluation| |puiseux| |stop| + |bernoulliB| |complete| |realEigenvalues| |diagonal?| |OMlistSymbols| + |coerceP| |expint| |getZechTable| |satisfy?| |expextendedint| + |upperCase!| |constantOpIfCan| |integralMatrix| |argumentList!| + |FormatRoman| |regime| |weakBiRank| |error| |adaptive| |ptFunc| + |d03edf| |sub| |setStatus!| |inv| |parent| |extractBottom!| + |singleFactorBound| |infRittWu?| |symFunc| |inGroundField?| |ground?| + |listConjugateBases| |rst| |jacobian| |myDegree| |e02adf| + |halfExtendedResultant2| |OMgetApp| |assert| |pushNewContour| + |subscriptedVariables| |realSolve| |integral?| |localAbs| |dec| + |addPoint2| |curveColorPalette| |validExponential| |readable?| + |ground| |f01ref| |definingInequation| |arity| |subCase?| |groebgen| + |traverse| |gethi| |SturmHabichtCoefficients| |bezoutMatrix| + |setprevious!| |groebnerFactorize| |explicitEntries?| |c06gcf| + |evenInfiniteProduct| |sup| |leadingMonomial| |f01qcf| + |univariatePolynomials| |cTan| |supRittWu?| + |ScanFloatIgnoreSpacesIfCan| |option?| |encodingDirectory| |nullary| + |crushedSet| |leadingCoefficient| |findCycle| |fortranCompilerName| + |SturmHabichtSequence| |rootBound| |OMsetEncoding| |principalIdeal| + |tanIfCan| |trace2PowMod| |rightUnits| |OMclose| |inverseColeman| + |makeMulti| |primitiveMonomials| |beauzamyBound| |bivariate?| + |irreducibleRepresentation| |coerceImages| |overset?| GF2FG + |listLoops| |expressIdealMember| |OMencodingSGML| + |structuralConstants| |selectsecond| |reductum| |datalist| |match?| + |normalizedAssociate| |certainlySubVariety?| |wordInGenerators| + |augment| |mirror| |schema| |startPolynomial| |OMputEndAtp| + |oneDimensionalArray| |roughSubIdeal?| |totalGroebner| |region| + |degree| |merge| |partition| |halfExtendedSubResultantGcd2| |double?| + |diagonal| |e01baf| |exQuo| |hdmpToP| |expIfCan| |redmat| |iisqrt2| + |d01alf| |uncouplingMatrices| |appendPoint| |OMlistCDs| + |sylvesterMatrix| |permutationRepresentation| |rootProduct| + |OMgetSymbol| |cAcsc| |complexEigenvectors| |OMreadStr| |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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(|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 (-1265 |#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 $) |has| |#2| (-172)) ((-1049) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2700 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2700 (|has| |#2| (-1099)) (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-726)) (|has| |#2| (-370)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1215) . T) ((-1272 |#2|) |has| |#2| (-365))) -((-2834 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-1936 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-1895 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2834 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1936 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -1895 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1215) (-1215)) (T -239)) -((-1895 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1215)) (-4 *7 (-1215)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-1936 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1215)) (-4 *2 (-1215)) (-5 *1 (-239 *5 *6 *2)))) (-2834 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1215)) (-4 *5 (-1215)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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|%noBranch|) (IF (|has| |t#2| (-131)) (-6 (-131)) |%noBranch|) (IF (|has| |t#2| (-726)) (PROGN (-6 (-726)) (-15 * ($ |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 -4412)) (-6 -4412) |%noBranch|) (IF (|has| |t#2| (-848)) (-6 (-848)) |%noBranch|) (IF (|has| |t#2| (-793)) (-6 (-793)) |%noBranch|) (IF (|has| |t#2| (-365)) (-6 (-1272 |t#2|)) |%noBranch|))) +(((-21) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-23) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-793)) (|has| |#2| (-365)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2676 (|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) -2676 (|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|) -2676 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2676 (|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)) -2676 (|has| |#2| (-1049)) (-12 (|has| |#2| (-1038 (-566))) (|has| |#2| (-1099))) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-616 |#2|) -2676 (|has| |#2| (-1099)) (|has| |#2| (-172))) ((-613 (-862)) -2676 (|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 (-1265 |#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)) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 |#2|) -2676 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-646 $) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-648 |#2|) -2676 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-648 $) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-640 |#2|) -2676 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-639 (-566)) -12 (|has| |#2| (-639 (-566))) (|has| |#2| (-1049))) ((-639 |#2|) |has| |#2| (-1049)) ((-717 |#2|) -2676 (|has| |#2| (-365)) (|has| |#2| (-172))) ((-726) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-791) |has| |#2| (-848)) ((-792) -2676 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-793) |has| |#2| (-793)) ((-794) -2676 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-795) -2676 (|has| |#2| (-848)) (|has| |#2| (-793))) ((-848) |has| |#2| (-848)) ((-850) -2676 (|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|) -2676 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1056 |#2|) -2676 (|has| |#2| (-1049)) (|has| |#2| (-365)) (|has| |#2| (-172))) ((-1056 $) |has| |#2| (-172)) ((-1049) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1057) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-172))) ((-1111) -2676 (|has| |#2| (-1049)) (|has| |#2| (-848)) (|has| |#2| (-726)) (|has| |#2| (-172))) ((-1099) -2676 (|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))) ((-1215) . T) ((-1272 |#2|) |has| |#2| (-365))) +((-3959 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2553 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2101 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3959 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2553 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2101 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-771) (-1215) (-1215)) (T -239)) +((-2101 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1215)) (-4 *7 (-1215)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2553 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-771)) (-4 *6 (-1215)) (-4 *2 (-1215)) (-5 *1 (-239 *5 *6 *2)))) (-3959 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-771)) (-4 *7 (-1215)) (-4 *5 (-1215)) (-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 $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-409 (-566)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #0#) -2676 (|has| |#1| (-1038 (-409 (-566)))) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 |#1|) . T) ((-616 |#2|) . T) ((-616 |#3|) . T) ((-616 $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-613 (-862)) . T) ((-172) -2676 (|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) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454))) ((-310 $) . T) ((-327 |#1| |#4|) . T) ((-379 |#1|) . T) ((-413 |#1|) . T) ((-454) -2676 (|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) -2676 (|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 $) -2676 (|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 $) -2676 (|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 $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1056 #0#) |has| |#1| (-38 (-409 (-566)))) ((-1056 |#1|) . T) ((-1056 $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . 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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 $) -2676 (|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 $) -2676 (|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 $) -2676 (|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 $) -2676 (|has| |#1| (-909)) (|has| |#1| (-558)) (|has| |#1| (-454)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-1049) . T) ((-1057) . T) ((-1111) . T) ((-1099) . 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T) ((-23) . T) ((-47 |#1| #0=(-409 (-566))) . T) ((-25) . T) ((-38 #1=(-409 (-566))) -2676 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2676 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-35) |has| |#1| (-38 (-409 (-566)))) ((-95) |has| |#1| (-38 (-409 (-566)))) ((-102) . T) ((-111 #1# #1#) -2676 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2676 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-616 #1#) -2676 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-616 (-566)) . T) ((-616 |#1|) |has| |#1| (-172)) ((-616 |#2|) . T) ((-616 $) -2676 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-613 (-862)) . T) ((-172) -2676 (|has| |#1| (-558)) (|has| |#1| (-365)) (|has| |#1| (-172))) ((-233) |has| |#1| (-15 * (|#1| (-409 (-566)) |#1|))) ((-243) |has| |#1| (-365)) ((-285) |has| |#1| (-38 (-409 (-566)))) ((-287 $ $) |has| (-409 (-566)) (-1111)) ((-291) -2676 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-308) |has| |#1| (-365)) ((-365) |has| |#1| (-365)) ((-454) |has| |#1| (-365)) ((-495) |has| |#1| (-38 (-409 (-566)))) ((-558) -2676 (|has| |#1| (-558)) (|has| |#1| (-365))) ((-646 #1#) -2676 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-646 (-566)) . T) ((-646 |#1|) . T) ((-646 $) . T) ((-648 #1#) -2676 (|has| |#1| (-365)) (|has| |#1| (-38 (-409 (-566))))) ((-648 |#1|) . T) ((-648 $) . 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NIL) (-1194 2895606 2895637 2895709 "TEX1" 2895788 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1193 2895254 2895317 2895407 "TEMUTL" 2895538 T TEMUTL (NIL) -7 NIL NIL NIL) (-1192 2893408 2893688 2894013 "TBCMPPK" 2894977 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1191 2885185 2891568 2891624 "TBAGG" 2892024 NIL TBAGG (NIL T T) -9 NIL 2892235 NIL) (-1190 2880255 2881743 2883497 "TBAGG-" 2883502 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1189 2879639 2879746 2879891 "TANEXP" 2880144 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1188 2873029 2879496 2879589 "TABLE" 2879594 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1187 2872441 2872540 2872678 "TABLEAU" 2872926 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1186 2867049 2868269 2869517 "TABLBUMP" 2871227 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1185 2866271 2866418 2866599 "SYSTEM" 2866890 T SYSTEM (NIL) -8 NIL NIL NIL) (-1184 2862730 2863429 2864212 "SYSSOLP" 2865522 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1183 2862528 2862685 2862716 "SYSPTR" 2862721 T SYSPTR (NIL) -8 NIL NIL NIL) (-1182 2861572 2862077 2862196 "SYSNNI" 2862382 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862467) (-1181 2860879 2861338 2861417 "SYSINT" 2861477 NIL SYSINT (NIL NIL) -8 NIL NIL 2861522) (-1180 2857211 2858157 2858867 "SYNTAX" 2860191 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854369 2854971 2855603 "SYMTAB" 2856601 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849618 2850520 2851503 "SYMS" 2853408 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2846853 2849076 2849306 "SYMPOLY" 2849423 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846370 2846445 2846568 "SYMFUNC" 2846765 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842389 2843682 2844495 "SYMBOL" 2845579 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2835928 2837617 2839337 "SWITCH" 2840691 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829162 2834749 2835052 "SUTS" 2835683 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821228 2828409 2828682 "SUPXS" 2828947 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2812987 2820846 2820972 "SUP" 2821137 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812146 2812273 2812490 "SUPFRACF" 2812855 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811767 2811826 2811939 "SUP2" 2812081 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810215 2810489 2810845 "SUMRF" 2811466 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809550 2809616 2809808 "SUMFS" 2810136 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793517 2808727 2808978 "SULS" 2809357 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793119 2793339 2793409 "SUCHTAST" 2793469 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792414 2792644 2792784 "SUCH" 2793027 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786280 2787320 2788279 "SUBSPACE" 2791502 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785710 2785800 2785964 "SUBRESP" 2786168 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2779075 2780375 2781686 "STTF" 2784446 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773248 2774368 2775515 "STTFNC" 2777975 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764558 2766430 2768224 "STTAYLOR" 2771489 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757688 2764422 2764505 "STRTBL" 2764510 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2753052 2757643 2757674 "STRING" 2757679 T STRING (NIL) -8 NIL NIL NIL) (-1156 2747913 2752425 2752455 "STRICAT" 2752514 T STRICAT (NIL) -9 NIL 2752576 NIL) (-1155 2740666 2745532 2746143 "STREAM" 2747337 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740176 2740253 2740397 "STREAM3" 2740583 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739158 2739341 2739576 "STREAM2" 2739989 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2738846 2738898 2738991 "STREAM1" 2739100 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2737862 2738043 2738274 "STINPROD" 2738662 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737414 2737624 2737654 "STEP" 2737734 T STEP (NIL) -9 NIL 2737812 NIL) (-1149 2730846 2737313 2737390 "STBL" 2737395 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2725972 2730067 2730110 "STAGG" 2730263 NIL STAGG (NIL T) -9 NIL 2730352 NIL) (-1147 2723674 2724276 2725148 "STAGG-" 2725153 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721821 2723444 2723536 "STACK" 2723617 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714516 2719962 2720418 "SREGSET" 2721451 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2706941 2708310 2709823 "SRDCMPK" 2713122 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2699858 2704381 2704411 "SRAGG" 2705714 T SRAGG (NIL) -9 NIL 2706322 NIL) (-1142 2698875 2699130 2699509 "SRAGG-" 2699514 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693335 2697822 2698243 "SQMATRIX" 2698501 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2687020 2690053 2690780 "SPLTREE" 2692680 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2682983 2683676 2684322 "SPLNODE" 2686446 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2682030 2682263 2682293 "SPFCAT" 2682737 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680767 2680977 2681241 "SPECOUT" 2681788 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672393 2674163 2674193 "SPADXPT" 2678585 T SPADXPT (NIL) -9 NIL 2680619 NIL) (-1135 2672154 2672194 2672263 "SPADPRSR" 2672346 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670309 2672109 2672140 "SPADAST" 2672145 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662254 2664027 2664070 "SPACEC" 2668443 NIL SPACEC (NIL T) -9 NIL 2670259 NIL) (-1132 2660384 2662186 2662235 "SPACE3" 2662240 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659136 2659307 2659598 "SORTPAK" 2660189 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657228 2657531 2657943 "SOLVETRA" 2658800 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656278 2656500 2656761 "SOLVESER" 2657001 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651582 2652470 2653465 "SOLVERAD" 2655330 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647397 2648006 2648735 "SOLVEFOR" 2650949 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641667 2646746 2646843 "SNTSCAT" 2646848 NIL SNTSCAT (NIL T T T T) -9 NIL 2646918 NIL) (-1125 2635773 2639990 2640381 "SMTS" 2641357 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630457 2635661 2635738 "SMP" 2635743 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628616 2628917 2629315 "SMITH" 2630154 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621329 2625525 2625628 "SMATCAT" 2626979 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627529 NIL) (-1121 2618269 2619092 2620270 "SMATCAT-" 2620275 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2615935 2617505 2617548 "SKAGG" 2617809 NIL SKAGG (NIL T) -9 NIL 2617944 NIL) (-1119 2612246 2615351 2615546 "SINT" 2615733 T SINT (NIL) -8 NIL NIL 2615906) (-1118 2612018 2612056 2612122 "SIMPAN" 2612202 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611297 2611553 2611693 "SIG" 2611900 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610135 2610356 2610631 "SIGNRF" 2611056 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2608968 2609119 2609403 "SIGNEF" 2609964 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608274 2608551 2608675 "SIGAST" 2608866 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2605963 2606418 2606924 "SHP" 2607815 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599815 2605864 2605940 "SHDP" 2605945 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599388 2599580 2599610 "SGROUP" 2599703 T SGROUP (NIL) -9 NIL 2599765 NIL) (-1110 2599246 2599272 2599345 "SGROUP-" 2599350 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596081 2596779 2597502 "SGCF" 2598545 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590449 2595528 2595625 "SFRTCAT" 2595630 NIL SFRTCAT (NIL T T T T) -9 NIL 2595669 NIL) (-1107 2583870 2584888 2586024 "SFRGCD" 2589432 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2576996 2578069 2579255 "SFQCMPK" 2582803 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576616 2576705 2576816 "SFORT" 2576937 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575734 2576456 2576577 "SEXOF" 2576582 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574841 2575615 2575683 "SEX" 2575688 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570354 2571069 2571164 "SEXCAT" 2574101 NIL SEXCAT (NIL T T T T T) -9 NIL 2574679 NIL) (-1101 2567507 2570288 2570336 "SET" 2570341 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565731 2566220 2566525 "SETMN" 2567248 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565227 2565379 2565409 "SETCAT" 2565585 T SETCAT (NIL) -9 NIL 2565695 NIL) (-1098 2564919 2564997 2565127 "SETCAT-" 2565132 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561280 2563380 2563423 "SETAGG" 2564293 NIL SETAGG (NIL T) -9 NIL 2564633 NIL) (-1096 2560738 2560854 2561091 "SETAGG-" 2561096 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560181 2560434 2560535 "SEQAST" 2560659 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559380 2559674 2559735 "SEGXCAT" 2560021 NIL SEGXCAT (NIL T T) -9 NIL 2560141 NIL) (-1093 2558386 2559046 2559228 "SEG" 2559233 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557365 2557579 2557622 "SEGCAT" 2558144 NIL SEGCAT (NIL T) -9 NIL 2558365 NIL) (-1091 2556366 2556744 2556944 "SEGBIND" 2557200 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2555987 2556046 2556159 "SEGBIND2" 2556301 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555560 2555788 2555865 "SEGAST" 2555932 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554779 2554905 2555109 "SEG2" 2555404 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554189 2554714 2554761 "SDVAR" 2554766 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546716 2553959 2554089 "SDPOL" 2554094 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545309 2545575 2545894 "SCPKG" 2546431 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544473 2544645 2544837 "SCOPE" 2545139 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543693 2543827 2544006 "SCACHE" 2544328 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543339 2543525 2543555 "SASTCAT" 2543560 T SASTCAT (NIL) -9 NIL 2543573 NIL) (-1081 2542826 2543174 2543250 "SAOS" 2543285 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542391 2542426 2542599 "SAERFFC" 2542785 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536330 2542288 2542368 "SAE" 2542373 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2535923 2535958 2536117 "SAEFACT" 2536289 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534244 2534558 2534959 "RURPK" 2535589 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2532881 2533187 2533492 "RULESET" 2534078 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530104 2530634 2531092 "RULE" 2532562 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529716 2529898 2529981 "RULECOLD" 2530056 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529506 2529534 2529605 "RTVALUE" 2529667 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2528977 2529223 2529317 "RSTRCAST" 2529434 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523825 2524620 2525540 "RSETGCD" 2528176 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2513055 2518134 2518231 "RSETCAT" 2522350 NIL RSETCAT (NIL T T T T) -9 NIL 2523447 NIL) (-1069 2510982 2511521 2512345 "RSETCAT-" 2512350 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503367 2504744 2506264 "RSDCMPK" 2509581 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501346 2501813 2501887 "RRCC" 2502973 NIL RRCC (NIL T T) -9 NIL 2503317 NIL) (-1066 2500697 2500871 2501150 "RRCC-" 2501155 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500140 2500393 2500494 "RPTAST" 2500618 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2473991 2483348 2483415 "RPOLCAT" 2494079 NIL RPOLCAT (NIL T T T) -9 NIL 2497238 NIL) (-1063 2465489 2467829 2470951 "RPOLCAT-" 2470956 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456420 2463700 2464182 "ROUTINE" 2465029 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453218 2456046 2456186 "ROMAN" 2456302 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451462 2452078 2452338 "ROIRC" 2453023 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447694 2449978 2450008 "RNS" 2450312 T RNS (NIL) -9 NIL 2450586 NIL) (-1058 2446203 2446586 2447120 "RNS-" 2447195 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445606 2446014 2446044 "RNG" 2446049 T RNG (NIL) -9 NIL 2446070 NIL) (-1056 2445005 2445393 2445436 "RMODULE" 2445441 NIL RMODULE (NIL T) -9 NIL 2445468 NIL) (-1055 2443841 2443935 2444271 "RMCAT2" 2444906 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440691 2443187 2443484 "RMATRIX" 2443603 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433518 2435778 2435893 "RMATCAT" 2439252 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440234 NIL) (-1052 2432893 2433040 2433347 "RMATCAT-" 2433352 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432294 2432515 2432558 "RLINSET" 2432752 NIL RLINSET (NIL T) -9 NIL 2432843 NIL) (-1050 2431861 2431936 2432064 "RINTERP" 2432213 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2430919 2431473 2431503 "RING" 2431559 T RING (NIL) -9 NIL 2431651 NIL) (-1048 2430711 2430755 2430852 "RING-" 2430857 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429552 2429789 2430047 "RIDIST" 2430475 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420841 2429020 2429226 "RGCHAIN" 2429400 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420191 2420597 2420638 "RGBCSPC" 2420696 NIL RGBCSPC (NIL T) -9 NIL 2420748 NIL) (-1044 2419349 2419730 2419771 "RGBCMDL" 2420003 NIL RGBCMDL (NIL T) -9 NIL 2420117 NIL) (-1043 2416343 2416957 2417627 "RF" 2418713 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2415989 2416052 2416155 "RFFACTOR" 2416274 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415714 2415749 2415846 "RFFACT" 2415948 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413831 2414195 2414577 "RFDIST" 2415354 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413284 2413376 2413539 "RETSOL" 2413733 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2412920 2413000 2413043 "RETRACT" 2413176 NIL RETRACT (NIL T) -9 NIL 2413263 NIL) (-1037 2412769 2412794 2412881 "RETRACT-" 2412886 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412371 2412591 2412661 "RETAST" 2412721 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405109 2412024 2412151 "RESULT" 2412266 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403700 2404378 2404577 "RESRING" 2405012 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403336 2403385 2403483 "RESLATC" 2403637 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2403041 2403076 2403183 "REPSQ" 2403295 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400463 2401043 2401645 "REP" 2402461 T REP (NIL) -7 NIL NIL NIL) (-1030 2400160 2400195 2400306 "REPDB" 2400422 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2394060 2395449 2396672 "REP2" 2398972 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390437 2391118 2391926 "REP1" 2393287 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383133 2388578 2389034 "REGSET" 2390067 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2381898 2382281 2382531 "REF" 2382918 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381275 2381378 2381545 "REDORDER" 2381782 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377243 2380488 2380715 "RECLOS" 2381103 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376295 2376476 2376691 "REALSOLV" 2377050 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376141 2376182 2376212 "REAL" 2376217 T REAL (NIL) -9 NIL 2376252 NIL) (-1021 2372624 2373426 2374310 "REAL0Q" 2375306 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368225 2369213 2370274 "REAL0" 2371605 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367696 2367942 2368036 "RDUCEAST" 2368153 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367101 2367173 2367380 "RDIV" 2367618 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366169 2366343 2366556 "RDIST" 2366923 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364766 2365053 2365425 "RDETRS" 2365877 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362578 2363032 2363570 "RDETR" 2364308 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2361203 2361481 2361878 "RDEEFS" 2362294 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 2359712 2360018 2360443 "RDEEF" 2360891 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1012 2353773 2356693 2356723 "RCFIELD" 2358018 T RCFIELD (NIL) -9 NIL 2358749 NIL) (-1011 2351837 2352341 2353037 "RCFIELD-" 2353112 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1010 2348106 2349938 2349981 "RCAGG" 2351065 NIL RCAGG (NIL T) -9 NIL 2351530 NIL) (-1009 2347734 2347828 2347991 "RCAGG-" 2347996 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1008 2347069 2347181 2347346 "RATRET" 2347618 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1007 2346622 2346689 2346810 "RATFACT" 2346997 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1006 2345930 2346050 2346202 "RANDSRC" 2346492 T RANDSRC (NIL) -7 NIL NIL NIL) (-1005 2345664 2345708 2345781 "RADUTIL" 2345879 T RADUTIL (NIL) -7 NIL NIL NIL) (-1004 2338780 2344497 2344807 "RADIX" 2345388 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330399 2338622 2338752 "RADFF" 2338757 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1002 2330046 2330121 2330151 "RADCAT" 2330311 T RADCAT (NIL) -9 NIL NIL NIL) (-1001 2329828 2329876 2329976 "RADCAT-" 2329981 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1000 2327928 2329600 2329691 "QUEUE" 2329772 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-999 2324469 2327865 2327910 "QUAT" 2327915 NIL QUAT (NIL T) -8 NIL NIL NIL) (-998 2324107 2324150 2324277 "QUATCT2" 2324420 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-997 2317569 2320914 2320954 "QUATCAT" 2321734 NIL QUATCAT (NIL T) -9 NIL 2322500 NIL) (-996 2313713 2314750 2316137 "QUATCAT-" 2316231 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-995 2311186 2312797 2312838 "QUAGG" 2313213 NIL QUAGG (NIL T) -9 NIL 2313388 NIL) (-994 2310791 2311011 2311079 "QQUTAST" 2311138 T QQUTAST 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OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961193 1961959 1961987 "OPTCAT" 1962806 T OPTCAT (NIL) -9 NIL 1963456 NIL) (-838 1960577 1960870 1960975 "OPSIG" 1961108 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960345 1960384 1960450 "OPQUERY" 1960531 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957476 1958656 1959160 "OP" 1959874 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1956850 1957076 1957117 "OPERCAT" 1957329 NIL OPERCAT (NIL T) -9 NIL 1957426 NIL) (-834 1956605 1956661 1956778 "OPERCAT-" 1956783 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953418 1955402 1955771 "ONECOMP" 1956269 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952723 1952838 1953012 "ONECOMP2" 1953290 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952142 1952248 1952378 "OMSERVER" 1952613 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1949004 1951582 1951622 "OMSAGG" 1951683 NIL OMSAGG (NIL T) -9 NIL 1951747 NIL) (-829 1947627 1947890 1948172 "OMPKG" 1948742 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1947057 1947160 1947188 "OM" 1947487 T OM (NIL) -9 NIL NIL NIL) (-827 1945604 1946606 1946775 "OMLO" 1946938 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944564 1944711 1944931 "OMEXPR" 1945430 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1943855 1944110 1944246 "OMERR" 1944448 T OMERR (NIL) -8 NIL NIL NIL) (-824 1943006 1943276 1943436 "OMERRK" 1943715 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942457 1942683 1942791 "OMENC" 1942918 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936352 1937537 1938708 "OMDEV" 1941306 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935421 1935592 1935786 "OMCONN" 1936178 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1933942 1934918 1934946 "OINTDOM" 1934951 T OINTDOM (NIL) -9 NIL 1934972 NIL) (-819 1929721 1930932 1931648 "OFMONOID" 1933258 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929132 1929658 1929703 "ODVAR" 1929708 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926555 1928877 1929032 "ODR" 1929037 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919136 1926331 1926457 "ODPOL" 1926462 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1912958 1919008 1919113 "ODP" 1919118 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911724 1911939 1912214 "ODETOOLS" 1912732 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908691 1909349 1910065 "ODESYS" 1911057 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903573 1904481 1905506 "ODERTRIC" 1907766 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1902999 1903081 1903275 "ODERED" 1903485 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1899887 1900435 1901112 "ODERAT" 1902422 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1896844 1897311 1897908 "ODEPRRIC" 1899416 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894787 1895383 1895869 "ODEPROB" 1896378 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891307 1891792 1892439 "ODEPRIM" 1894266 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890556 1890658 1890918 "ODEPAL" 1891199 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886718 1887509 1888373 "ODEPACK" 1889712 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885779 1885886 1886108 "ODEINT" 1886607 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1879880 1881305 1882752 "ODEIFTBL" 1884352 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875278 1876064 1877016 "ODEEF" 1879039 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874627 1874716 1874939 "ODECONST" 1875183 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872752 1873413 1873441 "ODECAT" 1874046 T ODECAT (NIL) -9 NIL 1874577 NIL) (-799 1869624 1872464 1872583 "OCT" 1872665 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869262 1869305 1869432 "OCTCT2" 1869575 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1863911 1866346 1866386 "OC" 1867483 NIL OC (NIL T) -9 NIL 1868341 NIL) (-796 1861138 1861886 1862876 "OC-" 1862970 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860490 1860958 1860986 "OCAMON" 1860991 T OCAMON (NIL) -9 NIL 1861012 NIL) (-794 1860021 1860362 1860390 "OASGP" 1860395 T OASGP (NIL) -9 NIL 1860415 NIL) (-793 1859282 1859771 1859799 "OAMONS" 1859839 T OAMONS (NIL) -9 NIL 1859882 NIL) (-792 1858696 1859129 1859157 "OAMON" 1859162 T OAMON (NIL) -9 NIL 1859182 NIL) (-791 1857954 1858472 1858500 "OAGROUP" 1858505 T OAGROUP (NIL) -9 NIL 1858525 NIL) (-790 1857644 1857694 1857782 "NUMTUBE" 1857898 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851217 1852735 1854271 "NUMQUAD" 1856128 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1846973 1847961 1848986 "NUMODE" 1850212 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844328 1845208 1845236 "NUMINT" 1846159 T NUMINT (NIL) -9 NIL 1846923 NIL) (-786 1843276 1843473 1843691 "NUMFMT" 1844130 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829635 1832580 1835112 "NUMERIC" 1840783 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1824005 1829084 1829179 "NTSCAT" 1829184 NIL NTSCAT (NIL T T T T) -9 NIL 1829223 NIL) (-783 1823199 1823364 1823557 "NTPOLFN" 1823844 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811276 1820024 1820836 "NSUP" 1822420 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1810908 1810965 1811074 "NSUP2" 1811213 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801136 1810682 1810815 "NSMP" 1810820 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799568 1799869 1800226 "NREP" 1800824 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798159 1798411 1798769 "NPCOEF" 1799311 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797225 1797340 1797556 "NORMRETR" 1798040 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795266 1795556 1795965 "NORMPK" 1796933 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1794951 1794979 1795103 "NORMMA" 1795232 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794751 1794908 1794937 "NONE" 1794942 T NONE (NIL) -8 NIL NIL NIL) (-773 1794540 1794569 1794638 "NONE1" 1794715 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1794037 1794099 1794278 "NODE1" 1794472 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792322 1793173 1793428 "NNI" 1793775 T NNI (NIL) -8 NIL NIL 1794010) (-770 1790742 1791055 1791419 "NLINSOL" 1791990 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1786983 1787978 1788877 "NIPROB" 1789863 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785740 1785974 1786276 "NFINTBAS" 1786745 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1784914 1785390 1785431 "NETCLT" 1785603 NIL NETCLT (NIL T) -9 NIL 1785685 NIL) (-766 1783622 1783853 1784134 "NCODIV" 1784682 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783384 1783421 1783496 "NCNTFRAC" 1783579 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781564 1781928 1782348 "NCEP" 1783009 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780415 1781188 1781216 "NASRING" 1781326 T NASRING (NIL) -9 NIL 1781406 NIL) (-762 1780210 1780254 1780348 "NASRING-" 1780353 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779317 1779842 1779870 "NARNG" 1779987 T NARNG (NIL) -9 NIL 1780078 NIL) (-760 1779009 1779076 1779210 "NARNG-" 1779215 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1777888 1778095 1778330 "NAGSP" 1778794 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769160 1770844 1772517 "NAGS" 1776235 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767708 1768016 1768347 "NAGF07" 1768849 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762246 1763537 1764844 "NAGF04" 1766421 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755214 1756828 1758461 "NAGF02" 1760633 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750438 1751538 1752655 "NAGF01" 1754117 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1744066 1745632 1747217 "NAGE04" 1748873 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735235 1737356 1739486 "NAGE02" 1741956 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731188 1732135 1733099 "NAGE01" 1734291 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1728983 1729517 1730075 "NAGD03" 1730650 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720733 1722661 1724615 "NAGD02" 1727049 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714544 1715969 1717409 "NAGD01" 1719313 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710753 1711575 1712412 "NAGC06" 1713727 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709218 1709550 1709906 "NAGC05" 1710417 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708594 1708713 1708857 "NAGC02" 1709094 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707553 1708136 1708176 "NAALG" 1708255 NIL NAALG (NIL T) -9 NIL 1708316 NIL) (-743 1707388 1707417 1707507 "NAALG-" 1707512 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701338 1702446 1703633 "MULTSQFR" 1706284 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700657 1700732 1700916 "MULTFACT" 1701250 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693381 1697294 1697347 "MTSCAT" 1698417 NIL MTSCAT (NIL T T) -9 NIL 1698932 NIL) (-739 1693093 1693147 1693239 "MTHING" 1693321 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1692885 1692918 1692978 "MSYSCMD" 1693053 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1688967 1691640 1691960 "MSET" 1692598 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1686036 1688528 1688569 "MSETAGG" 1688574 NIL MSETAGG (NIL T) -9 NIL 1688608 NIL) (-735 1681877 1683415 1684160 "MRING" 1685336 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681443 1681510 1681641 "MRF2" 1681804 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1681061 1681096 1681240 "MRATFAC" 1681402 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678673 1678968 1679399 "MPRFF" 1680766 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1672970 1678527 1678624 "MPOLY" 1678629 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672460 1672495 1672703 "MPCPF" 1672929 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1671974 1672017 1672201 "MPC3" 1672411 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671169 1671250 1671471 "MPC2" 1671889 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669470 1669807 1670197 "MONOTOOL" 1670829 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668695 1669012 1669040 "MONOID" 1669259 T MONOID (NIL) -9 NIL 1669406 NIL) (-725 1668241 1668360 1668541 "MONOID-" 1668546 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658716 1664667 1664726 "MONOGEN" 1665400 NIL MONOGEN (NIL T T) -9 NIL 1665856 NIL) (-723 1655934 1656669 1657669 "MONOGEN-" 1657788 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654767 1655213 1655241 "MONADWU" 1655633 T MONADWU (NIL) -9 NIL 1655871 NIL) (-721 1654139 1654298 1654546 "MONADWU-" 1654551 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653498 1653742 1653770 "MONAD" 1653977 T MONAD (NIL) -9 NIL 1654089 NIL) (-719 1653183 1653261 1653393 "MONAD-" 1653398 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651472 1652096 1652375 "MOEBIUS" 1652936 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650750 1651154 1651194 "MODULE" 1651199 NIL MODULE (NIL T) -9 NIL 1651238 NIL) (-716 1650318 1650414 1650604 "MODULE-" 1650609 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1647998 1648682 1649009 "MODRING" 1650142 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1644942 1646103 1646624 "MODOP" 1647527 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643530 1644009 1644286 "MODMONOM" 1644805 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633571 1641821 1642235 "MODMON" 1643167 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630727 1632415 1632691 "MODFIELD" 1633446 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629704 1630008 1630198 "MMLFORM" 1630557 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629230 1629273 1629452 "MMAP" 1629655 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627309 1628076 1628117 "MLO" 1628540 NIL MLO (NIL T) -9 NIL 1628782 NIL) (-707 1624675 1625191 1625793 "MLIFT" 1626790 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1624066 1624150 1624304 "MKUCFUNC" 1624586 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623665 1623735 1623858 "MKRECORD" 1623989 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622712 1622874 1623102 "MKFUNC" 1623476 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622100 1622204 1622360 "MKFLCFN" 1622595 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621377 1621479 1621664 "MKBCFUNC" 1621993 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618084 1620931 1621067 "MINT" 1621261 T MINT (NIL) -8 NIL NIL NIL) (-700 1616896 1617139 1617416 "MHROWRED" 1617839 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612275 1615431 1615836 "MFLOAT" 1616511 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611632 1611708 1611879 "MFINFACT" 1612187 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1607947 1608795 1609679 "MESH" 1610768 T MESH (NIL) -7 NIL NIL NIL) (-696 1606337 1606649 1607002 "MDDFACT" 1607634 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603132 1605496 1605537 "MDAGG" 1605792 NIL MDAGG (NIL T) -9 NIL 1605935 NIL) (-694 1592872 1602425 1602632 "MCMPLX" 1602945 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1592013 1592159 1592359 "MCDEN" 1592721 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1589903 1590173 1590553 "MCALCFN" 1591743 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588828 1589068 1589301 "MAYBE" 1589709 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586440 1586963 1587525 "MATSTOR" 1588299 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582397 1585812 1586060 "MATRIX" 1586225 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578161 1578870 1579606 "MATLIN" 1581754 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568267 1571453 1571530 "MATCAT" 1576410 NIL MATCAT (NIL T T T) -9 NIL 1577827 NIL) (-686 1564623 1565644 1567000 "MATCAT-" 1567005 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563217 1563370 1563703 "MATCAT2" 1564458 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561329 1561653 1562037 "MAPPKG3" 1562892 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560310 1560483 1560705 "MAPPKG2" 1561153 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558809 1559093 1559420 "MAPPKG1" 1560016 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1557888 1558215 1558392 "MAPPAST" 1558652 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557499 1557557 1557680 "MAPHACK3" 1557824 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557091 1557152 1557266 "MAPHACK2" 1557431 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556528 1556632 1556774 "MAPHACK1" 1556982 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554607 1555228 1555532 "MAGMA" 1556256 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554086 1554331 1554422 "MACROAST" 1554536 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550504 1552325 1552786 "M3D" 1553658 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544610 1548873 1548914 "LZSTAGG" 1549696 NIL LZSTAGG (NIL T) -9 NIL 1549991 NIL) (-673 1540567 1541741 1543198 "LZSTAGG-" 1543203 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537654 1538458 1538945 "LWORD" 1540112 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537230 1537458 1537533 "LSTAST" 1537599 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530396 1537001 1537135 "LSQM" 1537140 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529620 1529759 1529987 "LSPP" 1530251 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527432 1527733 1528189 "LSMP" 1529309 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524211 1524885 1525615 "LSMP1" 1526734 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518088 1523378 1523419 "LSAGG" 1523481 NIL LSAGG (NIL T) -9 NIL 1523559 NIL) (-665 1514783 1515707 1516920 "LSAGG-" 1516925 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512382 1513927 1514176 "LPOLY" 1514578 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1511964 1512049 1512172 "LPEFRAC" 1512291 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510285 1511058 1511311 "LO" 1511796 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1509937 1510049 1510077 "LOGIC" 1510188 T LOGIC (NIL) -9 NIL 1510269 NIL) (-660 1509799 1509822 1509893 "LOGIC-" 1509898 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1508992 1509132 1509325 "LODOOPS" 1509655 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506415 1508908 1508974 "LODO" 1508979 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1504953 1505188 1505541 "LODOF" 1506162 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501171 1503602 1503643 "LODOCAT" 1504081 NIL LODOCAT (NIL T) -9 NIL 1504292 NIL) (-655 1500904 1500962 1501089 "LODOCAT-" 1501094 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498224 1500745 1500863 "LODO2" 1500868 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495659 1498161 1498206 "LODO1" 1498211 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494540 1494705 1495010 "LODEEF" 1495482 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489779 1492670 1492711 "LNAGG" 1493658 NIL LNAGG (NIL T) -9 NIL 1494102 NIL) (-650 1488926 1489140 1489482 "LNAGG-" 1489487 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1485062 1485851 1486490 "LMOPS" 1488341 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484465 1484853 1484894 "LMODULE" 1484899 NIL LMODULE (NIL T) -9 NIL 1484925 NIL) (-647 1481663 1484110 1484233 "LMDICT" 1484375 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1481069 1481290 1481331 "LLINSET" 1481522 NIL LLINSET (NIL T) -9 NIL 1481613 NIL) (-645 1480768 1480977 1481037 "LITERAL" 1481042 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1473931 1479702 1480006 "LIST" 1480497 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473456 1473530 1473669 "LIST3" 1473851 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472463 1472641 1472869 "LIST2" 1473274 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470597 1470909 1471308 "LIST2MAP" 1472110 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470193 1470430 1470471 "LINSET" 1470476 NIL LINSET (NIL T) -9 NIL 1470510 NIL) (-639 1468854 1469524 1469565 "LINEXP" 1469820 NIL LINEXP (NIL T) -9 NIL 1469969 NIL) (-638 1467501 1467761 1468058 "LINDEP" 1468606 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464268 1464987 1465764 "LIMITRF" 1466756 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462571 1462867 1463276 "LIMITPS" 1463963 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1456999 1462082 1462310 "LIE" 1462392 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1455947 1456416 1456456 "LIECAT" 1456596 NIL LIECAT (NIL T) -9 NIL 1456747 NIL) (-633 1455788 1455815 1455903 "LIECAT-" 1455908 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448284 1455237 1455402 "LIB" 1455643 T LIB (NIL) -8 NIL NIL NIL) (-631 1443919 1444802 1445737 "LGROBP" 1447401 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1441917 1442191 1442541 "LF" 1443640 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440757 1441449 1441477 "LFCAT" 1441684 T LFCAT (NIL) -9 NIL 1441823 NIL) (-628 1437659 1438289 1438977 "LEXTRIPK" 1440121 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434403 1435229 1435732 "LEXP" 1437239 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1433879 1434124 1434216 "LETAST" 1434331 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432277 1432590 1432991 "LEADCDET" 1433561 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431467 1431541 1431770 "LAZM3PK" 1432198 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426384 1429544 1430082 "LAUPOL" 1430979 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1425963 1426007 1426168 "LAPLACE" 1426334 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1423902 1425064 1425315 "LA" 1425796 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1422896 1423480 1423521 "LALG" 1423583 NIL LALG (NIL T) -9 NIL 1423642 NIL) (-619 1422610 1422669 1422805 "LALG-" 1422810 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422445 1422469 1422510 "KVTFROM" 1422572 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421368 1421812 1421997 "KTVLOGIC" 1422280 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421203 1421227 1421268 "KRCFROM" 1421330 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420107 1420294 1420593 "KOVACIC" 1421003 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1419942 1419966 1420007 "KONVERT" 1420069 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419777 1419801 1419842 "KOERCE" 1419904 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417607 1418370 1418747 "KERNEL" 1419433 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417103 1417184 1417316 "KERNEL2" 1417521 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1410873 1415642 1415696 "KDAGG" 1416073 NIL KDAGG (NIL T T) -9 NIL 1416279 NIL) (-609 1410402 1410526 1410731 "KDAGG-" 1410736 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403550 1410063 1410218 "KAFILE" 1410280 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1397978 1403061 1403289 "JORDAN" 1403371 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397357 1397627 1397748 "JOINAST" 1397877 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397203 1397262 1397317 "JAVACODE" 1397322 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393455 1395408 1395462 "IXAGG" 1396391 NIL IXAGG (NIL T T) -9 NIL 1396850 NIL) (-603 1392374 1392680 1393099 "IXAGG-" 1393104 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1387904 1392296 1392355 "IVECTOR" 1392360 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386670 1386907 1387173 "ITUPLE" 1387671 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385172 1385349 1385644 "ITRIGMNP" 1386492 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1383917 1384121 1384404 "ITFUN3" 1384948 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383549 1383606 1383715 "ITFUN2" 1383854 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381351 1382411 1382710 "ITAYLOR" 1383283 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370296 1375488 1376651 "ISUPS" 1380221 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369400 1369540 1369776 "ISUMP" 1370143 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364614 1369201 1369280 "ISTRING" 1369353 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364090 1364335 1364427 "ISAST" 1364542 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363299 1363381 1363597 "IRURPK" 1364004 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362235 1362436 1362676 "IRSN" 1363079 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360306 1360661 1361090 "IRRF2F" 1361873 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1360053 1360091 1360167 "IRREDFFX" 1360262 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358668 1358927 1359226 "IROOT" 1359786 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355272 1356352 1357044 "IR" 1358008 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1352885 1353380 1353946 "IR2" 1354750 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1351985 1352098 1352312 "IR2F" 1352768 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351776 1351810 1351870 "IPRNTPK" 1351945 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348357 1351665 1351734 "IPF" 1351739 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346684 1348282 1348339 "IPADIC" 1348344 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1345996 1346244 1346374 "IP4ADDR" 1346574 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345469 1345700 1345810 "IOMODE" 1345906 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344542 1345066 1345193 "IOBFILE" 1345362 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1344030 1344446 1344474 "IOBCON" 1344479 T IOBCON (NIL) -9 NIL 1344500 NIL) (-577 1343541 1343599 1343782 "INVLAPLA" 1343966 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333189 1335543 1337929 "INTTR" 1341205 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329524 1330266 1331131 "INTTOOLS" 1332374 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329110 1329201 1329318 "INTSLPE" 1329427 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327063 1329033 1329092 "INTRVL" 1329097 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324665 1325177 1325752 "INTRF" 1326548 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324076 1324173 1324315 "INTRET" 1324563 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322073 1322462 1322932 "INTRAT" 1323684 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319336 1319919 1320538 "INTPM" 1321558 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316081 1316680 1317418 "INTPAF" 1318722 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311260 1312222 1313273 "INTPACK" 1315050 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308140 1310989 1311116 "INT" 1311153 T INT (NIL) -8 NIL NIL NIL) (-565 1307392 1307544 1307752 "INTHERTR" 1307982 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1306831 1306911 1307099 "INTHERAL" 1307306 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304677 1305120 1305577 "INTHEORY" 1306394 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296083 1297704 1299476 "INTG0" 1303029 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276656 1281446 1286256 "INTFTBL" 1291293 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1275905 1276043 1276216 "INTFACT" 1276515 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273332 1273778 1274335 "INTEF" 1275459 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271699 1272438 1272466 "INTDOM" 1272767 T INTDOM (NIL) -9 NIL 1272974 NIL) (-557 1271068 1271242 1271484 "INTDOM-" 1271489 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267456 1269384 1269438 "INTCAT" 1270237 NIL INTCAT (NIL T) -9 NIL 1270558 NIL) (-555 1266928 1267031 1267159 "INTBIT" 1267348 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265627 1265781 1266088 "INTALG" 1266773 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265110 1265200 1265357 "INTAF" 1265531 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258453 1264920 1265060 "INTABL" 1265065 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257794 1258260 1258325 "INT8" 1258359 T INT8 (NIL) -8 NIL NIL 1258404) (-550 1257134 1257600 1257665 "INT64" 1257699 T INT64 (NIL) -8 NIL NIL 1257744) (-549 1256474 1256940 1257005 "INT32" 1257039 T INT32 (NIL) -8 NIL NIL 1257084) (-548 1255814 1256280 1256345 "INT16" 1256379 T INT16 (NIL) -8 NIL NIL 1256424) (-547 1250724 1253437 1253465 "INS" 1254399 T INS (NIL) -9 NIL 1255064 NIL) (-546 1247964 1248735 1249709 "INS-" 1249782 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246739 1246966 1247264 "INPSIGN" 1247717 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1245857 1245974 1246171 "INPRODPF" 1246619 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244751 1244868 1245105 "INPRODFF" 1245737 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243751 1243903 1244163 "INNMFACT" 1244587 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1242948 1243045 1243233 "INMODGCD" 1243650 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241456 1241701 1242025 "INFSP" 1242693 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240640 1240757 1240940 "INFPROD0" 1241336 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237495 1238705 1239220 "INFORM" 1240133 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237105 1237165 1237263 "INFORM1" 1237430 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236628 1236717 1236831 "INFINITY" 1237011 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235804 1236348 1236449 "INETCLTS" 1236547 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234420 1234670 1234991 "INEP" 1235552 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233669 1234317 1234382 "INDE" 1234387 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233233 1233301 1233418 "INCRMAPS" 1233596 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1232051 1232502 1232708 "INBFILE" 1233047 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227350 1228287 1229231 "INBFF" 1231139 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226258 1226527 1226555 "INBCON" 1227068 T INBCON (NIL) -9 NIL 1227334 NIL) (-528 1225510 1225733 1226009 "INBCON-" 1226014 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1224989 1225234 1225325 "INAST" 1225439 T INAST (NIL) -8 NIL NIL NIL) (-526 1224416 1224668 1224774 "IMPTAST" 1224903 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1220862 1224260 1224364 "IMATRIX" 1224369 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219574 1219697 1220012 "IMATQF" 1220718 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217794 1218021 1218358 "IMATLIN" 1219330 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212372 1217718 1217776 "ILIST" 1217781 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210277 1212232 1212345 "IIARRAY2" 1212350 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205675 1210188 1210252 "IFF" 1210257 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1205022 1205292 1205408 "IFAST" 1205579 T IFAST (NIL) -8 NIL NIL NIL) (-518 1200017 1204314 1204502 "IFARRAY" 1204879 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199197 1199921 1199994 "IFAMON" 1199999 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198781 1198846 1198900 "IEVALAB" 1199107 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198456 1198524 1198684 "IEVALAB-" 1198689 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198087 1198370 1198433 "IDPO" 1198438 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197337 1197976 1198051 "IDPOAMS" 1198056 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196644 1197226 1197301 "IDPOAM" 1197306 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195703 1195979 1196032 "IDPC" 1196445 NIL IDPC (NIL T T) -9 NIL 1196594 NIL) (-510 1195172 1195595 1195668 "IDPAM" 1195673 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194548 1195064 1195137 "IDPAG" 1195142 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194193 1194384 1194459 "IDENT" 1194493 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190448 1191296 1192191 "IDECOMP" 1193350 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183286 1184371 1185418 "IDEAL" 1189484 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182450 1182562 1182761 "ICDEN" 1183170 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181521 1181930 1182077 "ICARD" 1182323 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179581 1179894 1180299 "IBPTOOLS" 1181198 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175188 1179201 1179314 "IBITS" 1179500 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1171911 1172487 1173182 "IBATOOL" 1174605 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169690 1170152 1170685 "IBACHIN" 1171446 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167519 1169536 1169639 "IARRAY2" 1169644 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163625 1167445 1167502 "IARRAY1" 1167507 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157734 1162037 1162518 "IAN" 1163164 T IAN (NIL) -8 NIL NIL NIL) (-496 1157245 1157302 1157475 "IALGFACT" 1157671 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156773 1156886 1156914 "HYPCAT" 1157121 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156311 1156428 1156614 "HYPCAT-" 1156619 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1155906 1156106 1156189 "HOSTNAME" 1156248 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155751 1155788 1155829 "HOMOTOP" 1155834 NIL HOMOTOP (NIL T) -9 NIL 1155867 NIL) (-491 1152383 1153761 1153802 "HOAGG" 1154783 NIL HOAGG (NIL T) -9 NIL 1155462 NIL) (-490 1150977 1151376 1151902 "HOAGG-" 1151907 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1144981 1150572 1150721 "HEXADEC" 1150848 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143728 1143951 1144214 "HEUGCD" 1144758 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142804 1143565 1143695 "HELLFDIV" 1143700 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1140983 1142581 1142669 "HEAP" 1142748 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140246 1140535 1140669 "HEADAST" 1140869 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134112 1140161 1140223 "HDP" 1140228 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128100 1133747 1133899 "HDMP" 1134013 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127424 1127564 1127728 "HB" 1127956 T HB (NIL) -7 NIL NIL NIL) (-481 1120810 1127270 1127374 "HASHTBL" 1127379 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120286 1120531 1120623 "HASAST" 1120738 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118064 1119908 1120090 "HACKPI" 1120124 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113732 1117917 1118030 "GTSET" 1118035 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107147 1113610 1113708 "GSTBL" 1113713 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099425 1106178 1106443 "GSERIES" 1106938 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098566 1098983 1099011 "GROUP" 1099214 T GROUP (NIL) -9 NIL 1099348 NIL) (-474 1097932 1098091 1098342 "GROUP-" 1098347 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096299 1096620 1097007 "GROEBSOL" 1097609 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095213 1095501 1095552 "GRMOD" 1096081 NIL GRMOD (NIL T T) -9 NIL 1096249 NIL) (-471 1094981 1095017 1095145 "GRMOD-" 1095150 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090271 1091335 1092335 "GRIMAGE" 1094001 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088737 1088998 1089322 "GRDEF" 1089967 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088181 1088297 1088438 "GRAY" 1088616 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087368 1087774 1087825 "GRALG" 1087978 NIL GRALG (NIL T T) -9 NIL 1088071 NIL) (-466 1087029 1087102 1087265 "GRALG-" 1087270 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083806 1086614 1086792 "GPOLSET" 1086936 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083160 1083217 1083475 "GOSPER" 1083743 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1078892 1079598 1080124 "GMODPOL" 1082859 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1077897 1078081 1078319 "GHENSEL" 1078704 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1072053 1072896 1073916 "GENUPS" 1076981 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071750 1071801 1071890 "GENUFACT" 1071996 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071162 1071239 1071404 "GENPGCD" 1071668 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070636 1070671 1070884 "GENMFACT" 1071121 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069202 1069459 1069766 "GENEEZ" 1070379 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063348 1068813 1068975 "GDMP" 1069125 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052690 1057119 1058225 "GCNAALG" 1062331 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1051017 1051879 1051907 "GCDDOM" 1052162 T GCDDOM (NIL) -9 NIL 1052319 NIL) (-453 1050487 1050614 1050829 "GCDDOM-" 1050834 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049159 1049344 1049648 "GB" 1050266 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037775 1040105 1042497 "GBINTERN" 1046850 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035612 1035904 1036325 "GBF" 1037450 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034393 1034558 1034825 "GBEUCLID" 1035428 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033742 1033867 1034016 "GAUSSFAC" 1034264 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032109 1032411 1032725 "GALUTIL" 1033461 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030417 1030691 1031015 "GALPOLYU" 1031836 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027782 1028072 1028479 "GALFACTU" 1030114 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019587 1021087 1022695 "GALFACT" 1026214 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1016975 1017633 1017661 "FVFUN" 1018817 T FVFUN (NIL) -9 NIL 1019537 NIL) (-442 1016241 1016423 1016451 "FVC" 1016742 T FVC (NIL) -9 NIL 1016925 NIL) (-441 1015884 1016066 1016134 "FUNDESC" 1016193 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015499 1015681 1015762 "FUNCTION" 1015836 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013243 1013821 1014287 "FT" 1015053 T FT (NIL) -8 NIL NIL NIL) (-438 1012034 1012544 1012747 "FTEM" 1013060 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010325 1010614 1011011 "FSUPFACT" 1011725 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008722 1009011 1009343 "FST" 1010013 T FST (NIL) -8 NIL NIL NIL) (-435 1007921 1008027 1008215 "FSRED" 1008604 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006620 1006876 1007223 "FSPRMELT" 1007636 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1003926 1004364 1004850 "FSPECF" 1006183 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985564 993895 993936 "FS" 997820 NIL FS (NIL T) -9 NIL 1000109 NIL) (-431 974207 977200 981257 "FS-" 981557 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973735 973789 973959 "FSINT" 974148 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 972027 972728 973031 "FSERIES" 973514 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971069 971185 971409 "FSCINT" 971907 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967277 970013 970054 "FSAGG" 970424 NIL FSAGG (NIL T) -9 NIL 970683 NIL) (-426 965039 965640 966436 "FSAGG-" 966531 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964081 964224 964451 "FSAGG2" 964892 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961763 962043 962590 "FS2UPS" 963799 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961397 961440 961569 "FS2" 961714 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960275 960446 960748 "FS2EXPXP" 961222 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959701 959816 959968 "FRUTIL" 960155 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951114 955196 956554 "FR" 958375 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946083 948757 948797 "FRNAALG" 950193 NIL FRNAALG (NIL T) -9 NIL 950800 NIL) (-418 941756 942832 944107 "FRNAALG-" 944857 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941394 941437 941564 "FRNAAF2" 941707 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939774 940248 940543 "FRMOD" 941206 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937525 938157 938474 "FRIDEAL" 939565 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936720 936807 937096 "FRIDEAL2" 937432 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935853 936267 936308 "FRETRCT" 936313 NIL FRETRCT (NIL T) -9 NIL 936489 NIL) (-412 934965 935196 935547 "FRETRCT-" 935552 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 932053 933263 933322 "FRAMALG" 934204 NIL FRAMALG (NIL T T) -9 NIL 934496 NIL) (-410 930187 930642 931272 "FRAMALG-" 931495 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924108 929662 929938 "FRAC" 929943 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923744 923801 923908 "FRAC2" 924045 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923380 923437 923544 "FR2" 923681 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 917893 920786 920814 "FPS" 921933 T FPS (NIL) -9 NIL 922490 NIL) (-405 917342 917451 917615 "FPS-" 917761 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914644 916313 916341 "FPC" 916566 T FPC (NIL) -9 NIL 916708 NIL) (-403 914437 914477 914574 "FPC-" 914579 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913227 913925 913966 "FPATMAB" 913971 NIL FPATMAB (NIL T) -9 NIL 914123 NIL) (-401 910900 911403 911829 "FPARFRAC" 912864 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906293 906792 907474 "FORTRAN" 910332 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 904009 904509 905048 "FORT" 905774 T FORT (NIL) -7 NIL NIL NIL) (-398 901685 902247 902275 "FORTFN" 903335 T FORTFN (NIL) -9 NIL 903959 NIL) (-397 901449 901499 901527 "FORTCAT" 901586 T FORTCAT (NIL) -9 NIL 901648 NIL) (-396 899555 900065 900455 "FORMULA" 901079 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899343 899373 899442 "FORMULA1" 899519 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 898866 898918 899091 "FORDER" 899285 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 897962 898126 898319 "FOP" 898693 T FOP (NIL) -7 NIL NIL NIL) (-392 896543 897242 897416 "FNLA" 897844 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895272 895687 895715 "FNCAT" 896175 T FNCAT (NIL) -9 NIL 896435 NIL) (-390 894811 895231 895259 "FNAME" 895264 T FNAME (NIL) -8 NIL NIL NIL) (-389 893374 894337 894365 "FMTC" 894370 T FMTC (NIL) -9 NIL 894406 NIL) (-388 889707 890897 891526 "FMONOID" 892778 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 888899 889449 889598 "FM" 889603 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886323 886969 886997 "FMFUN" 888141 T FMFUN (NIL) -9 NIL 888849 NIL) (-385 885592 885773 885801 "FMC" 886091 T FMC (NIL) -9 NIL 886273 NIL) (-384 882671 883531 883585 "FMCAT" 884780 NIL FMCAT (NIL T T) -9 NIL 885275 NIL) (-383 881537 882437 882537 "FM1" 882616 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879311 879727 880221 "FLOATRP" 881088 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872886 877040 877661 "FLOAT" 878710 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870324 870824 871402 "FLOATCP" 872353 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869064 869902 869943 "FLINEXP" 869948 NIL FLINEXP (NIL T) -9 NIL 870041 NIL) (-378 868218 868453 868781 "FLINEXP-" 868786 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867294 867438 867662 "FLASORT" 868070 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864410 865278 865330 "FLALG" 866557 NIL FLALG (NIL T T) -9 NIL 867024 NIL) (-375 858146 861896 861937 "FLAGG" 863199 NIL FLAGG (NIL T) -9 NIL 863851 NIL) (-374 856872 857211 857701 "FLAGG-" 857706 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855914 856057 856284 "FLAGG2" 856725 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852765 853773 853832 "FINRALG" 854960 NIL FINRALG (NIL T T) -9 NIL 855468 NIL) (-371 851925 852154 852493 "FINRALG-" 852498 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851305 851544 851572 "FINITE" 851768 T FINITE (NIL) -9 NIL 851875 NIL) (-369 843662 845849 845889 "FINAALG" 849556 NIL FINAALG (NIL T) -9 NIL 851009 NIL) (-368 838994 840044 841188 "FINAALG-" 842567 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838362 838749 838852 "FILE" 838924 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837020 837358 837412 "FILECAT" 838096 NIL FILECAT (NIL T T) -9 NIL 838312 NIL) (-365 834736 836264 836292 "FIELD" 836332 T FIELD (NIL) -9 NIL 836412 NIL) (-364 833356 833741 834252 "FIELD-" 834257 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831206 831991 832338 "FGROUP" 833042 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830296 830460 830680 "FGLMICPK" 831038 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826128 830221 830278 "FFX" 830283 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825729 825790 825925 "FFSLPE" 826061 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821718 822501 823297 "FFPOLY" 824965 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821222 821258 821467 "FFPOLY2" 821676 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817065 821141 821204 "FFP" 821209 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812463 816976 817040 "FF" 817045 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807589 811806 811996 "FFNBX" 812317 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802518 806724 806982 "FFNBP" 807443 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797151 801802 802013 "FFNB" 802351 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795983 796181 796496 "FFINTBAS" 796948 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792052 794272 794300 "FFIELDC" 794920 T FFIELDC (NIL) -9 NIL 795296 NIL) (-350 790714 791085 791582 "FFIELDC-" 791587 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790283 790329 790453 "FFHOM" 790656 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787978 788465 788982 "FFF" 789798 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783596 787720 787821 "FFCGX" 787921 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779217 783328 783435 "FFCGP" 783539 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774400 778944 779052 "FFCG" 779153 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755796 764877 764963 "FFCAT" 770128 NIL FFCAT (NIL T T T) -9 NIL 771579 NIL) (-343 750994 752041 753355 "FFCAT-" 754585 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750405 750448 750683 "FFCAT2" 750945 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739726 743377 744597 "FEXPR" 749257 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738726 739161 739202 "FEVALAB" 739286 NIL FEVALAB (NIL T) -9 NIL 739547 NIL) (-339 737885 738095 738433 "FEVALAB-" 738438 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736451 737268 737471 "FDIV" 737784 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733471 734212 734327 "FDIVCAT" 735895 NIL FDIVCAT (NIL T T T T) -9 NIL 736332 NIL) (-336 733233 733260 733430 "FDIVCAT-" 733435 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732453 732540 732817 "FDIV2" 733140 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731427 731748 731950 "FCTRDATA" 732271 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730113 730372 730661 "FCPAK1" 731158 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729212 729613 729754 "FCOMP" 730004 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712914 716362 719900 "FC" 725694 T FC (NIL) -8 NIL NIL NIL) (-330 705277 709305 709345 "FAXF" 711147 NIL FAXF (NIL T) -9 NIL 711839 NIL) (-329 702553 703211 704036 "FAXF-" 704501 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697605 701929 702105 "FARRAY" 702410 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692499 694566 694619 "FAMR" 695642 NIL FAMR (NIL T T) -9 NIL 696102 NIL) (-326 691389 691691 692126 "FAMR-" 692131 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690558 691311 691364 "FAMONOID" 691369 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688344 689054 689107 "FAMONC" 690048 NIL FAMONC (NIL T T) -9 NIL 690434 NIL) (-323 687008 688098 688235 "FAGROUP" 688240 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684803 685122 685525 "FACUTIL" 686689 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683902 684087 684309 "FACTFUNC" 684613 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676324 683205 683404 "EXPUPXS" 683758 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673807 674347 674933 "EXPRTUBE" 675758 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670078 670670 671400 "EXPRODE" 673146 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655563 668727 669156 "EXPR" 669682 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650117 650704 651510 "EXPR2UPS" 654861 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649749 649806 649915 "EXPR2" 650054 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641139 648902 649192 "EXPEXPAN" 649586 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640939 641096 641125 "EXIT" 641130 T EXIT (NIL) -8 NIL NIL NIL) (-312 640419 640663 640754 "EXITAST" 640868 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640046 640108 640221 "EVALCYC" 640351 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639587 639705 639746 "EVALAB" 639916 NIL EVALAB (NIL T) -9 NIL 640020 NIL) (-309 639068 639190 639411 "EVALAB-" 639416 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636436 637738 637766 "EUCDOM" 638321 T EUCDOM (NIL) -9 NIL 638671 NIL) (-307 634841 635283 635873 "EUCDOM-" 635878 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622379 625139 627889 "ESTOOLS" 632111 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622011 622068 622177 "ESTOOLS2" 622316 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621762 621804 621884 "ESTOOLS1" 621963 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615799 617407 617435 "ES" 620203 T ES (NIL) -9 NIL 621613 NIL) (-302 610746 612033 613850 "ES-" 614014 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607120 607881 608661 "ESCONT" 609986 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606865 606897 606979 "ESCONT1" 607082 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606540 606590 606690 "ES2" 606809 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606170 606228 606337 "ES1" 606476 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605386 605515 605691 "ERROR" 606014 T ERROR (NIL) -7 NIL NIL NIL) (-296 598778 605245 605336 "EQTBL" 605341 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591281 594092 595541 "EQ" 597362 NIL -2014 (NIL T) -8 NIL NIL NIL) (-294 590913 590970 591079 "EQ2" 591218 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586202 587251 588344 "EP" 589852 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584802 585093 585399 "ENV" 585916 T ENV (NIL) -8 NIL NIL NIL) (-291 583896 584450 584478 "ENTIRER" 584483 T ENTIRER (NIL) -9 NIL 584529 NIL) (-290 580363 581851 582221 "EMR" 583695 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579507 579692 579746 "ELTAGG" 580126 NIL ELTAGG (NIL T T) -9 NIL 580337 NIL) (-288 579226 579288 579429 "ELTAGG-" 579434 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579015 579044 579098 "ELTAB" 579182 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578141 578287 578486 "ELFUTS" 578866 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577883 577939 577967 "ELEMFUN" 578072 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577753 577774 577842 "ELEMFUN-" 577847 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572597 575853 575894 "ELAGG" 576834 NIL ELAGG (NIL T) -9 NIL 577297 NIL) (-282 570882 571316 571979 "ELAGG-" 571984 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569543 569822 570116 "ELABEXPR" 570608 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562407 564210 565037 "EFUPXS" 568819 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555857 557658 558468 "EFULS" 561683 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553342 553700 554172 "EFSTRUC" 555489 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543133 544699 546247 "EF" 551857 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542207 542618 542767 "EAB" 543004 T EAB (NIL) -8 NIL NIL NIL) (-275 541389 542166 542194 "E04UCFA" 542199 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540571 541348 541376 "E04NAFA" 541381 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539753 540530 540558 "E04MBFA" 540563 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538935 539712 539740 "E04JAFA" 539745 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538119 538894 538922 "E04GCFA" 538927 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537303 538078 538106 "E04FDFA" 538111 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536485 537262 537290 "E04DGFA" 537295 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530658 532010 533374 "E04AGNT" 535141 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529338 529844 529884 "DVARCAT" 530359 NIL DVARCAT (NIL T) -9 NIL 530558 NIL) (-266 528542 528754 529068 "DVARCAT-" 529073 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521679 528341 528470 "DSMP" 528475 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516460 517624 518692 "DROPT" 520631 T DROPT (NIL) -8 NIL NIL NIL) (-263 516125 516184 516282 "DROPT1" 516395 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511240 512366 513503 "DROPT0" 515008 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509585 509910 510296 "DRAWPT" 510874 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504172 505095 506174 "DRAW" 508559 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503805 503858 503976 "DRAWHACK" 504113 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502536 502805 503096 "DRAWCX" 503534 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502051 502120 502271 "DRAWCURV" 502462 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492519 494481 496596 "DRAWCFUN" 499956 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489285 491214 491255 "DQAGG" 491884 NIL DQAGG (NIL T) -9 NIL 492157 NIL) (-254 477409 483878 483961 "DPOLCAT" 485813 NIL DPOLCAT (NIL T T T T) -9 NIL 486358 NIL) (-253 472245 473594 475552 "DPOLCAT-" 475557 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465367 472106 472204 "DPMO" 472209 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458392 465147 465314 "DPMM" 465319 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457870 458084 458182 "DOMTMPLT" 458314 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457303 457672 457752 "DOMCTOR" 457810 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456515 456783 456934 "DOMAIN" 457172 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450503 456150 456302 "DMP" 456416 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450103 450159 450303 "DLP" 450441 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443925 449430 449620 "DLIST" 449945 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440722 442778 442819 "DLAGG" 443369 NIL DLAGG (NIL T) -9 NIL 443599 NIL) (-243 439398 440062 440090 "DIVRING" 440182 T DIVRING (NIL) -9 NIL 440265 NIL) (-242 438635 438825 439125 "DIVRING-" 439130 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436737 437094 437500 "DISPLAY" 438249 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430625 436651 436714 "DIRPROD" 436719 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429473 429676 429941 "DIRPROD2" 430418 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418248 424254 424307 "DIRPCAT" 424717 NIL DIRPCAT (NIL NIL T) -9 NIL 425557 NIL) (-237 415574 416216 417097 "DIRPCAT-" 417434 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414861 415021 415207 "DIOSP" 415408 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411516 413773 413814 "DIOPS" 414248 NIL DIOPS (NIL T) -9 NIL 414477 NIL) (-234 411065 411179 411370 "DIOPS-" 411375 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409888 410516 410544 "DIFRING" 410731 T DIFRING (NIL) -9 NIL 410841 NIL) (-232 409534 409611 409763 "DIFRING-" 409768 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407270 408542 408583 "DIFEXT" 408946 NIL DIFEXT (NIL T) -9 NIL 409240 NIL) (-230 405555 405983 406649 "DIFEXT-" 406654 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402830 405087 405128 "DIAGG" 405133 NIL DIAGG (NIL T) -9 NIL 405153 NIL) (-228 402214 402371 402623 "DIAGG-" 402628 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397631 401173 401450 "DHMATRIX" 401983 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393243 394152 395162 "DFSFUN" 396641 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388321 392174 392486 "DFLOAT" 392951 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386584 386865 387254 "DFINTTLS" 388029 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383613 384605 385005 "DERHAM" 386250 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381414 383388 383477 "DEQUEUE" 383557 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380668 380801 380984 "DEGRED" 381276 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377098 377843 378689 "DEFINTRF" 379896 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374653 375122 375714 "DEFINTEF" 376617 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 374003 374273 374388 "DEFAST" 374558 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368007 373598 373747 "DECIMAL" 373874 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365519 365977 366483 "DDFACT" 367551 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365115 365158 365309 "DBLRESP" 365470 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362987 363348 363708 "DBASE" 364882 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362229 362467 362613 "DATAARY" 362886 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361335 362188 362216 "D03FAFA" 362221 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360442 361294 361322 "D03EEFA" 361327 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358392 358858 359347 "D03AGNT" 359973 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357681 358351 358379 "D02EJFA" 358384 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356970 357640 357668 "D02CJFA" 357673 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356259 356929 356957 "D02BHFA" 356962 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355548 356218 356246 "D02BBFA" 356251 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348745 350334 351940 "D02AGNT" 353962 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346513 347036 347582 "D01WGTS" 348219 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345580 346472 346500 "D01TRNS" 346505 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344648 345539 345567 "D01GBFA" 345572 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343716 344607 344635 "D01FCFA" 344640 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342784 343675 343703 "D01ASFA" 343708 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341852 342743 342771 "D01AQFA" 342776 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340920 341811 341839 "D01APFA" 341844 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339988 340879 340907 "D01ANFA" 340912 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339056 339947 339975 "D01AMFA" 339980 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338124 339015 339043 "D01ALFA" 339048 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337192 338083 338111 "D01AKFA" 338116 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336260 337151 337179 "D01AJFA" 337184 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329555 331108 332669 "D01AGNT" 334719 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328892 329020 329172 "CYCLOTOM" 329423 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325626 326340 327067 "CYCLES" 328185 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324938 325072 325243 "CVMP" 325487 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322779 323037 323406 "CTRIGMNP" 324666 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322215 322573 322646 "CTOR" 322726 T CTOR (NIL) -8 NIL NIL NIL) (-186 321724 321946 322047 "CTORKIND" 322134 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321015 321331 321359 "CTORCAT" 321541 T CTORCAT (NIL) -9 NIL 321654 NIL) (-184 320613 320724 320883 "CTORCAT-" 320888 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320075 320287 320395 "CTORCALL" 320537 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319449 319548 319701 "CSTTOOLS" 319972 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315248 315905 316663 "CRFP" 318761 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314723 314969 315061 "CRCEAST" 315176 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313770 313955 314183 "CRAPACK" 314527 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313154 313255 313459 "CPMATCH" 313646 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312879 312907 313013 "CPIMA" 313120 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309227 309899 310618 "COORDSYS" 312214 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308639 308760 308902 "CONTOUR" 309105 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304530 306642 307134 "CONTFRAC" 308179 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304410 304431 304459 "CONDUIT" 304496 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303498 304052 304080 "COMRING" 304085 T COMRING (NIL) -9 NIL 304137 NIL) (-171 302552 302856 303040 "COMPPROP" 303334 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302213 302248 302376 "COMPLPAT" 302511 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292504 302022 302131 "COMPLEX" 302136 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292140 292197 292304 "COMPLEX2" 292441 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291858 291893 291991 "COMPFACT" 292099 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275938 285932 285972 "COMPCAT" 286976 NIL COMPCAT (NIL T) -9 NIL 288324 NIL) (-165 265450 268377 272004 "COMPCAT-" 272360 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265179 265207 265310 "COMMUPC" 265416 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264973 265007 265066 "COMMONOP" 265140 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264529 264724 264811 "COMM" 264906 T COMM (NIL) -8 NIL NIL NIL) (-161 264105 264333 264408 "COMMAAST" 264474 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263354 263548 263576 "COMBOPC" 263914 T COMBOPC (NIL) -9 NIL 264089 NIL) (-159 262250 262460 262702 "COMBINAT" 263144 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258707 259281 259908 "COMBF" 261672 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257465 257823 258058 "COLOR" 258492 T COLOR (NIL) -8 NIL NIL NIL) (-156 256941 257186 257278 "COLONAST" 257393 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256581 256628 256753 "CMPLXRT" 256888 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256029 256281 256380 "CLLCTAST" 256502 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251527 252559 253639 "CLIP" 254969 T CLIP (NIL) -7 NIL NIL NIL) (-152 249873 250633 250872 "CLIF" 251354 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246048 248019 248060 "CLAGG" 248989 NIL CLAGG (NIL T) -9 NIL 249525 NIL) (-150 244470 244927 245510 "CLAGG-" 245515 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244014 244099 244239 "CINTSLPE" 244379 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241515 241986 242534 "CHVAR" 243542 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240689 241243 241271 "CHARZ" 241276 T CHARZ (NIL) -9 NIL 241291 NIL) (-146 240443 240483 240561 "CHARPOL" 240643 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239501 240088 240116 "CHARNZ" 240163 T CHARNZ (NIL) -9 NIL 240219 NIL) (-144 237407 238155 238508 "CHAR" 239168 T CHAR (NIL) -8 NIL NIL NIL) (-143 237133 237194 237222 "CFCAT" 237333 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236378 236489 236671 "CDEN" 237017 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232343 235531 235811 "CCLASS" 236118 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231594 231751 231928 "CATEGORY" 232186 T -10 (NIL) -8 NIL NIL NIL) (-139 231167 231513 231561 "CATCTOR" 231566 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230618 230870 230968 "CATAST" 231089 T CATAST (NIL) -8 NIL NIL NIL) (-137 230094 230339 230431 "CASEAST" 230546 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225103 226123 226876 "CARTEN" 229397 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224211 224359 224580 "CARTEN2" 224950 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222527 223361 223618 "CARD" 223974 T CARD (NIL) -8 NIL NIL NIL) (-133 222103 222331 222406 "CAPSLAST" 222472 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221607 221815 221843 "CACHSET" 221975 T CACHSET (NIL) -9 NIL 222053 NIL) (-131 221077 221399 221427 "CABMON" 221477 T CABMON (NIL) -9 NIL 221533 NIL) (-130 220550 220781 220891 "BYTEORD" 220987 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220084 220226 "BYTE" 220389 T BYTE (NIL) -8 NIL NIL 220511) (-128 214879 219034 219206 "BYTEBUF" 219377 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212388 214571 214678 "BTREE" 214805 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209837 212036 212158 "BTOURN" 212298 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207207 209307 209348 "BTCAT" 209416 NIL BTCAT (NIL T) -9 NIL 209493 NIL) (-124 206874 206954 207103 "BTCAT-" 207108 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202139 206017 206045 "BTAGG" 206267 T BTAGG (NIL) -9 NIL 206428 NIL) (-122 201629 201754 201960 "BTAGG-" 201965 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198624 200907 201122 "BSTREE" 201446 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197762 197888 198072 "BRILL" 198480 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194414 196488 196529 "BRAGG" 197178 NIL BRAGG (NIL T) -9 NIL 197436 NIL) (-118 192943 193349 193904 "BRAGG-" 193909 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186172 192289 192473 "BPADICRT" 192791 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184487 186109 186154 "BPADIC" 186159 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184185 184215 184329 "BOUNDZRO" 184451 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179413 180611 181523 "BOP" 183293 T BOP (NIL) -8 NIL NIL NIL) (-113 177194 177598 178073 "BOP1" 178971 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164527 170117 170265 "BINARY" 170392 T BINARY (NIL) -8 NIL NIL NIL) (-107 162307 163782 163823 "BGAGG" 164083 NIL BGAGG (NIL T) -9 NIL 164220 NIL) (-106 162138 162170 162261 "BGAGG-" 162266 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161209 161522 161727 "BFUNCT" 161953 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159899 160077 160365 "BEZOUT" 161033 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156368 158751 159081 "BBTREE" 159602 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156102 156155 156183 "BASTYPE" 156302 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155954 155983 156056 "BASTYPE-" 156061 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155388 155464 155616 "BALFACT" 155865 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154244 154803 154989 "AUTOMOR" 155233 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153970 153975 154001 "ATTREG" 154006 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152222 152667 153019 "ATTRBUT" 153636 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151830 152050 152116 "ATTRAST" 152174 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151366 151479 151505 "ATRIG" 151706 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151175 151216 151303 "ATRIG-" 151308 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150820 151006 151032 "ASTCAT" 151037 T ASTCAT (NIL) -9 NIL 151067 NIL) (-92 150547 150606 150725 "ASTCAT-" 150730 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148696 150323 150411 "ASTACK" 150490 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147201 147498 147863 "ASSOCEQ" 148378 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146233 146860 146984 "ASP9" 147108 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145996 146181 146220 "ASP8" 146225 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144864 145601 145743 "ASP80" 145885 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143762 144499 144631 "ASP7" 144763 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142716 143439 143557 "ASP78" 143675 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141685 142396 142513 "ASP77" 142630 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140597 141323 141454 "ASP74" 141585 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139497 140232 140364 "ASP73" 140496 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138601 139323 139423 "ASP6" 139428 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137545 138278 138396 "ASP55" 138514 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136494 137219 137338 "ASP50" 137457 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135582 136195 136305 "ASP4" 136415 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134670 135283 135393 "ASP49" 135503 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133454 134209 134377 "ASP42" 134559 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132230 132987 133157 "ASP41" 133341 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131180 131907 132025 "ASP35" 132143 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130945 131128 131167 "ASP34" 131172 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130682 130749 130825 "ASP33" 130900 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129575 130317 130449 "ASP31" 130581 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129340 129523 129562 "ASP30" 129567 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129075 129144 129220 "ASP29" 129295 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128840 129023 129062 "ASP28" 129067 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128605 128788 128827 "ASP27" 128832 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127689 128303 128414 "ASP24" 128525 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126765 127491 127603 "ASP20" 127608 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125853 126466 126576 "ASP1" 126686 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124795 125527 125646 "ASP19" 125765 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124532 124599 124675 "ASP12" 124750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123384 124131 124275 "ASP10" 124419 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121235 123228 123319 "ARRAY2" 123324 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117000 120883 120997 "ARRAY1" 121152 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116032 116205 116426 "ARRAY12" 116823 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110344 112262 112337 "ARR2CAT" 114967 NIL ARR2CAT (NIL T T T) -9 NIL 115725 NIL) (-56 107778 108522 109476 "ARR2CAT-" 109481 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107095 107405 107530 "ARITY" 107671 T ARITY (NIL) -8 NIL NIL NIL) (-54 105871 106023 106322 "APPRULE" 106931 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105522 105570 105689 "APPLYORE" 105817 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105115 105235 "ANY" 105420 T ANY (NIL) -8 NIL NIL NIL) (-51 104154 104277 104434 "ANY1" 104750 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101684 102591 102918 "ANTISYM" 103878 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101176 101391 101487 "ANON" 101606 T ANON (NIL) -8 NIL NIL NIL) (-48 95425 99715 100169 "AN" 100740 T AN (NIL) -8 NIL NIL NIL) (-47 91323 92711 92762 "AMR" 93510 NIL AMR (NIL T T) -9 NIL 94110 NIL) (-46 90435 90656 91019 "AMR-" 91024 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74874 90352 90413 "ALIST" 90418 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74468 74637 "ALGSC" 74792 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3221361 3221366 3221371 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3221346 3221351 3221356 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3221331 3221336 3221341 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3221316 3221321 3221326 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1293 3220459 3221191 3221268 "ZMOD" 3221273 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1292 3219569 3219733 3219942 "ZLINDEP" 3220291 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1291 3208869 3210637 3212609 "ZDSOLVE" 3217699 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1290 3208115 3208256 3208445 "YSTREAM" 3208715 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1289 3205889 3207416 3207620 "XRPOLY" 3207958 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1288 3202442 3203760 3204335 "XPR" 3205361 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1287 3200163 3201773 3201977 "XPOLY" 3202273 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1286 3197816 3199184 3199239 "XPOLYC" 3199527 NIL XPOLYC (NIL T T) -9 NIL 3199640 NIL) (-1285 3194191 3196333 3196721 "XPBWPOLY" 3197474 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1284 3189886 3192181 3192223 "XF" 3192844 NIL XF (NIL T) -9 NIL 3193244 NIL) (-1283 3189507 3189595 3189764 "XF-" 3189769 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1282 3184703 3185992 3186047 "XFALG" 3188219 NIL XFALG (NIL T T) -9 NIL 3189008 NIL) (-1281 3183836 3183940 3184145 "XEXPPKG" 3184595 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1280 3181945 3183686 3183782 "XDPOLY" 3183787 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1279 3180752 3181352 3181395 "XALG" 3181400 NIL XALG (NIL T) -9 NIL 3181511 NIL) (-1278 3174194 3178729 3179223 "WUTSET" 3180344 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1277 3172450 3173246 3173569 "WP" 3174005 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1276 3172052 3172272 3172342 "WHILEAST" 3172402 T WHILEAST (NIL) -8 NIL NIL NIL) (-1275 3171524 3171769 3171863 "WHEREAST" 3171980 T WHEREAST (NIL) -8 NIL NIL NIL) (-1274 3170410 3170608 3170903 "WFFINTBS" 3171321 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1273 3168314 3168741 3169203 "WEIER" 3169982 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1272 3167360 3167810 3167852 "VSPACE" 3167988 NIL VSPACE (NIL T) -9 NIL 3168062 NIL) (-1271 3167198 3167225 3167316 "VSPACE-" 3167321 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1270 3167006 3167049 3167117 "VOID" 3167152 T VOID (NIL) -8 NIL NIL NIL) (-1269 3165142 3165501 3165907 "VIEW" 3166622 T VIEW (NIL) -7 NIL NIL NIL) (-1268 3161566 3162205 3162942 "VIEWDEF" 3164427 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1267 3150870 3153114 3155287 "VIEW3D" 3159415 T VIEW3D (NIL) -8 NIL NIL NIL) (-1266 3143121 3144781 3146360 "VIEW2D" 3149313 T VIEW2D (NIL) -8 NIL NIL NIL) (-1265 3138473 3142891 3142983 "VECTOR" 3143064 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1264 3137050 3137309 3137627 "VECTOR2" 3138203 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1263 3130524 3134831 3134874 "VECTCAT" 3135869 NIL VECTCAT (NIL T) -9 NIL 3136456 NIL) (-1262 3129538 3129792 3130182 "VECTCAT-" 3130187 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1261 3128992 3129189 3129309 "VARIABLE" 3129453 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1260 3128925 3128930 3128960 "UTYPE" 3128965 T UTYPE (NIL) -9 NIL NIL NIL) (-1259 3127755 3127909 3128171 "UTSODETL" 3128751 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1258 3125195 3125655 3126179 "UTSODE" 3127296 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1257 3117032 3122821 3123310 "UTS" 3124764 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1256 3107906 3113273 3113316 "UTSCAT" 3114428 NIL UTSCAT (NIL T) -9 NIL 3115186 NIL) (-1255 3105253 3105976 3106965 "UTSCAT-" 3106970 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1254 3104880 3104923 3105056 "UTS2" 3105204 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1253 3099106 3101718 3101761 "URAGG" 3103831 NIL URAGG (NIL T) -9 NIL 3104554 NIL) (-1252 3096045 3096908 3098031 "URAGG-" 3098036 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1251 3091754 3094680 3095145 "UPXSSING" 3095709 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1250 3083820 3091001 3091274 "UPXS" 3091539 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1249 3076893 3083724 3083796 "UPXSCONS" 3083801 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1248 3066638 3073431 3073493 "UPXSCCA" 3074067 NIL UPXSCCA (NIL T T) -9 NIL 3074300 NIL) (-1247 3066276 3066361 3066535 "UPXSCCA-" 3066540 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1246 3055873 3062439 3062482 "UPXSCAT" 3063130 NIL UPXSCAT (NIL T) -9 NIL 3063739 NIL) (-1245 3055303 3055382 3055561 "UPXS2" 3055788 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1244 3053957 3054210 3054561 "UPSQFREE" 3055046 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1243 3047378 3050435 3050490 "UPSCAT" 3051651 NIL UPSCAT (NIL T T) -9 NIL 3052425 NIL) (-1242 3046582 3046789 3047116 "UPSCAT-" 3047121 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1241 3032237 3040005 3040048 "UPOLYC" 3042149 NIL UPOLYC (NIL T) -9 NIL 3043370 NIL) (-1240 3023565 3025991 3029138 "UPOLYC-" 3029143 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1239 3023192 3023235 3023368 "UPOLYC2" 3023516 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1238 3015003 3022875 3023004 "UP" 3023111 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1237 3014342 3014449 3014613 "UPMP" 3014892 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1236 3013895 3013976 3014115 "UPDIVP" 3014255 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1235 3012463 3012712 3013028 "UPDECOMP" 3013644 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1234 3011698 3011810 3011995 "UPCDEN" 3012347 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1233 3011217 3011286 3011435 "UP2" 3011623 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1232 3009684 3010421 3010698 "UNISEG" 3010975 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1231 3008899 3009026 3009231 "UNISEG2" 3009527 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1230 3007959 3008139 3008365 "UNIFACT" 3008715 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1229 2991891 3007136 3007387 "ULS" 3007766 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1228 2979889 2991795 2991867 "ULSCONS" 2991872 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1227 2961908 2973893 2973955 "ULSCCAT" 2974593 NIL ULSCCAT (NIL T T) -9 NIL 2974881 NIL) (-1226 2960958 2961203 2961591 "ULSCCAT-" 2961596 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1225 2950332 2956812 2956855 "ULSCAT" 2957718 NIL ULSCAT (NIL T) -9 NIL 2958449 NIL) (-1224 2949762 2949841 2950020 "ULS2" 2950247 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1223 2948889 2949399 2949506 "UINT8" 2949617 T UINT8 (NIL) -8 NIL NIL 2949702) (-1222 2948015 2948525 2948632 "UINT64" 2948743 T UINT64 (NIL) -8 NIL NIL 2948828) (-1221 2947141 2947651 2947758 "UINT32" 2947869 T UINT32 (NIL) -8 NIL NIL 2947954) (-1220 2946267 2946777 2946884 "UINT16" 2946995 T UINT16 (NIL) -8 NIL NIL 2947080) (-1219 2944570 2945527 2945557 "UFD" 2945769 T UFD (NIL) -9 NIL 2945883 NIL) (-1218 2944364 2944410 2944505 "UFD-" 2944510 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1217 2943446 2943629 2943845 "UDVO" 2944170 T UDVO (NIL) -7 NIL NIL NIL) (-1216 2941262 2941671 2942142 "UDPO" 2943010 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1215 2941195 2941200 2941230 "TYPE" 2941235 T TYPE (NIL) -9 NIL NIL NIL) (-1214 2940955 2941150 2941181 "TYPEAST" 2941186 T TYPEAST (NIL) -8 NIL NIL NIL) (-1213 2939926 2940128 2940368 "TWOFACT" 2940749 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1212 2938949 2939335 2939570 "TUPLE" 2939726 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1211 2936640 2937159 2937698 "TUBETOOL" 2938432 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1210 2935489 2935694 2935935 "TUBE" 2936433 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1209 2930218 2934461 2934744 "TS" 2935241 NIL TS (NIL T) -8 NIL NIL NIL) (-1208 2918858 2922977 2923074 "TSETCAT" 2928343 NIL TSETCAT (NIL T T T T) -9 NIL 2929874 NIL) (-1207 2913590 2915190 2917081 "TSETCAT-" 2917086 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1206 2908229 2909076 2910005 "TRMANIP" 2912726 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1205 2907670 2907733 2907896 "TRIMAT" 2908161 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1204 2905536 2905773 2906130 "TRIGMNIP" 2907419 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1203 2905056 2905169 2905199 "TRIGCAT" 2905412 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1202 2904725 2904804 2904945 "TRIGCAT-" 2904950 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1201 2901570 2903583 2903864 "TREE" 2904479 NIL TREE (NIL T) -8 NIL NIL NIL) (-1200 2900844 2901372 2901402 "TRANFUN" 2901437 T TRANFUN (NIL) -9 NIL 2901503 NIL) (-1199 2900123 2900314 2900594 "TRANFUN-" 2900599 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1198 2899927 2899959 2900020 "TOPSP" 2900084 T TOPSP (NIL) -7 NIL NIL NIL) (-1197 2899275 2899390 2899544 "TOOLSIGN" 2899808 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1196 2897909 2898452 2898691 "TEXTFILE" 2899058 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1195 2895821 2896362 2896791 "TEX" 2897502 T TEX (NIL) -8 NIL NIL NIL) (-1194 2895602 2895633 2895705 "TEX1" 2895784 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1193 2895250 2895313 2895403 "TEMUTL" 2895534 T TEMUTL (NIL) -7 NIL NIL NIL) (-1192 2893404 2893684 2894009 "TBCMPPK" 2894973 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1191 2885181 2891564 2891620 "TBAGG" 2892020 NIL TBAGG (NIL T T) -9 NIL 2892231 NIL) (-1190 2880251 2881739 2883493 "TBAGG-" 2883498 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1189 2879635 2879742 2879887 "TANEXP" 2880140 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1188 2873025 2879492 2879585 "TABLE" 2879590 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1187 2872437 2872536 2872674 "TABLEAU" 2872922 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1186 2867045 2868265 2869513 "TABLBUMP" 2871223 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1185 2866267 2866414 2866595 "SYSTEM" 2866886 T SYSTEM (NIL) -8 NIL NIL NIL) (-1184 2862726 2863425 2864208 "SYSSOLP" 2865518 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1183 2862524 2862681 2862712 "SYSPTR" 2862717 T SYSPTR (NIL) -8 NIL NIL NIL) (-1182 2861568 2862073 2862192 "SYSNNI" 2862378 NIL SYSNNI (NIL NIL) -8 NIL NIL 2862463) (-1181 2860875 2861334 2861413 "SYSINT" 2861473 NIL SYSINT (NIL NIL) -8 NIL NIL 2861518) (-1180 2857207 2858153 2858863 "SYNTAX" 2860187 T SYNTAX (NIL) -8 NIL NIL NIL) (-1179 2854365 2854967 2855599 "SYMTAB" 2856597 T SYMTAB (NIL) -8 NIL NIL NIL) (-1178 2849614 2850516 2851499 "SYMS" 2853404 T SYMS (NIL) -8 NIL NIL NIL) (-1177 2846849 2849072 2849302 "SYMPOLY" 2849419 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1176 2846366 2846441 2846564 "SYMFUNC" 2846761 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1175 2842385 2843678 2844491 "SYMBOL" 2845575 T SYMBOL (NIL) -8 NIL NIL NIL) (-1174 2835924 2837613 2839333 "SWITCH" 2840687 T SWITCH (NIL) -8 NIL NIL NIL) (-1173 2829158 2834745 2835048 "SUTS" 2835679 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1172 2821224 2828405 2828678 "SUPXS" 2828943 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1171 2812983 2820842 2820968 "SUP" 2821133 NIL SUP (NIL T) -8 NIL NIL NIL) (-1170 2812142 2812269 2812486 "SUPFRACF" 2812851 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1169 2811763 2811822 2811935 "SUP2" 2812077 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1168 2810211 2810485 2810841 "SUMRF" 2811462 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1167 2809546 2809612 2809804 "SUMFS" 2810132 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1166 2793513 2808723 2808974 "SULS" 2809353 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1165 2793115 2793335 2793405 "SUCHTAST" 2793465 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1164 2792410 2792640 2792780 "SUCH" 2793023 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1163 2786276 2787316 2788275 "SUBSPACE" 2791498 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1162 2785706 2785796 2785960 "SUBRESP" 2786164 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1161 2779071 2780371 2781682 "STTF" 2784442 NIL STTF (NIL T) -7 NIL NIL NIL) (-1160 2773244 2774364 2775511 "STTFNC" 2777971 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1159 2764554 2766426 2768220 "STTAYLOR" 2771485 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1158 2757684 2764418 2764501 "STRTBL" 2764506 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1157 2753048 2757639 2757670 "STRING" 2757675 T STRING (NIL) -8 NIL NIL NIL) (-1156 2747909 2752421 2752451 "STRICAT" 2752510 T STRICAT (NIL) -9 NIL 2752572 NIL) (-1155 2740662 2745528 2746139 "STREAM" 2747333 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1154 2740172 2740249 2740393 "STREAM3" 2740579 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1153 2739154 2739337 2739572 "STREAM2" 2739985 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1152 2738842 2738894 2738987 "STREAM1" 2739096 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1151 2737858 2738039 2738270 "STINPROD" 2738658 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1150 2737410 2737620 2737650 "STEP" 2737730 T STEP (NIL) -9 NIL 2737808 NIL) (-1149 2730842 2737309 2737386 "STBL" 2737391 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1148 2725968 2730063 2730106 "STAGG" 2730259 NIL STAGG (NIL T) -9 NIL 2730348 NIL) (-1147 2723670 2724272 2725144 "STAGG-" 2725149 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1146 2721817 2723440 2723532 "STACK" 2723613 NIL STACK (NIL T) -8 NIL NIL NIL) (-1145 2714512 2719958 2720414 "SREGSET" 2721447 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1144 2706937 2708306 2709819 "SRDCMPK" 2713118 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1143 2699854 2704377 2704407 "SRAGG" 2705710 T SRAGG (NIL) -9 NIL 2706318 NIL) (-1142 2698871 2699126 2699505 "SRAGG-" 2699510 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1141 2693331 2697818 2698239 "SQMATRIX" 2698497 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1140 2687016 2690049 2690776 "SPLTREE" 2692676 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1139 2682979 2683672 2684318 "SPLNODE" 2686442 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1138 2682026 2682259 2682289 "SPFCAT" 2682733 T SPFCAT (NIL) -9 NIL NIL NIL) (-1137 2680763 2680973 2681237 "SPECOUT" 2681784 T SPECOUT (NIL) -7 NIL NIL NIL) (-1136 2672389 2674159 2674189 "SPADXPT" 2678581 T SPADXPT (NIL) -9 NIL 2680615 NIL) (-1135 2672150 2672190 2672259 "SPADPRSR" 2672342 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1134 2670305 2672105 2672136 "SPADAST" 2672141 T SPADAST (NIL) -8 NIL NIL NIL) (-1133 2662250 2664023 2664066 "SPACEC" 2668439 NIL SPACEC (NIL T) -9 NIL 2670255 NIL) (-1132 2660380 2662182 2662231 "SPACE3" 2662236 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1131 2659132 2659303 2659594 "SORTPAK" 2660185 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1130 2657224 2657527 2657939 "SOLVETRA" 2658796 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1129 2656274 2656496 2656757 "SOLVESER" 2656997 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1128 2651578 2652466 2653461 "SOLVERAD" 2655326 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1127 2647393 2648002 2648731 "SOLVEFOR" 2650945 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1126 2641663 2646742 2646839 "SNTSCAT" 2646844 NIL SNTSCAT (NIL T T T T) -9 NIL 2646914 NIL) (-1125 2635769 2639986 2640377 "SMTS" 2641353 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1124 2630453 2635657 2635734 "SMP" 2635739 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1123 2628612 2628913 2629311 "SMITH" 2630150 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1122 2621325 2625521 2625624 "SMATCAT" 2626975 NIL SMATCAT (NIL NIL T T T) -9 NIL 2627525 NIL) (-1121 2618265 2619088 2620266 "SMATCAT-" 2620271 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1120 2615931 2617501 2617544 "SKAGG" 2617805 NIL SKAGG (NIL T) -9 NIL 2617940 NIL) (-1119 2612242 2615347 2615542 "SINT" 2615729 T SINT (NIL) -8 NIL NIL 2615902) (-1118 2612014 2612052 2612118 "SIMPAN" 2612198 T SIMPAN (NIL) -7 NIL NIL NIL) (-1117 2611293 2611549 2611689 "SIG" 2611896 T SIG (NIL) -8 NIL NIL NIL) (-1116 2610131 2610352 2610627 "SIGNRF" 2611052 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1115 2608964 2609115 2609399 "SIGNEF" 2609960 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1114 2608270 2608547 2608671 "SIGAST" 2608862 T SIGAST (NIL) -8 NIL NIL NIL) (-1113 2605959 2606414 2606920 "SHP" 2607811 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1112 2599811 2605860 2605936 "SHDP" 2605941 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1111 2599384 2599576 2599606 "SGROUP" 2599699 T SGROUP (NIL) -9 NIL 2599761 NIL) (-1110 2599242 2599268 2599341 "SGROUP-" 2599346 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1109 2596077 2596775 2597498 "SGCF" 2598541 T SGCF (NIL) -7 NIL NIL NIL) (-1108 2590445 2595524 2595621 "SFRTCAT" 2595626 NIL SFRTCAT (NIL T T T T) -9 NIL 2595665 NIL) (-1107 2583866 2584884 2586020 "SFRGCD" 2589428 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1106 2576992 2578065 2579251 "SFQCMPK" 2582799 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1105 2576612 2576701 2576812 "SFORT" 2576933 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1104 2575730 2576452 2576573 "SEXOF" 2576578 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1103 2574837 2575611 2575679 "SEX" 2575684 T SEX (NIL) -8 NIL NIL NIL) (-1102 2570350 2571065 2571160 "SEXCAT" 2574097 NIL SEXCAT (NIL T T T T T) -9 NIL 2574675 NIL) (-1101 2567503 2570284 2570332 "SET" 2570337 NIL SET (NIL T) -8 NIL NIL NIL) (-1100 2565727 2566216 2566521 "SETMN" 2567244 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1099 2565223 2565375 2565405 "SETCAT" 2565581 T SETCAT (NIL) -9 NIL 2565691 NIL) (-1098 2564915 2564993 2565123 "SETCAT-" 2565128 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1097 2561276 2563376 2563419 "SETAGG" 2564289 NIL SETAGG (NIL T) -9 NIL 2564629 NIL) (-1096 2560734 2560850 2561087 "SETAGG-" 2561092 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1095 2560177 2560430 2560531 "SEQAST" 2560655 T SEQAST (NIL) -8 NIL NIL NIL) (-1094 2559376 2559670 2559731 "SEGXCAT" 2560017 NIL SEGXCAT (NIL T T) -9 NIL 2560137 NIL) (-1093 2558382 2559042 2559224 "SEG" 2559229 NIL SEG (NIL T) -8 NIL NIL NIL) (-1092 2557361 2557575 2557618 "SEGCAT" 2558140 NIL SEGCAT (NIL T) -9 NIL 2558361 NIL) (-1091 2556362 2556740 2556940 "SEGBIND" 2557196 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1090 2555983 2556042 2556155 "SEGBIND2" 2556297 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1089 2555556 2555784 2555861 "SEGAST" 2555928 T SEGAST (NIL) -8 NIL NIL NIL) (-1088 2554775 2554901 2555105 "SEG2" 2555400 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1087 2554185 2554710 2554757 "SDVAR" 2554762 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1086 2546712 2553955 2554085 "SDPOL" 2554090 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1085 2545305 2545571 2545890 "SCPKG" 2546427 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1084 2544469 2544641 2544833 "SCOPE" 2545135 T SCOPE (NIL) -8 NIL NIL NIL) (-1083 2543689 2543823 2544002 "SCACHE" 2544324 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1082 2543335 2543521 2543551 "SASTCAT" 2543556 T SASTCAT (NIL) -9 NIL 2543569 NIL) (-1081 2542822 2543170 2543246 "SAOS" 2543281 T SAOS (NIL) -8 NIL NIL NIL) (-1080 2542387 2542422 2542595 "SAERFFC" 2542781 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1079 2536326 2542284 2542364 "SAE" 2542369 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1078 2535919 2535954 2536113 "SAEFACT" 2536285 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1077 2534240 2534554 2534955 "RURPK" 2535585 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1076 2532877 2533183 2533488 "RULESET" 2534074 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1075 2530100 2530630 2531088 "RULE" 2532558 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1074 2529712 2529894 2529977 "RULECOLD" 2530052 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1073 2529502 2529530 2529601 "RTVALUE" 2529663 T RTVALUE (NIL) -8 NIL NIL NIL) (-1072 2528973 2529219 2529313 "RSTRCAST" 2529430 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1071 2523821 2524616 2525536 "RSETGCD" 2528172 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1070 2513051 2518130 2518227 "RSETCAT" 2522346 NIL RSETCAT (NIL T T T T) -9 NIL 2523443 NIL) (-1069 2510978 2511517 2512341 "RSETCAT-" 2512346 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1068 2503363 2504740 2506260 "RSDCMPK" 2509577 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1067 2501342 2501809 2501883 "RRCC" 2502969 NIL RRCC (NIL T T) -9 NIL 2503313 NIL) (-1066 2500693 2500867 2501146 "RRCC-" 2501151 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1065 2500136 2500389 2500490 "RPTAST" 2500614 T RPTAST (NIL) -8 NIL NIL NIL) (-1064 2473987 2483344 2483411 "RPOLCAT" 2494075 NIL RPOLCAT (NIL T T T) -9 NIL 2497234 NIL) (-1063 2465485 2467825 2470947 "RPOLCAT-" 2470952 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1062 2456416 2463696 2464178 "ROUTINE" 2465025 T ROUTINE (NIL) -8 NIL NIL NIL) (-1061 2453214 2456042 2456182 "ROMAN" 2456298 T ROMAN (NIL) -8 NIL NIL NIL) (-1060 2451458 2452074 2452334 "ROIRC" 2453019 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1059 2447690 2449974 2450004 "RNS" 2450308 T RNS (NIL) -9 NIL 2450582 NIL) (-1058 2446199 2446582 2447116 "RNS-" 2447191 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1057 2445602 2446010 2446040 "RNG" 2446045 T RNG (NIL) -9 NIL 2446066 NIL) (-1056 2445001 2445389 2445432 "RMODULE" 2445437 NIL RMODULE (NIL T) -9 NIL 2445464 NIL) (-1055 2443837 2443931 2444267 "RMCAT2" 2444902 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1054 2440687 2443183 2443480 "RMATRIX" 2443599 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1053 2433514 2435774 2435889 "RMATCAT" 2439248 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2440230 NIL) (-1052 2432889 2433036 2433343 "RMATCAT-" 2433348 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1051 2432290 2432511 2432554 "RLINSET" 2432748 NIL RLINSET (NIL T) -9 NIL 2432839 NIL) (-1050 2431857 2431932 2432060 "RINTERP" 2432209 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1049 2430915 2431469 2431499 "RING" 2431555 T RING (NIL) -9 NIL 2431647 NIL) (-1048 2430707 2430751 2430848 "RING-" 2430853 NIL RING- (NIL T) -8 NIL NIL NIL) (-1047 2429548 2429785 2430043 "RIDIST" 2430471 T RIDIST (NIL) -7 NIL NIL NIL) (-1046 2420837 2429016 2429222 "RGCHAIN" 2429396 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1045 2420187 2420593 2420634 "RGBCSPC" 2420692 NIL RGBCSPC (NIL T) -9 NIL 2420744 NIL) (-1044 2419345 2419726 2419767 "RGBCMDL" 2419999 NIL RGBCMDL (NIL T) -9 NIL 2420113 NIL) (-1043 2416339 2416953 2417623 "RF" 2418709 NIL RF (NIL T) -7 NIL NIL NIL) (-1042 2415985 2416048 2416151 "RFFACTOR" 2416270 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1041 2415710 2415745 2415842 "RFFACT" 2415944 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1040 2413827 2414191 2414573 "RFDIST" 2415350 T RFDIST (NIL) -7 NIL NIL NIL) (-1039 2413280 2413372 2413535 "RETSOL" 2413729 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1038 2412916 2412996 2413039 "RETRACT" 2413172 NIL RETRACT (NIL T) -9 NIL 2413259 NIL) (-1037 2412765 2412790 2412877 "RETRACT-" 2412882 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1036 2412367 2412587 2412657 "RETAST" 2412717 T RETAST (NIL) -8 NIL NIL NIL) (-1035 2405105 2412020 2412147 "RESULT" 2412262 T RESULT (NIL) -8 NIL NIL NIL) (-1034 2403696 2404374 2404573 "RESRING" 2405008 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1033 2403332 2403381 2403479 "RESLATC" 2403633 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1032 2403037 2403072 2403179 "REPSQ" 2403291 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1031 2400459 2401039 2401641 "REP" 2402457 T REP (NIL) -7 NIL NIL NIL) (-1030 2400156 2400191 2400302 "REPDB" 2400418 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1029 2394056 2395445 2396668 "REP2" 2398968 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1028 2390433 2391114 2391922 "REP1" 2393283 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1027 2383129 2388574 2389030 "REGSET" 2390063 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1026 2381894 2382277 2382527 "REF" 2382914 NIL REF (NIL T) -8 NIL NIL NIL) (-1025 2381271 2381374 2381541 "REDORDER" 2381778 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1024 2377239 2380484 2380711 "RECLOS" 2381099 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1023 2376291 2376472 2376687 "REALSOLV" 2377046 T REALSOLV (NIL) -7 NIL NIL NIL) (-1022 2376137 2376178 2376208 "REAL" 2376213 T REAL (NIL) -9 NIL 2376248 NIL) (-1021 2372620 2373422 2374306 "REAL0Q" 2375302 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1020 2368221 2369209 2370270 "REAL0" 2371601 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1019 2367692 2367938 2368032 "RDUCEAST" 2368149 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1018 2367097 2367169 2367376 "RDIV" 2367614 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1017 2366165 2366339 2366552 "RDIST" 2366919 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1016 2364762 2365049 2365421 "RDETRS" 2365873 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1015 2362574 2363028 2363566 "RDETR" 2364304 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1014 2361199 2361477 2361874 "RDEEFS" 2362290 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1013 2359708 2360014 2360439 "RDEEF" 2360887 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1012 2353769 2356689 2356719 "RCFIELD" 2358014 T RCFIELD (NIL) -9 NIL 2358745 NIL) (-1011 2351833 2352337 2353033 "RCFIELD-" 2353108 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1010 2348102 2349934 2349977 "RCAGG" 2351061 NIL RCAGG (NIL T) -9 NIL 2351526 NIL) (-1009 2347730 2347824 2347987 "RCAGG-" 2347992 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1008 2347065 2347177 2347342 "RATRET" 2347614 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1007 2346618 2346685 2346806 "RATFACT" 2346993 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1006 2345926 2346046 2346198 "RANDSRC" 2346488 T RANDSRC (NIL) -7 NIL NIL NIL) (-1005 2345660 2345704 2345777 "RADUTIL" 2345875 T RADUTIL (NIL) -7 NIL NIL NIL) (-1004 2338776 2344493 2344803 "RADIX" 2345384 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1003 2330395 2338618 2338748 "RADFF" 2338753 NIL RADFF (NIL T T T NIL NIL) 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T) -8 NIL NIL NIL) (-848 1976769 1977560 1977588 "ORDRING" 1977790 T ORDRING (NIL) -9 NIL 1977915 NIL) (-847 1976414 1976508 1976652 "ORDRING-" 1976657 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-846 1975794 1976257 1976285 "ORDMON" 1976290 T ORDMON (NIL) -9 NIL 1976311 NIL) (-845 1974956 1975103 1975298 "ORDFUNS" 1975643 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-844 1974294 1974713 1974741 "ORDFIN" 1974806 T ORDFIN (NIL) -9 NIL 1974880 NIL) (-843 1970853 1972880 1973289 "ORDCOMP" 1973918 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-842 1970119 1970246 1970432 "ORDCOMP2" 1970713 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-841 1966700 1967610 1968424 "OPTPROB" 1969325 T OPTPROB (NIL) -8 NIL NIL NIL) (-840 1963502 1964141 1964845 "OPTPACK" 1966016 T OPTPACK (NIL) -7 NIL NIL NIL) (-839 1961189 1961955 1961983 "OPTCAT" 1962802 T OPTCAT (NIL) -9 NIL 1963452 NIL) (-838 1960573 1960866 1960971 "OPSIG" 1961104 T OPSIG (NIL) -8 NIL NIL NIL) (-837 1960341 1960380 1960446 "OPQUERY" 1960527 T OPQUERY (NIL) -7 NIL NIL NIL) (-836 1957472 1958652 1959156 "OP" 1959870 NIL OP (NIL T) -8 NIL NIL NIL) (-835 1956846 1957072 1957113 "OPERCAT" 1957325 NIL OPERCAT (NIL T) -9 NIL 1957422 NIL) (-834 1956601 1956657 1956774 "OPERCAT-" 1956779 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-833 1953414 1955398 1955767 "ONECOMP" 1956265 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-832 1952719 1952834 1953008 "ONECOMP2" 1953286 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-831 1952138 1952244 1952374 "OMSERVER" 1952609 T OMSERVER (NIL) -7 NIL NIL NIL) (-830 1949000 1951578 1951618 "OMSAGG" 1951679 NIL OMSAGG (NIL T) -9 NIL 1951743 NIL) (-829 1947623 1947886 1948168 "OMPKG" 1948738 T OMPKG (NIL) -7 NIL NIL NIL) (-828 1947053 1947156 1947184 "OM" 1947483 T OM (NIL) -9 NIL NIL NIL) (-827 1945600 1946602 1946771 "OMLO" 1946934 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-826 1944560 1944707 1944927 "OMEXPR" 1945426 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-825 1943851 1944106 1944242 "OMERR" 1944444 T OMERR (NIL) -8 NIL NIL NIL) (-824 1943002 1943272 1943432 "OMERRK" 1943711 T OMERRK (NIL) -8 NIL NIL NIL) (-823 1942453 1942679 1942787 "OMENC" 1942914 T OMENC (NIL) -8 NIL NIL NIL) (-822 1936348 1937533 1938704 "OMDEV" 1941302 T OMDEV (NIL) -8 NIL NIL NIL) (-821 1935417 1935588 1935782 "OMCONN" 1936174 T OMCONN (NIL) -8 NIL NIL NIL) (-820 1933938 1934914 1934942 "OINTDOM" 1934947 T OINTDOM (NIL) -9 NIL 1934968 NIL) (-819 1929717 1930928 1931644 "OFMONOID" 1933254 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-818 1929128 1929654 1929699 "ODVAR" 1929704 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-817 1926551 1928873 1929028 "ODR" 1929033 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-816 1919132 1926327 1926453 "ODPOL" 1926458 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-815 1912954 1919004 1919109 "ODP" 1919114 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-814 1911720 1911935 1912210 "ODETOOLS" 1912728 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-813 1908687 1909345 1910061 "ODESYS" 1911053 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-812 1903569 1904477 1905502 "ODERTRIC" 1907762 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-811 1902995 1903077 1903271 "ODERED" 1903481 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-810 1899883 1900431 1901108 "ODERAT" 1902418 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-809 1896840 1897307 1897904 "ODEPRRIC" 1899412 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-808 1894783 1895379 1895865 "ODEPROB" 1896374 T ODEPROB (NIL) -8 NIL NIL NIL) (-807 1891303 1891788 1892435 "ODEPRIM" 1894262 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-806 1890552 1890654 1890914 "ODEPAL" 1891195 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-805 1886714 1887505 1888369 "ODEPACK" 1889708 T ODEPACK (NIL) -7 NIL NIL NIL) (-804 1885775 1885882 1886104 "ODEINT" 1886603 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-803 1879876 1881301 1882748 "ODEIFTBL" 1884348 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-802 1875274 1876060 1877012 "ODEEF" 1879035 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-801 1874623 1874712 1874935 "ODECONST" 1875179 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-800 1872748 1873409 1873437 "ODECAT" 1874042 T ODECAT (NIL) -9 NIL 1874573 NIL) (-799 1869620 1872460 1872579 "OCT" 1872661 NIL OCT (NIL T) -8 NIL NIL NIL) (-798 1869258 1869301 1869428 "OCTCT2" 1869571 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-797 1863907 1866342 1866382 "OC" 1867479 NIL OC (NIL T) -9 NIL 1868337 NIL) (-796 1861134 1861882 1862872 "OC-" 1862966 NIL OC- (NIL T T) -8 NIL NIL NIL) (-795 1860486 1860954 1860982 "OCAMON" 1860987 T OCAMON (NIL) -9 NIL 1861008 NIL) (-794 1860017 1860358 1860386 "OASGP" 1860391 T OASGP (NIL) -9 NIL 1860411 NIL) (-793 1859278 1859767 1859795 "OAMONS" 1859835 T OAMONS (NIL) -9 NIL 1859878 NIL) (-792 1858692 1859125 1859153 "OAMON" 1859158 T OAMON (NIL) -9 NIL 1859178 NIL) (-791 1857950 1858468 1858496 "OAGROUP" 1858501 T OAGROUP (NIL) -9 NIL 1858521 NIL) (-790 1857640 1857690 1857778 "NUMTUBE" 1857894 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-789 1851213 1852731 1854267 "NUMQUAD" 1856124 T NUMQUAD (NIL) -7 NIL NIL NIL) (-788 1846969 1847957 1848982 "NUMODE" 1850208 T NUMODE (NIL) -7 NIL NIL NIL) (-787 1844324 1845204 1845232 "NUMINT" 1846155 T NUMINT (NIL) -9 NIL 1846919 NIL) (-786 1843272 1843469 1843687 "NUMFMT" 1844126 T NUMFMT (NIL) -7 NIL NIL NIL) (-785 1829631 1832576 1835108 "NUMERIC" 1840779 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-784 1824001 1829080 1829175 "NTSCAT" 1829180 NIL NTSCAT (NIL T T T T) -9 NIL 1829219 NIL) (-783 1823195 1823360 1823553 "NTPOLFN" 1823840 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-782 1811272 1820020 1820832 "NSUP" 1822416 NIL NSUP (NIL T) -8 NIL NIL NIL) (-781 1810904 1810961 1811070 "NSUP2" 1811209 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-780 1801132 1810678 1810811 "NSMP" 1810816 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-779 1799564 1799865 1800222 "NREP" 1800820 NIL NREP (NIL T) -7 NIL NIL NIL) (-778 1798155 1798407 1798765 "NPCOEF" 1799307 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-777 1797221 1797336 1797552 "NORMRETR" 1798036 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-776 1795262 1795552 1795961 "NORMPK" 1796929 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-775 1794947 1794975 1795099 "NORMMA" 1795228 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-774 1794747 1794904 1794933 "NONE" 1794938 T NONE (NIL) -8 NIL NIL NIL) (-773 1794536 1794565 1794634 "NONE1" 1794711 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-772 1794033 1794095 1794274 "NODE1" 1794468 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-771 1792318 1793169 1793424 "NNI" 1793771 T NNI (NIL) -8 NIL NIL 1794006) (-770 1790738 1791051 1791415 "NLINSOL" 1791986 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-769 1786979 1787974 1788873 "NIPROB" 1789859 T NIPROB (NIL) -8 NIL NIL NIL) (-768 1785736 1785970 1786272 "NFINTBAS" 1786741 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-767 1784910 1785386 1785427 "NETCLT" 1785599 NIL NETCLT (NIL T) -9 NIL 1785681 NIL) (-766 1783618 1783849 1784130 "NCODIV" 1784678 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-765 1783380 1783417 1783492 "NCNTFRAC" 1783575 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-764 1781560 1781924 1782344 "NCEP" 1783005 NIL NCEP (NIL T) -7 NIL NIL NIL) (-763 1780411 1781184 1781212 "NASRING" 1781322 T NASRING (NIL) -9 NIL 1781402 NIL) (-762 1780206 1780250 1780344 "NASRING-" 1780349 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-761 1779313 1779838 1779866 "NARNG" 1779983 T NARNG (NIL) -9 NIL 1780074 NIL) (-760 1779005 1779072 1779206 "NARNG-" 1779211 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-759 1777884 1778091 1778326 "NAGSP" 1778790 T NAGSP (NIL) -7 NIL NIL NIL) (-758 1769156 1770840 1772513 "NAGS" 1776231 T NAGS (NIL) -7 NIL NIL NIL) (-757 1767704 1768012 1768343 "NAGF07" 1768845 T NAGF07 (NIL) -7 NIL NIL NIL) (-756 1762242 1763533 1764840 "NAGF04" 1766417 T NAGF04 (NIL) -7 NIL NIL NIL) (-755 1755210 1756824 1758457 "NAGF02" 1760629 T NAGF02 (NIL) -7 NIL NIL NIL) (-754 1750434 1751534 1752651 "NAGF01" 1754113 T NAGF01 (NIL) -7 NIL NIL NIL) (-753 1744062 1745628 1747213 "NAGE04" 1748869 T NAGE04 (NIL) -7 NIL NIL NIL) (-752 1735231 1737352 1739482 "NAGE02" 1741952 T NAGE02 (NIL) -7 NIL NIL NIL) (-751 1731184 1732131 1733095 "NAGE01" 1734287 T NAGE01 (NIL) -7 NIL NIL NIL) (-750 1728979 1729513 1730071 "NAGD03" 1730646 T NAGD03 (NIL) -7 NIL NIL NIL) (-749 1720729 1722657 1724611 "NAGD02" 1727045 T NAGD02 (NIL) -7 NIL NIL NIL) (-748 1714540 1715965 1717405 "NAGD01" 1719309 T NAGD01 (NIL) -7 NIL NIL NIL) (-747 1710749 1711571 1712408 "NAGC06" 1713723 T NAGC06 (NIL) -7 NIL NIL NIL) (-746 1709214 1709546 1709902 "NAGC05" 1710413 T NAGC05 (NIL) -7 NIL NIL NIL) (-745 1708590 1708709 1708853 "NAGC02" 1709090 T NAGC02 (NIL) -7 NIL NIL NIL) (-744 1707549 1708132 1708172 "NAALG" 1708251 NIL NAALG (NIL T) -9 NIL 1708312 NIL) (-743 1707384 1707413 1707503 "NAALG-" 1707508 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-742 1701334 1702442 1703629 "MULTSQFR" 1706280 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-741 1700653 1700728 1700912 "MULTFACT" 1701246 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-740 1693377 1697290 1697343 "MTSCAT" 1698413 NIL MTSCAT (NIL T T) -9 NIL 1698928 NIL) (-739 1693089 1693143 1693235 "MTHING" 1693317 NIL MTHING (NIL T) -7 NIL NIL NIL) (-738 1692881 1692914 1692974 "MSYSCMD" 1693049 T MSYSCMD (NIL) -7 NIL NIL NIL) (-737 1688963 1691636 1691956 "MSET" 1692594 NIL MSET (NIL T) -8 NIL NIL NIL) (-736 1686032 1688524 1688565 "MSETAGG" 1688570 NIL MSETAGG (NIL T) -9 NIL 1688604 NIL) (-735 1681873 1683411 1684156 "MRING" 1685332 NIL MRING (NIL T T) -8 NIL NIL NIL) (-734 1681439 1681506 1681637 "MRF2" 1681800 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-733 1681057 1681092 1681236 "MRATFAC" 1681398 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-732 1678669 1678964 1679395 "MPRFF" 1680762 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-731 1672966 1678523 1678620 "MPOLY" 1678625 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-730 1672456 1672491 1672699 "MPCPF" 1672925 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-729 1671970 1672013 1672197 "MPC3" 1672407 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-728 1671165 1671246 1671467 "MPC2" 1671885 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-727 1669466 1669803 1670193 "MONOTOOL" 1670825 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-726 1668691 1669008 1669036 "MONOID" 1669255 T MONOID (NIL) -9 NIL 1669402 NIL) (-725 1668237 1668356 1668537 "MONOID-" 1668542 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-724 1658712 1664663 1664722 "MONOGEN" 1665396 NIL MONOGEN (NIL T T) -9 NIL 1665852 NIL) (-723 1655930 1656665 1657665 "MONOGEN-" 1657784 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-722 1654763 1655209 1655237 "MONADWU" 1655629 T MONADWU (NIL) -9 NIL 1655867 NIL) (-721 1654135 1654294 1654542 "MONADWU-" 1654547 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-720 1653494 1653738 1653766 "MONAD" 1653973 T MONAD (NIL) -9 NIL 1654085 NIL) (-719 1653179 1653257 1653389 "MONAD-" 1653394 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-718 1651468 1652092 1652371 "MOEBIUS" 1652932 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-717 1650746 1651150 1651190 "MODULE" 1651195 NIL MODULE (NIL T) -9 NIL 1651234 NIL) (-716 1650314 1650410 1650600 "MODULE-" 1650605 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-715 1647994 1648678 1649005 "MODRING" 1650138 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-714 1644938 1646099 1646620 "MODOP" 1647523 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-713 1643526 1644005 1644282 "MODMONOM" 1644801 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-712 1633567 1641817 1642231 "MODMON" 1643163 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-711 1630723 1632411 1632687 "MODFIELD" 1633442 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1629700 1630004 1630194 "MMLFORM" 1630553 T MMLFORM (NIL) -8 NIL NIL NIL) (-709 1629226 1629269 1629448 "MMAP" 1629651 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-708 1627305 1628072 1628113 "MLO" 1628536 NIL MLO (NIL T) -9 NIL 1628778 NIL) (-707 1624671 1625187 1625789 "MLIFT" 1626786 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-706 1624062 1624146 1624300 "MKUCFUNC" 1624582 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-705 1623661 1623731 1623854 "MKRECORD" 1623985 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-704 1622708 1622870 1623098 "MKFUNC" 1623472 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-703 1622096 1622200 1622356 "MKFLCFN" 1622591 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-702 1621373 1621475 1621660 "MKBCFUNC" 1621989 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-701 1618080 1620927 1621063 "MINT" 1621257 T MINT (NIL) -8 NIL NIL NIL) (-700 1616892 1617135 1617412 "MHROWRED" 1617835 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-699 1612271 1615427 1615832 "MFLOAT" 1616507 T MFLOAT (NIL) -8 NIL NIL NIL) (-698 1611628 1611704 1611875 "MFINFACT" 1612183 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-697 1607943 1608791 1609675 "MESH" 1610764 T MESH (NIL) -7 NIL NIL NIL) (-696 1606333 1606645 1606998 "MDDFACT" 1607630 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-695 1603128 1605492 1605533 "MDAGG" 1605788 NIL MDAGG (NIL T) -9 NIL 1605931 NIL) (-694 1592868 1602421 1602628 "MCMPLX" 1602941 T MCMPLX (NIL) -8 NIL NIL NIL) (-693 1592009 1592155 1592355 "MCDEN" 1592717 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-692 1589899 1590169 1590549 "MCALCFN" 1591739 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-691 1588824 1589064 1589297 "MAYBE" 1589705 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-690 1586436 1586959 1587521 "MATSTOR" 1588295 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-689 1582393 1585808 1586056 "MATRIX" 1586221 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-688 1578157 1578866 1579602 "MATLIN" 1581750 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-687 1568263 1571449 1571526 "MATCAT" 1576406 NIL MATCAT (NIL T T T) -9 NIL 1577823 NIL) (-686 1564619 1565640 1566996 "MATCAT-" 1567001 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-685 1563213 1563366 1563699 "MATCAT2" 1564454 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-684 1561325 1561649 1562033 "MAPPKG3" 1562888 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-683 1560306 1560479 1560701 "MAPPKG2" 1561149 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-682 1558805 1559089 1559416 "MAPPKG1" 1560012 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-681 1557884 1558211 1558388 "MAPPAST" 1558648 T MAPPAST (NIL) -8 NIL NIL NIL) (-680 1557495 1557553 1557676 "MAPHACK3" 1557820 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-679 1557087 1557148 1557262 "MAPHACK2" 1557427 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-678 1556524 1556628 1556770 "MAPHACK1" 1556978 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-677 1554603 1555224 1555528 "MAGMA" 1556252 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-676 1554082 1554327 1554418 "MACROAST" 1554532 T MACROAST (NIL) -8 NIL NIL NIL) (-675 1550500 1552321 1552782 "M3D" 1553654 NIL M3D (NIL T) -8 NIL NIL NIL) (-674 1544606 1548869 1548910 "LZSTAGG" 1549692 NIL LZSTAGG (NIL T) -9 NIL 1549987 NIL) (-673 1540563 1541737 1543194 "LZSTAGG-" 1543199 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-672 1537650 1538454 1538941 "LWORD" 1540108 NIL LWORD (NIL T) -8 NIL NIL NIL) (-671 1537226 1537454 1537529 "LSTAST" 1537595 T LSTAST (NIL) -8 NIL NIL NIL) (-670 1530392 1536997 1537131 "LSQM" 1537136 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-669 1529616 1529755 1529983 "LSPP" 1530247 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-668 1527428 1527729 1528185 "LSMP" 1529305 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-667 1524207 1524881 1525611 "LSMP1" 1526730 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-666 1518084 1523374 1523415 "LSAGG" 1523477 NIL LSAGG (NIL T) -9 NIL 1523555 NIL) (-665 1514779 1515703 1516916 "LSAGG-" 1516921 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-664 1512378 1513923 1514172 "LPOLY" 1514574 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-663 1511960 1512045 1512168 "LPEFRAC" 1512287 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-662 1510281 1511054 1511307 "LO" 1511792 NIL LO (NIL T T T) -8 NIL NIL NIL) (-661 1509933 1510045 1510073 "LOGIC" 1510184 T LOGIC (NIL) -9 NIL 1510265 NIL) (-660 1509795 1509818 1509889 "LOGIC-" 1509894 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-659 1508988 1509128 1509321 "LODOOPS" 1509651 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-658 1506411 1508904 1508970 "LODO" 1508975 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-657 1504949 1505184 1505537 "LODOF" 1506158 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-656 1501167 1503598 1503639 "LODOCAT" 1504077 NIL LODOCAT (NIL T) -9 NIL 1504288 NIL) (-655 1500900 1500958 1501085 "LODOCAT-" 1501090 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-654 1498220 1500741 1500859 "LODO2" 1500864 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-653 1495655 1498157 1498202 "LODO1" 1498207 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-652 1494536 1494701 1495006 "LODEEF" 1495478 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-651 1489775 1492666 1492707 "LNAGG" 1493654 NIL LNAGG (NIL T) -9 NIL 1494098 NIL) (-650 1488922 1489136 1489478 "LNAGG-" 1489483 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-649 1485058 1485847 1486486 "LMOPS" 1488337 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-648 1484461 1484849 1484890 "LMODULE" 1484895 NIL LMODULE (NIL T) -9 NIL 1484921 NIL) (-647 1481659 1484106 1484229 "LMDICT" 1484371 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-646 1481065 1481286 1481327 "LLINSET" 1481518 NIL LLINSET (NIL T) -9 NIL 1481609 NIL) (-645 1480764 1480973 1481033 "LITERAL" 1481038 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-644 1473927 1479698 1480002 "LIST" 1480493 NIL LIST (NIL T) -8 NIL NIL NIL) (-643 1473452 1473526 1473665 "LIST3" 1473847 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-642 1472459 1472637 1472865 "LIST2" 1473270 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-641 1470593 1470905 1471304 "LIST2MAP" 1472106 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-640 1470189 1470426 1470467 "LINSET" 1470472 NIL LINSET (NIL T) -9 NIL 1470506 NIL) (-639 1468850 1469520 1469561 "LINEXP" 1469816 NIL LINEXP (NIL T) -9 NIL 1469965 NIL) (-638 1467497 1467757 1468054 "LINDEP" 1468602 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-637 1464264 1464983 1465760 "LIMITRF" 1466752 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-636 1462567 1462863 1463272 "LIMITPS" 1463959 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-635 1456995 1462078 1462306 "LIE" 1462388 NIL LIE (NIL T T) -8 NIL NIL NIL) (-634 1455943 1456412 1456452 "LIECAT" 1456592 NIL LIECAT (NIL T) -9 NIL 1456743 NIL) (-633 1455784 1455811 1455899 "LIECAT-" 1455904 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-632 1448280 1455233 1455398 "LIB" 1455639 T LIB (NIL) -8 NIL NIL NIL) (-631 1443915 1444798 1445733 "LGROBP" 1447397 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-630 1441913 1442187 1442537 "LF" 1443636 NIL LF (NIL T T) -7 NIL NIL NIL) (-629 1440753 1441445 1441473 "LFCAT" 1441680 T LFCAT (NIL) -9 NIL 1441819 NIL) (-628 1437655 1438285 1438973 "LEXTRIPK" 1440117 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-627 1434399 1435225 1435728 "LEXP" 1437235 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-626 1433875 1434120 1434212 "LETAST" 1434327 T LETAST (NIL) -8 NIL NIL NIL) (-625 1432273 1432586 1432987 "LEADCDET" 1433557 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-624 1431463 1431537 1431766 "LAZM3PK" 1432194 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-623 1426380 1429540 1430078 "LAUPOL" 1430975 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-622 1425959 1426003 1426164 "LAPLACE" 1426330 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-621 1423898 1425060 1425311 "LA" 1425792 NIL LA (NIL T T T) -8 NIL NIL NIL) (-620 1422892 1423476 1423517 "LALG" 1423579 NIL LALG (NIL T) -9 NIL 1423638 NIL) (-619 1422606 1422665 1422801 "LALG-" 1422806 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-618 1422441 1422465 1422506 "KVTFROM" 1422568 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-617 1421364 1421808 1421993 "KTVLOGIC" 1422276 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-616 1421199 1421223 1421264 "KRCFROM" 1421326 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-615 1420103 1420290 1420589 "KOVACIC" 1420999 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-614 1419938 1419962 1420003 "KONVERT" 1420065 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-613 1419773 1419797 1419838 "KOERCE" 1419900 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-612 1417603 1418366 1418743 "KERNEL" 1419429 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-611 1417099 1417180 1417312 "KERNEL2" 1417517 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-610 1410869 1415638 1415692 "KDAGG" 1416069 NIL KDAGG (NIL T T) -9 NIL 1416275 NIL) (-609 1410398 1410522 1410727 "KDAGG-" 1410732 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-608 1403546 1410059 1410214 "KAFILE" 1410276 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-607 1397974 1403057 1403285 "JORDAN" 1403367 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-606 1397353 1397623 1397744 "JOINAST" 1397873 T JOINAST (NIL) -8 NIL NIL NIL) (-605 1397199 1397258 1397313 "JAVACODE" 1397318 T JAVACODE (NIL) -8 NIL NIL NIL) (-604 1393451 1395404 1395458 "IXAGG" 1396387 NIL IXAGG (NIL T T) -9 NIL 1396846 NIL) (-603 1392370 1392676 1393095 "IXAGG-" 1393100 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-602 1387900 1392292 1392351 "IVECTOR" 1392356 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-601 1386666 1386903 1387169 "ITUPLE" 1387667 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-600 1385168 1385345 1385640 "ITRIGMNP" 1386488 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-599 1383913 1384117 1384400 "ITFUN3" 1384944 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-598 1383545 1383602 1383711 "ITFUN2" 1383850 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-597 1381347 1382407 1382706 "ITAYLOR" 1383279 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-596 1370292 1375484 1376647 "ISUPS" 1380217 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-595 1369396 1369536 1369772 "ISUMP" 1370139 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-594 1364610 1369197 1369276 "ISTRING" 1369349 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-593 1364086 1364331 1364423 "ISAST" 1364538 T ISAST (NIL) -8 NIL NIL NIL) (-592 1363295 1363377 1363593 "IRURPK" 1364000 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-591 1362231 1362432 1362672 "IRSN" 1363075 T IRSN (NIL) -7 NIL NIL NIL) (-590 1360302 1360657 1361086 "IRRF2F" 1361869 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-589 1360049 1360087 1360163 "IRREDFFX" 1360258 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-588 1358664 1358923 1359222 "IROOT" 1359782 NIL IROOT (NIL T) -7 NIL NIL NIL) (-587 1355268 1356348 1357040 "IR" 1358004 NIL IR (NIL T) -8 NIL NIL NIL) (-586 1352881 1353376 1353942 "IR2" 1354746 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-585 1351981 1352094 1352308 "IR2F" 1352764 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-584 1351772 1351806 1351866 "IPRNTPK" 1351941 T IPRNTPK (NIL) -7 NIL NIL NIL) (-583 1348353 1351661 1351730 "IPF" 1351735 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-582 1346680 1348278 1348335 "IPADIC" 1348340 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-581 1345992 1346240 1346370 "IP4ADDR" 1346570 T IP4ADDR (NIL) -8 NIL NIL NIL) (-580 1345465 1345696 1345806 "IOMODE" 1345902 T IOMODE (NIL) -8 NIL NIL NIL) (-579 1344538 1345062 1345189 "IOBFILE" 1345358 T IOBFILE (NIL) -8 NIL NIL NIL) (-578 1344026 1344442 1344470 "IOBCON" 1344475 T IOBCON (NIL) -9 NIL 1344496 NIL) (-577 1343537 1343595 1343778 "INVLAPLA" 1343962 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-576 1333185 1335539 1337925 "INTTR" 1341201 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-575 1329520 1330262 1331127 "INTTOOLS" 1332370 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-574 1329106 1329197 1329314 "INTSLPE" 1329423 T INTSLPE (NIL) -7 NIL NIL NIL) (-573 1327059 1329029 1329088 "INTRVL" 1329093 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-572 1324661 1325173 1325748 "INTRF" 1326544 NIL INTRF (NIL T) -7 NIL NIL NIL) (-571 1324072 1324169 1324311 "INTRET" 1324559 NIL INTRET (NIL T) -7 NIL NIL NIL) (-570 1322069 1322458 1322928 "INTRAT" 1323680 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-569 1319332 1319915 1320534 "INTPM" 1321554 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-568 1316077 1316676 1317414 "INTPAF" 1318718 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-567 1311256 1312218 1313269 "INTPACK" 1315046 T INTPACK (NIL) -7 NIL NIL NIL) (-566 1308136 1310985 1311112 "INT" 1311149 T INT (NIL) -8 NIL NIL NIL) (-565 1307388 1307540 1307748 "INTHERTR" 1307978 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-564 1306827 1306907 1307095 "INTHERAL" 1307302 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-563 1304673 1305116 1305573 "INTHEORY" 1306390 T INTHEORY (NIL) -7 NIL NIL NIL) (-562 1296079 1297700 1299472 "INTG0" 1303025 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-561 1276652 1281442 1286252 "INTFTBL" 1291289 T INTFTBL (NIL) -8 NIL NIL NIL) (-560 1275901 1276039 1276212 "INTFACT" 1276511 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-559 1273328 1273774 1274331 "INTEF" 1275455 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-558 1271695 1272434 1272462 "INTDOM" 1272763 T INTDOM (NIL) -9 NIL 1272970 NIL) (-557 1271064 1271238 1271480 "INTDOM-" 1271485 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-556 1267452 1269380 1269434 "INTCAT" 1270233 NIL INTCAT (NIL T) -9 NIL 1270554 NIL) (-555 1266924 1267027 1267155 "INTBIT" 1267344 T INTBIT (NIL) -7 NIL NIL NIL) (-554 1265623 1265777 1266084 "INTALG" 1266769 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-553 1265106 1265196 1265353 "INTAF" 1265527 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-552 1258449 1264916 1265056 "INTABL" 1265061 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-551 1257790 1258256 1258321 "INT8" 1258355 T INT8 (NIL) -8 NIL NIL 1258400) (-550 1257130 1257596 1257661 "INT64" 1257695 T INT64 (NIL) -8 NIL NIL 1257740) (-549 1256470 1256936 1257001 "INT32" 1257035 T INT32 (NIL) -8 NIL NIL 1257080) (-548 1255810 1256276 1256341 "INT16" 1256375 T INT16 (NIL) -8 NIL NIL 1256420) (-547 1250720 1253433 1253461 "INS" 1254395 T INS (NIL) -9 NIL 1255060 NIL) (-546 1247960 1248731 1249705 "INS-" 1249778 NIL INS- (NIL T) -8 NIL NIL NIL) (-545 1246735 1246962 1247260 "INPSIGN" 1247713 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-544 1245853 1245970 1246167 "INPRODPF" 1246615 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-543 1244747 1244864 1245101 "INPRODFF" 1245733 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-542 1243747 1243899 1244159 "INNMFACT" 1244583 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-541 1242944 1243041 1243229 "INMODGCD" 1243646 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-540 1241452 1241697 1242021 "INFSP" 1242689 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-539 1240636 1240753 1240936 "INFPROD0" 1241332 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-538 1237491 1238701 1239216 "INFORM" 1240129 T INFORM (NIL) -8 NIL NIL NIL) (-537 1237101 1237161 1237259 "INFORM1" 1237426 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-536 1236624 1236713 1236827 "INFINITY" 1237007 T INFINITY (NIL) -7 NIL NIL NIL) (-535 1235800 1236344 1236445 "INETCLTS" 1236543 T INETCLTS (NIL) -8 NIL NIL NIL) (-534 1234416 1234666 1234987 "INEP" 1235548 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-533 1233665 1234313 1234378 "INDE" 1234383 NIL INDE (NIL T) -8 NIL NIL NIL) (-532 1233229 1233297 1233414 "INCRMAPS" 1233592 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-531 1232047 1232498 1232704 "INBFILE" 1233043 T INBFILE (NIL) -8 NIL NIL NIL) (-530 1227346 1228283 1229227 "INBFF" 1231135 NIL INBFF (NIL T) -7 NIL NIL NIL) (-529 1226254 1226523 1226551 "INBCON" 1227064 T INBCON (NIL) -9 NIL 1227330 NIL) (-528 1225506 1225729 1226005 "INBCON-" 1226010 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-527 1224985 1225230 1225321 "INAST" 1225435 T INAST (NIL) -8 NIL NIL NIL) (-526 1224412 1224664 1224770 "IMPTAST" 1224899 T IMPTAST (NIL) -8 NIL NIL NIL) (-525 1220858 1224256 1224360 "IMATRIX" 1224365 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-524 1219570 1219693 1220008 "IMATQF" 1220714 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-523 1217790 1218017 1218354 "IMATLIN" 1219326 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-522 1212368 1217714 1217772 "ILIST" 1217777 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-521 1210273 1212228 1212341 "IIARRAY2" 1212346 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-520 1205671 1210184 1210248 "IFF" 1210253 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-519 1205018 1205288 1205404 "IFAST" 1205575 T IFAST (NIL) -8 NIL NIL NIL) (-518 1200013 1204310 1204498 "IFARRAY" 1204875 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-517 1199193 1199917 1199990 "IFAMON" 1199995 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-516 1198777 1198842 1198896 "IEVALAB" 1199103 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-515 1198452 1198520 1198680 "IEVALAB-" 1198685 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-514 1198083 1198366 1198429 "IDPO" 1198434 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-513 1197333 1197972 1198047 "IDPOAMS" 1198052 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-512 1196640 1197222 1197297 "IDPOAM" 1197302 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-511 1195699 1195975 1196028 "IDPC" 1196441 NIL IDPC (NIL T T) -9 NIL 1196590 NIL) (-510 1195168 1195591 1195664 "IDPAM" 1195669 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-509 1194544 1195060 1195133 "IDPAG" 1195138 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-508 1194189 1194380 1194455 "IDENT" 1194489 T IDENT (NIL) -8 NIL NIL NIL) (-507 1190444 1191292 1192187 "IDECOMP" 1193346 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-506 1183282 1184367 1185414 "IDEAL" 1189480 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-505 1182446 1182558 1182757 "ICDEN" 1183166 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-504 1181517 1181926 1182073 "ICARD" 1182319 T ICARD (NIL) -8 NIL NIL NIL) (-503 1179577 1179890 1180295 "IBPTOOLS" 1181194 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-502 1175184 1179197 1179310 "IBITS" 1179496 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-501 1171907 1172483 1173178 "IBATOOL" 1174601 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-500 1169686 1170148 1170681 "IBACHIN" 1171442 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-499 1167515 1169532 1169635 "IARRAY2" 1169640 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-498 1163621 1167441 1167498 "IARRAY1" 1167503 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-497 1157730 1162033 1162514 "IAN" 1163160 T IAN (NIL) -8 NIL NIL NIL) (-496 1157241 1157298 1157471 "IALGFACT" 1157667 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-495 1156769 1156882 1156910 "HYPCAT" 1157117 T HYPCAT (NIL) -9 NIL NIL NIL) (-494 1156307 1156424 1156610 "HYPCAT-" 1156615 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-493 1155902 1156102 1156185 "HOSTNAME" 1156244 T HOSTNAME (NIL) -8 NIL NIL NIL) (-492 1155747 1155784 1155825 "HOMOTOP" 1155830 NIL HOMOTOP (NIL T) -9 NIL 1155863 NIL) (-491 1152379 1153757 1153798 "HOAGG" 1154779 NIL HOAGG (NIL T) -9 NIL 1155458 NIL) (-490 1150973 1151372 1151898 "HOAGG-" 1151903 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-489 1144977 1150568 1150717 "HEXADEC" 1150844 T HEXADEC (NIL) -8 NIL NIL NIL) (-488 1143724 1143947 1144210 "HEUGCD" 1144754 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-487 1142800 1143561 1143691 "HELLFDIV" 1143696 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-486 1140979 1142577 1142665 "HEAP" 1142744 NIL HEAP (NIL T) -8 NIL NIL NIL) (-485 1140242 1140531 1140665 "HEADAST" 1140865 T HEADAST (NIL) -8 NIL NIL NIL) (-484 1134108 1140157 1140219 "HDP" 1140224 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-483 1128096 1133743 1133895 "HDMP" 1134009 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-482 1127420 1127560 1127724 "HB" 1127952 T HB (NIL) -7 NIL NIL NIL) (-481 1120806 1127266 1127370 "HASHTBL" 1127375 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-480 1120282 1120527 1120619 "HASAST" 1120734 T HASAST (NIL) -8 NIL NIL NIL) (-479 1118060 1119904 1120086 "HACKPI" 1120120 T HACKPI (NIL) -8 NIL NIL NIL) (-478 1113728 1117913 1118026 "GTSET" 1118031 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-477 1107143 1113606 1113704 "GSTBL" 1113709 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-476 1099421 1106174 1106439 "GSERIES" 1106934 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-475 1098562 1098979 1099007 "GROUP" 1099210 T GROUP (NIL) -9 NIL 1099344 NIL) (-474 1097928 1098087 1098338 "GROUP-" 1098343 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-473 1096295 1096616 1097003 "GROEBSOL" 1097605 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-472 1095209 1095497 1095548 "GRMOD" 1096077 NIL GRMOD (NIL T T) -9 NIL 1096245 NIL) (-471 1094977 1095013 1095141 "GRMOD-" 1095146 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-470 1090267 1091331 1092331 "GRIMAGE" 1093997 T GRIMAGE (NIL) -8 NIL NIL NIL) (-469 1088733 1088994 1089318 "GRDEF" 1089963 T GRDEF (NIL) -7 NIL NIL NIL) (-468 1088177 1088293 1088434 "GRAY" 1088612 T GRAY (NIL) -7 NIL NIL NIL) (-467 1087364 1087770 1087821 "GRALG" 1087974 NIL GRALG (NIL T T) -9 NIL 1088067 NIL) (-466 1087025 1087098 1087261 "GRALG-" 1087266 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-465 1083802 1086610 1086788 "GPOLSET" 1086932 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-464 1083156 1083213 1083471 "GOSPER" 1083739 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-463 1078888 1079594 1080120 "GMODPOL" 1082855 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-462 1077893 1078077 1078315 "GHENSEL" 1078700 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-461 1072049 1072892 1073912 "GENUPS" 1076977 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-460 1071746 1071797 1071886 "GENUFACT" 1071992 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-459 1071158 1071235 1071400 "GENPGCD" 1071664 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-458 1070632 1070667 1070880 "GENMFACT" 1071117 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-457 1069198 1069455 1069762 "GENEEZ" 1070375 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-456 1063344 1068809 1068971 "GDMP" 1069121 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-455 1052686 1057115 1058221 "GCNAALG" 1062327 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-454 1051013 1051875 1051903 "GCDDOM" 1052158 T GCDDOM (NIL) -9 NIL 1052315 NIL) (-453 1050483 1050610 1050825 "GCDDOM-" 1050830 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-452 1049155 1049340 1049644 "GB" 1050262 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-451 1037771 1040101 1042493 "GBINTERN" 1046846 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-450 1035608 1035900 1036321 "GBF" 1037446 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-449 1034389 1034554 1034821 "GBEUCLID" 1035424 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-448 1033738 1033863 1034012 "GAUSSFAC" 1034260 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-447 1032105 1032407 1032721 "GALUTIL" 1033457 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-446 1030413 1030687 1031011 "GALPOLYU" 1031832 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-445 1027778 1028068 1028475 "GALFACTU" 1030110 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-444 1019583 1021083 1022691 "GALFACT" 1026210 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-443 1016971 1017629 1017657 "FVFUN" 1018813 T FVFUN (NIL) -9 NIL 1019533 NIL) (-442 1016237 1016419 1016447 "FVC" 1016738 T FVC (NIL) -9 NIL 1016921 NIL) (-441 1015880 1016062 1016130 "FUNDESC" 1016189 T FUNDESC (NIL) -8 NIL NIL NIL) (-440 1015495 1015677 1015758 "FUNCTION" 1015832 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-439 1013239 1013817 1014283 "FT" 1015049 T FT (NIL) -8 NIL NIL NIL) (-438 1012030 1012540 1012743 "FTEM" 1013056 T FTEM (NIL) -8 NIL NIL NIL) (-437 1010321 1010610 1011007 "FSUPFACT" 1011721 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-436 1008718 1009007 1009339 "FST" 1010009 T FST (NIL) -8 NIL NIL NIL) (-435 1007917 1008023 1008211 "FSRED" 1008600 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-434 1006616 1006872 1007219 "FSPRMELT" 1007632 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-433 1003922 1004360 1004846 "FSPECF" 1006179 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-432 985560 993891 993932 "FS" 997816 NIL FS (NIL T) -9 NIL 1000105 NIL) (-431 974203 977196 981253 "FS-" 981553 NIL FS- (NIL T T) -8 NIL NIL NIL) (-430 973731 973785 973955 "FSINT" 974144 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-429 972023 972724 973027 "FSERIES" 973510 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-428 971065 971181 971405 "FSCINT" 971903 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-427 967273 970009 970050 "FSAGG" 970420 NIL FSAGG (NIL T) -9 NIL 970679 NIL) (-426 965035 965636 966432 "FSAGG-" 966527 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-425 964077 964220 964447 "FSAGG2" 964888 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-424 961759 962039 962586 "FS2UPS" 963795 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-423 961393 961436 961565 "FS2" 961710 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-422 960271 960442 960744 "FS2EXPXP" 961218 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-421 959697 959812 959964 "FRUTIL" 960151 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-420 951110 955192 956550 "FR" 958371 NIL FR (NIL T) -8 NIL NIL NIL) (-419 946079 948753 948793 "FRNAALG" 950189 NIL FRNAALG (NIL T) -9 NIL 950796 NIL) (-418 941752 942828 944103 "FRNAALG-" 944853 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-417 941390 941433 941560 "FRNAAF2" 941703 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-416 939770 940244 940539 "FRMOD" 941202 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-415 937521 938153 938470 "FRIDEAL" 939561 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-414 936716 936803 937092 "FRIDEAL2" 937428 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-413 935849 936263 936304 "FRETRCT" 936309 NIL FRETRCT (NIL T) -9 NIL 936485 NIL) (-412 934961 935192 935543 "FRETRCT-" 935548 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-411 932049 933259 933318 "FRAMALG" 934200 NIL FRAMALG (NIL T T) -9 NIL 934492 NIL) (-410 930183 930638 931268 "FRAMALG-" 931491 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-409 924104 929658 929934 "FRAC" 929939 NIL FRAC (NIL T) -8 NIL NIL NIL) (-408 923740 923797 923904 "FRAC2" 924041 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-407 923376 923433 923540 "FR2" 923677 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-406 917889 920782 920810 "FPS" 921929 T FPS (NIL) -9 NIL 922486 NIL) (-405 917338 917447 917611 "FPS-" 917757 NIL FPS- (NIL T) -8 NIL NIL NIL) (-404 914640 916309 916337 "FPC" 916562 T FPC (NIL) -9 NIL 916704 NIL) (-403 914433 914473 914570 "FPC-" 914575 NIL FPC- (NIL T) -8 NIL NIL NIL) (-402 913223 913921 913962 "FPATMAB" 913967 NIL FPATMAB (NIL T) -9 NIL 914119 NIL) (-401 910896 911399 911825 "FPARFRAC" 912860 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-400 906289 906788 907470 "FORTRAN" 910328 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-399 904005 904505 905044 "FORT" 905770 T FORT (NIL) -7 NIL NIL NIL) (-398 901681 902243 902271 "FORTFN" 903331 T FORTFN (NIL) -9 NIL 903955 NIL) (-397 901445 901495 901523 "FORTCAT" 901582 T FORTCAT (NIL) -9 NIL 901644 NIL) (-396 899551 900061 900451 "FORMULA" 901075 T FORMULA (NIL) -8 NIL NIL NIL) (-395 899339 899369 899438 "FORMULA1" 899515 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-394 898862 898914 899087 "FORDER" 899281 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-393 897958 898122 898315 "FOP" 898689 T FOP (NIL) -7 NIL NIL NIL) (-392 896539 897238 897412 "FNLA" 897840 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-391 895268 895683 895711 "FNCAT" 896171 T FNCAT (NIL) -9 NIL 896431 NIL) (-390 894807 895227 895255 "FNAME" 895260 T FNAME (NIL) -8 NIL NIL NIL) (-389 893370 894333 894361 "FMTC" 894366 T FMTC (NIL) -9 NIL 894402 NIL) (-388 889703 890893 891522 "FMONOID" 892774 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-387 888895 889445 889594 "FM" 889599 NIL FM (NIL T T) -8 NIL NIL NIL) (-386 886319 886965 886993 "FMFUN" 888137 T FMFUN (NIL) -9 NIL 888845 NIL) (-385 885588 885769 885797 "FMC" 886087 T FMC (NIL) -9 NIL 886269 NIL) (-384 882667 883527 883581 "FMCAT" 884776 NIL FMCAT (NIL T T) -9 NIL 885271 NIL) (-383 881533 882433 882533 "FM1" 882612 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-382 879307 879723 880217 "FLOATRP" 881084 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-381 872882 877036 877657 "FLOAT" 878706 T FLOAT (NIL) -8 NIL NIL NIL) (-380 870320 870820 871398 "FLOATCP" 872349 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-379 869060 869898 869939 "FLINEXP" 869944 NIL FLINEXP (NIL T) -9 NIL 870037 NIL) (-378 868214 868449 868777 "FLINEXP-" 868782 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-377 867290 867434 867658 "FLASORT" 868066 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-376 864406 865274 865326 "FLALG" 866553 NIL FLALG (NIL T T) -9 NIL 867020 NIL) (-375 858142 861892 861933 "FLAGG" 863195 NIL FLAGG (NIL T) -9 NIL 863847 NIL) (-374 856868 857207 857697 "FLAGG-" 857702 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-373 855910 856053 856280 "FLAGG2" 856721 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-372 852761 853769 853828 "FINRALG" 854956 NIL FINRALG (NIL T T) -9 NIL 855464 NIL) (-371 851921 852150 852489 "FINRALG-" 852494 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-370 851301 851540 851568 "FINITE" 851764 T FINITE (NIL) -9 NIL 851871 NIL) (-369 843658 845845 845885 "FINAALG" 849552 NIL FINAALG (NIL T) -9 NIL 851005 NIL) (-368 838990 840040 841184 "FINAALG-" 842563 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-367 838358 838745 838848 "FILE" 838920 NIL FILE (NIL T) -8 NIL NIL NIL) (-366 837016 837354 837408 "FILECAT" 838092 NIL FILECAT (NIL T T) -9 NIL 838308 NIL) (-365 834732 836260 836288 "FIELD" 836328 T FIELD (NIL) -9 NIL 836408 NIL) (-364 833352 833737 834248 "FIELD-" 834253 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-363 831202 831987 832334 "FGROUP" 833038 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-362 830292 830456 830676 "FGLMICPK" 831034 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-361 826124 830217 830274 "FFX" 830279 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-360 825725 825786 825921 "FFSLPE" 826057 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-359 821714 822497 823293 "FFPOLY" 824961 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-358 821218 821254 821463 "FFPOLY2" 821672 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-357 817061 821137 821200 "FFP" 821205 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-356 812459 816972 817036 "FF" 817041 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-355 807585 811802 811992 "FFNBX" 812313 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-354 802514 806720 806978 "FFNBP" 807439 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-353 797147 801798 802009 "FFNB" 802347 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-352 795979 796177 796492 "FFINTBAS" 796944 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-351 792048 794268 794296 "FFIELDC" 794916 T FFIELDC (NIL) -9 NIL 795292 NIL) (-350 790710 791081 791578 "FFIELDC-" 791583 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-349 790279 790325 790449 "FFHOM" 790652 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-348 787974 788461 788978 "FFF" 789794 NIL FFF (NIL T) -7 NIL NIL NIL) (-347 783592 787716 787817 "FFCGX" 787917 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-346 779213 783324 783431 "FFCGP" 783535 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-345 774396 778940 779048 "FFCG" 779149 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-344 755792 764873 764959 "FFCAT" 770124 NIL FFCAT (NIL T T T) -9 NIL 771575 NIL) (-343 750990 752037 753351 "FFCAT-" 754581 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-342 750401 750444 750679 "FFCAT2" 750941 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-341 739722 743373 744593 "FEXPR" 749253 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-340 738722 739157 739198 "FEVALAB" 739282 NIL FEVALAB (NIL T) -9 NIL 739543 NIL) (-339 737881 738091 738429 "FEVALAB-" 738434 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-338 736447 737264 737467 "FDIV" 737780 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-337 733467 734208 734323 "FDIVCAT" 735891 NIL FDIVCAT (NIL T T T T) -9 NIL 736328 NIL) (-336 733229 733256 733426 "FDIVCAT-" 733431 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-335 732449 732536 732813 "FDIV2" 733136 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-334 731423 731744 731946 "FCTRDATA" 732267 T FCTRDATA (NIL) -8 NIL NIL NIL) (-333 730109 730368 730657 "FCPAK1" 731154 T FCPAK1 (NIL) -7 NIL NIL NIL) (-332 729208 729609 729750 "FCOMP" 730000 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-331 712910 716358 719896 "FC" 725690 T FC (NIL) -8 NIL NIL NIL) (-330 705273 709301 709341 "FAXF" 711143 NIL FAXF (NIL T) -9 NIL 711835 NIL) (-329 702549 703207 704032 "FAXF-" 704497 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-328 697601 701925 702101 "FARRAY" 702406 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-327 692495 694562 694615 "FAMR" 695638 NIL FAMR (NIL T T) -9 NIL 696098 NIL) (-326 691385 691687 692122 "FAMR-" 692127 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-325 690554 691307 691360 "FAMONOID" 691365 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-324 688340 689050 689103 "FAMONC" 690044 NIL FAMONC (NIL T T) -9 NIL 690430 NIL) (-323 687004 688094 688231 "FAGROUP" 688236 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-322 684799 685118 685521 "FACUTIL" 686685 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-321 683898 684083 684305 "FACTFUNC" 684609 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-320 676320 683201 683400 "EXPUPXS" 683754 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-319 673803 674343 674929 "EXPRTUBE" 675754 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-318 670074 670666 671396 "EXPRODE" 673142 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-317 655559 668723 669152 "EXPR" 669678 NIL EXPR (NIL T) -8 NIL NIL NIL) (-316 650113 650700 651506 "EXPR2UPS" 654857 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-315 649745 649802 649911 "EXPR2" 650050 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-314 641135 648898 649188 "EXPEXPAN" 649582 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-313 640935 641092 641121 "EXIT" 641126 T EXIT (NIL) -8 NIL NIL NIL) (-312 640415 640659 640750 "EXITAST" 640864 T EXITAST (NIL) -8 NIL NIL NIL) (-311 640042 640104 640217 "EVALCYC" 640347 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-310 639583 639701 639742 "EVALAB" 639912 NIL EVALAB (NIL T) -9 NIL 640016 NIL) (-309 639064 639186 639407 "EVALAB-" 639412 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-308 636432 637734 637762 "EUCDOM" 638317 T EUCDOM (NIL) -9 NIL 638667 NIL) (-307 634837 635279 635869 "EUCDOM-" 635874 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-306 622375 625135 627885 "ESTOOLS" 632107 T ESTOOLS (NIL) -7 NIL NIL NIL) (-305 622007 622064 622173 "ESTOOLS2" 622312 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-304 621758 621800 621880 "ESTOOLS1" 621959 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-303 615795 617403 617431 "ES" 620199 T ES (NIL) -9 NIL 621609 NIL) (-302 610742 612029 613846 "ES-" 614010 NIL ES- (NIL T) -8 NIL NIL NIL) (-301 607116 607877 608657 "ESCONT" 609982 T ESCONT (NIL) -7 NIL NIL NIL) (-300 606861 606893 606975 "ESCONT1" 607078 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-299 606536 606586 606686 "ES2" 606805 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-298 606166 606224 606333 "ES1" 606472 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-297 605382 605511 605687 "ERROR" 606010 T ERROR (NIL) -7 NIL NIL NIL) (-296 598774 605241 605332 "EQTBL" 605337 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-295 591277 594088 595537 "EQ" 597358 NIL -2035 (NIL T) -8 NIL NIL NIL) (-294 590909 590966 591075 "EQ2" 591214 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-293 586198 587247 588340 "EP" 589848 NIL EP (NIL T) -7 NIL NIL NIL) (-292 584798 585089 585395 "ENV" 585912 T ENV (NIL) -8 NIL NIL NIL) (-291 583892 584446 584474 "ENTIRER" 584479 T ENTIRER (NIL) -9 NIL 584525 NIL) (-290 580359 581847 582217 "EMR" 583691 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-289 579503 579688 579742 "ELTAGG" 580122 NIL ELTAGG (NIL T T) -9 NIL 580333 NIL) (-288 579222 579284 579425 "ELTAGG-" 579430 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-287 579011 579040 579094 "ELTAB" 579178 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-286 578137 578283 578482 "ELFUTS" 578862 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-285 577879 577935 577963 "ELEMFUN" 578068 T ELEMFUN (NIL) -9 NIL NIL NIL) (-284 577749 577770 577838 "ELEMFUN-" 577843 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-283 572593 575849 575890 "ELAGG" 576830 NIL ELAGG (NIL T) -9 NIL 577293 NIL) (-282 570878 571312 571975 "ELAGG-" 571980 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-281 569539 569818 570112 "ELABEXPR" 570604 T ELABEXPR (NIL) -8 NIL NIL NIL) (-280 562403 564206 565033 "EFUPXS" 568815 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-279 555853 557654 558464 "EFULS" 561679 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-278 553338 553696 554168 "EFSTRUC" 555485 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-277 543129 544695 546243 "EF" 551853 NIL EF (NIL T T) -7 NIL NIL NIL) (-276 542203 542614 542763 "EAB" 543000 T EAB (NIL) -8 NIL NIL NIL) (-275 541385 542162 542190 "E04UCFA" 542195 T E04UCFA (NIL) -8 NIL NIL NIL) (-274 540567 541344 541372 "E04NAFA" 541377 T E04NAFA (NIL) -8 NIL NIL NIL) (-273 539749 540526 540554 "E04MBFA" 540559 T E04MBFA (NIL) -8 NIL NIL NIL) (-272 538931 539708 539736 "E04JAFA" 539741 T E04JAFA (NIL) -8 NIL NIL NIL) (-271 538115 538890 538918 "E04GCFA" 538923 T E04GCFA (NIL) -8 NIL NIL NIL) (-270 537299 538074 538102 "E04FDFA" 538107 T E04FDFA (NIL) -8 NIL NIL NIL) (-269 536481 537258 537286 "E04DGFA" 537291 T E04DGFA (NIL) -8 NIL NIL NIL) (-268 530654 532006 533370 "E04AGNT" 535137 T E04AGNT (NIL) -7 NIL NIL NIL) (-267 529334 529840 529880 "DVARCAT" 530355 NIL DVARCAT (NIL T) -9 NIL 530554 NIL) (-266 528538 528750 529064 "DVARCAT-" 529069 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-265 521675 528337 528466 "DSMP" 528471 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-264 516456 517620 518688 "DROPT" 520627 T DROPT (NIL) -8 NIL NIL NIL) (-263 516121 516180 516278 "DROPT1" 516391 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-262 511236 512362 513499 "DROPT0" 515004 T DROPT0 (NIL) -7 NIL NIL NIL) (-261 509581 509906 510292 "DRAWPT" 510870 T DRAWPT (NIL) -7 NIL NIL NIL) (-260 504168 505091 506170 "DRAW" 508555 NIL DRAW (NIL T) -7 NIL NIL NIL) (-259 503801 503854 503972 "DRAWHACK" 504109 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-258 502532 502801 503092 "DRAWCX" 503530 T DRAWCX (NIL) -7 NIL NIL NIL) (-257 502047 502116 502267 "DRAWCURV" 502458 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-256 492515 494477 496592 "DRAWCFUN" 499952 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-255 489281 491210 491251 "DQAGG" 491880 NIL DQAGG (NIL T) -9 NIL 492153 NIL) (-254 477405 483874 483957 "DPOLCAT" 485809 NIL DPOLCAT (NIL T T T T) -9 NIL 486354 NIL) (-253 472241 473590 475548 "DPOLCAT-" 475553 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-252 465363 472102 472200 "DPMO" 472205 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-251 458388 465143 465310 "DPMM" 465315 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-250 457866 458080 458178 "DOMTMPLT" 458310 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-249 457299 457668 457748 "DOMCTOR" 457806 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 456511 456779 456930 "DOMAIN" 457168 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 450499 456146 456298 "DMP" 456412 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 450099 450155 450299 "DLP" 450437 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 443921 449426 449616 "DLIST" 449941 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 440718 442774 442815 "DLAGG" 443365 NIL DLAGG (NIL T) -9 NIL 443595 NIL) (-243 439394 440058 440086 "DIVRING" 440178 T DIVRING (NIL) -9 NIL 440261 NIL) (-242 438631 438821 439121 "DIVRING-" 439126 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 436733 437090 437496 "DISPLAY" 438245 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 430621 436647 436710 "DIRPROD" 436715 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 429469 429672 429937 "DIRPROD2" 430414 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 418244 424250 424303 "DIRPCAT" 424713 NIL DIRPCAT (NIL NIL T) -9 NIL 425553 NIL) (-237 415570 416212 417093 "DIRPCAT-" 417430 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 414857 415017 415203 "DIOSP" 415404 T DIOSP (NIL) -7 NIL NIL NIL) (-235 411512 413769 413810 "DIOPS" 414244 NIL DIOPS (NIL T) -9 NIL 414473 NIL) (-234 411061 411175 411366 "DIOPS-" 411371 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 409884 410512 410540 "DIFRING" 410727 T DIFRING (NIL) -9 NIL 410837 NIL) (-232 409530 409607 409759 "DIFRING-" 409764 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 407266 408538 408579 "DIFEXT" 408942 NIL DIFEXT (NIL T) -9 NIL 409236 NIL) (-230 405551 405979 406645 "DIFEXT-" 406650 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 402826 405083 405124 "DIAGG" 405129 NIL DIAGG (NIL T) -9 NIL 405149 NIL) (-228 402210 402367 402619 "DIAGG-" 402624 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 397627 401169 401446 "DHMATRIX" 401979 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 393239 394148 395158 "DFSFUN" 396637 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 388317 392170 392482 "DFLOAT" 392947 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 386580 386861 387250 "DFINTTLS" 388025 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 383609 384601 385001 "DERHAM" 386246 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 381410 383384 383473 "DEQUEUE" 383553 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 380664 380797 380980 "DEGRED" 381272 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 377094 377839 378685 "DEFINTRF" 379892 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 374649 375118 375710 "DEFINTEF" 376613 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 373999 374269 374384 "DEFAST" 374554 T DEFAST (NIL) -8 NIL NIL NIL) (-217 368003 373594 373743 "DECIMAL" 373870 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 365515 365973 366479 "DDFACT" 367547 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 365111 365154 365305 "DBLRESP" 365466 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 362983 363344 363704 "DBASE" 364878 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 362225 362463 362609 "DATAARY" 362882 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 361331 362184 362212 "D03FAFA" 362217 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 360438 361290 361318 "D03EEFA" 361323 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 358388 358854 359343 "D03AGNT" 359969 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 357677 358347 358375 "D02EJFA" 358380 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 356966 357636 357664 "D02CJFA" 357669 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 356255 356925 356953 "D02BHFA" 356958 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 355544 356214 356242 "D02BBFA" 356247 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 348741 350330 351936 "D02AGNT" 353958 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 346509 347032 347578 "D01WGTS" 348215 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 345576 346468 346496 "D01TRNS" 346501 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 344644 345535 345563 "D01GBFA" 345568 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 343712 344603 344631 "D01FCFA" 344636 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 342780 343671 343699 "D01ASFA" 343704 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 341848 342739 342767 "D01AQFA" 342772 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 340916 341807 341835 "D01APFA" 341840 T D01APFA (NIL) -8 NIL NIL NIL) (-197 339984 340875 340903 "D01ANFA" 340908 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 339052 339943 339971 "D01AMFA" 339976 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 338120 339011 339039 "D01ALFA" 339044 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 337188 338079 338107 "D01AKFA" 338112 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 336256 337147 337175 "D01AJFA" 337180 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 329551 331104 332665 "D01AGNT" 334715 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 328888 329016 329168 "CYCLOTOM" 329419 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 325622 326336 327063 "CYCLES" 328181 T CYCLES (NIL) -7 NIL NIL NIL) (-189 324934 325068 325239 "CVMP" 325483 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 322775 323033 323402 "CTRIGMNP" 324662 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 322211 322569 322642 "CTOR" 322722 T CTOR (NIL) -8 NIL NIL NIL) (-186 321720 321942 322043 "CTORKIND" 322130 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 321011 321327 321355 "CTORCAT" 321537 T CTORCAT (NIL) -9 NIL 321650 NIL) (-184 320609 320720 320879 "CTORCAT-" 320884 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 320071 320283 320391 "CTORCALL" 320533 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-182 319445 319544 319697 "CSTTOOLS" 319968 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 315244 315901 316659 "CRFP" 318757 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 314719 314965 315057 "CRCEAST" 315172 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 313766 313951 314179 "CRAPACK" 314523 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 313150 313251 313455 "CPMATCH" 313642 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312875 312903 313009 "CPIMA" 313116 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 309223 309895 310614 "COORDSYS" 312210 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 308635 308756 308898 "CONTOUR" 309101 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 304526 306638 307130 "CONTFRAC" 308175 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 304406 304427 304455 "CONDUIT" 304492 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 303494 304048 304076 "COMRING" 304081 T COMRING (NIL) -9 NIL 304133 NIL) (-171 302548 302852 303036 "COMPPROP" 303330 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 302209 302244 302372 "COMPLPAT" 302507 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 292500 302018 302127 "COMPLEX" 302132 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 292136 292193 292300 "COMPLEX2" 292437 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 291854 291889 291987 "COMPFACT" 292095 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275934 285928 285968 "COMPCAT" 286972 NIL COMPCAT (NIL T) -9 NIL 288320 NIL) (-165 265446 268373 272000 "COMPCAT-" 272356 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 265175 265203 265306 "COMMUPC" 265412 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264969 265003 265062 "COMMONOP" 265136 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 264525 264720 264807 "COMM" 264902 T COMM (NIL) -8 NIL NIL NIL) (-161 264101 264329 264404 "COMMAAST" 264470 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 263350 263544 263572 "COMBOPC" 263910 T COMBOPC (NIL) -9 NIL 264085 NIL) (-159 262246 262456 262698 "COMBINAT" 263140 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 258703 259277 259904 "COMBF" 261668 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 257461 257819 258054 "COLOR" 258488 T COLOR (NIL) -8 NIL NIL NIL) (-156 256937 257182 257274 "COLONAST" 257389 T COLONAST (NIL) -8 NIL NIL NIL) (-155 256577 256624 256749 "CMPLXRT" 256884 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 256025 256277 256376 "CLLCTAST" 256498 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 251523 252555 253635 "CLIP" 254965 T CLIP (NIL) -7 NIL NIL NIL) (-152 249869 250629 250868 "CLIF" 251350 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 246044 248015 248056 "CLAGG" 248985 NIL CLAGG (NIL T) -9 NIL 249521 NIL) (-150 244466 244923 245506 "CLAGG-" 245511 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 244010 244095 244235 "CINTSLPE" 244375 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 241511 241982 242530 "CHVAR" 243538 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 240685 241239 241267 "CHARZ" 241272 T CHARZ (NIL) -9 NIL 241287 NIL) (-146 240439 240479 240557 "CHARPOL" 240639 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 239497 240084 240112 "CHARNZ" 240159 T CHARNZ (NIL) -9 NIL 240215 NIL) (-144 237403 238151 238504 "CHAR" 239164 T CHAR (NIL) -8 NIL NIL NIL) (-143 237129 237190 237218 "CFCAT" 237329 T CFCAT (NIL) -9 NIL NIL NIL) (-142 236374 236485 236667 "CDEN" 237013 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 232339 235527 235807 "CCLASS" 236114 T CCLASS (NIL) -8 NIL NIL NIL) (-140 231590 231747 231924 "CATEGORY" 232182 T -10 (NIL) -8 NIL NIL NIL) (-139 231163 231509 231557 "CATCTOR" 231562 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230614 230866 230964 "CATAST" 231085 T CATAST (NIL) -8 NIL NIL NIL) (-137 230090 230335 230427 "CASEAST" 230542 T CASEAST (NIL) -8 NIL NIL NIL) (-136 225099 226119 226872 "CARTEN" 229393 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 224207 224355 224576 "CARTEN2" 224946 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222523 223357 223614 "CARD" 223970 T CARD (NIL) -8 NIL NIL NIL) (-133 222099 222327 222402 "CAPSLAST" 222468 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221603 221811 221839 "CACHSET" 221971 T CACHSET (NIL) -9 NIL 222049 NIL) (-131 221073 221395 221423 "CABMON" 221473 T CABMON (NIL) -9 NIL 221529 NIL) (-130 220546 220777 220887 "BYTEORD" 220983 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219529 220080 220222 "BYTE" 220385 T BYTE (NIL) -8 NIL NIL 220507) (-128 214879 219034 219206 "BYTEBUF" 219377 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 212388 214571 214678 "BTREE" 214805 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209837 212036 212158 "BTOURN" 212298 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 207207 209307 209348 "BTCAT" 209416 NIL BTCAT (NIL T) -9 NIL 209493 NIL) (-124 206874 206954 207103 "BTCAT-" 207108 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 202139 206017 206045 "BTAGG" 206267 T BTAGG (NIL) -9 NIL 206428 NIL) (-122 201629 201754 201960 "BTAGG-" 201965 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198624 200907 201122 "BSTREE" 201446 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197762 197888 198072 "BRILL" 198480 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194414 196488 196529 "BRAGG" 197178 NIL BRAGG (NIL T) -9 NIL 197436 NIL) (-118 192943 193349 193904 "BRAGG-" 193909 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 186172 192289 192473 "BPADICRT" 192791 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184487 186109 186154 "BPADIC" 186159 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184185 184215 184329 "BOUNDZRO" 184451 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179413 180611 181523 "BOP" 183293 T BOP (NIL) -8 NIL NIL NIL) (-113 177194 177598 178073 "BOP1" 178971 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 176019 176768 176917 "BOOLEAN" 177065 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 175298 175702 175756 "BMODULE" 175761 NIL BMODULE (NIL T T) -9 NIL 175826 NIL) (-110 171099 175096 175169 "BITS" 175245 T BITS (NIL) -8 NIL NIL NIL) (-109 170520 170639 170779 "BINDING" 170979 T BINDING (NIL) -8 NIL NIL NIL) (-108 164527 170117 170265 "BINARY" 170392 T BINARY (NIL) -8 NIL NIL NIL) (-107 162307 163782 163823 "BGAGG" 164083 NIL BGAGG (NIL T) -9 NIL 164220 NIL) (-106 162138 162170 162261 "BGAGG-" 162266 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 161209 161522 161727 "BFUNCT" 161953 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159899 160077 160365 "BEZOUT" 161033 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 156368 158751 159081 "BBTREE" 159602 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 156102 156155 156183 "BASTYPE" 156302 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155954 155983 156056 "BASTYPE-" 156061 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 155388 155464 155616 "BALFACT" 155865 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 154244 154803 154989 "AUTOMOR" 155233 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153970 153975 154001 "ATTREG" 154006 T ATTREG (NIL) -9 NIL NIL NIL) (-97 152222 152667 153019 "ATTRBUT" 153636 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151830 152050 152116 "ATTRAST" 152174 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151366 151479 151505 "ATRIG" 151706 T ATRIG (NIL) -9 NIL NIL NIL) (-94 151175 151216 151303 "ATRIG-" 151308 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150820 151006 151032 "ASTCAT" 151037 T ASTCAT (NIL) -9 NIL 151067 NIL) (-92 150547 150606 150725 "ASTCAT-" 150730 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148696 150323 150411 "ASTACK" 150490 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 147201 147498 147863 "ASSOCEQ" 148378 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 146233 146860 146984 "ASP9" 147108 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145996 146181 146220 "ASP8" 146225 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144864 145601 145743 "ASP80" 145885 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143762 144499 144631 "ASP7" 144763 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142716 143439 143557 "ASP78" 143675 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141685 142396 142513 "ASP77" 142630 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140597 141323 141454 "ASP74" 141585 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139497 140232 140364 "ASP73" 140496 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138601 139323 139423 "ASP6" 139428 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137545 138278 138396 "ASP55" 138514 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136494 137219 137338 "ASP50" 137457 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135582 136195 136305 "ASP4" 136415 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134670 135283 135393 "ASP49" 135503 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133454 134209 134377 "ASP42" 134559 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 132230 132987 133157 "ASP41" 133341 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 131180 131907 132025 "ASP35" 132143 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130945 131128 131167 "ASP34" 131172 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130682 130749 130825 "ASP33" 130900 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129575 130317 130449 "ASP31" 130581 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129340 129523 129562 "ASP30" 129567 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 129075 129144 129220 "ASP29" 129295 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128840 129023 129062 "ASP28" 129067 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128605 128788 128827 "ASP27" 128832 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127689 128303 128414 "ASP24" 128525 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126765 127491 127603 "ASP20" 127608 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125853 126466 126576 "ASP1" 126686 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124795 125527 125646 "ASP19" 125765 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124532 124599 124675 "ASP12" 124750 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123384 124131 124275 "ASP10" 124419 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121235 123228 123319 "ARRAY2" 123324 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 117000 120883 120997 "ARRAY1" 121152 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 116032 116205 116426 "ARRAY12" 116823 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110344 112262 112337 "ARR2CAT" 114967 NIL ARR2CAT (NIL T T T) -9 NIL 115725 NIL) (-56 107778 108522 109476 "ARR2CAT-" 109481 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 107095 107405 107530 "ARITY" 107671 T ARITY (NIL) -8 NIL NIL NIL) (-54 105871 106023 106322 "APPRULE" 106931 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105522 105570 105689 "APPLYORE" 105817 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104876 105115 105235 "ANY" 105420 T ANY (NIL) -8 NIL NIL NIL) (-51 104154 104277 104434 "ANY1" 104750 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101684 102591 102918 "ANTISYM" 103878 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 101176 101391 101487 "ANON" 101606 T ANON (NIL) -8 NIL NIL NIL) (-48 95425 99715 100169 "AN" 100740 T AN (NIL) -8 NIL NIL NIL) (-47 91323 92711 92762 "AMR" 93510 NIL AMR (NIL T T) -9 NIL 94110 NIL) (-46 90435 90656 91019 "AMR-" 91024 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74874 90352 90413 "ALIST" 90418 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71676 74468 74637 "ALGSC" 74792 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68231 68786 69393 "ALGPKG" 71116 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67508 67609 67793 "ALGMFACT" 68117 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63543 64122 64716 "ALGMANIP" 67092 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54913 63169 63319 "ALGFF" 63476 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 54109 54240 54419 "ALGFACT" 54771 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 53050 53650 53688 "ALGEBRA" 53693 NIL ALGEBRA (NIL T) -9 NIL 53734 NIL) (-37 52768 52827 52959 "ALGEBRA-" 52964 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34861 50770 50822 "ALAGG" 50958 NIL ALAGG (NIL T T) -9 NIL 51119 NIL) (-35 34397 34510 34536 "AHYP" 34737 T AHYP (NIL) -9 NIL NIL NIL) (-34 33328 33576 33602 "AGG" 34101 T AGG (NIL) -9 NIL 34380 NIL) (-33 32762 32924 33138 "AGG-" 33143 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30568 30991 31396 "AF" 32404 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30048 30293 30383 "ADDAST" 30496 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29316 29575 29731 "ACPLOT" 29910 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18639 26443 26481 "ACFS" 27088 NIL ACFS (NIL T) -9 NIL 27327 NIL) (-28 16666 17156 17918 "ACFS-" 17923 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12784 14713 14739 "ACF" 15618 T ACF (NIL) -9 NIL 16031 NIL) (-26 11488 11822 12315 "ACF-" 12320 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 11060 11255 11281 "ABELSG" 11373 T ABELSG (NIL) -9 NIL 11438 NIL) (-24 10927 10952 11018 "ABELSG-" 11023 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10270 10557 10583 "ABELMON" 10753 T ABELMON (NIL) -9 NIL 10865 NIL) (-22 9934 10018 10156 "ABELMON-" 10161 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9282 9654 9680 "ABELGRP" 9752 T ABELGRP (NIL) -9 NIL 9827 NIL) (-20 8745 8874 9090 "ABELGRP-" 9095 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4334 8084 8123 "A1AGG" 8128 NIL A1AGG (NIL T) -9 NIL 8168 NIL) (-18 30 1252 2814 "A1AGG-" 2819 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 1c032b12..73c9ac24 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,409 +1,106 @@ -(732279 . 3461381195) -(((*1 *2 *1 *3) (-12 (-4 *1 (-34)) (-5 *3 (-771)) (-5 *2 (-112)))) - ((*1 *2 *3 *3) - (|partial| -12 (-5 *2 (-112)) (-5 *1 (-1216 *3)) (-4 *3 (-1099)))) - ((*1 *2 *3 *3 *4) - (-12 (-5 *4 (-1 (-112) *3 *3)) (-4 *3 (-1099)) (-5 *2 (-112)) - (-5 *1 (-1216 *3))))) -(((*1 *2 *3) (-12 (-5 *3 (-771)) (-5 *2 (-381)) (-5 *1 (-1040))))) -(((*1 *2 *1) (-12 (-4 *1 (-529)) (-5 *2 (-691 (-549)))))) -(((*1 *2 *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))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1265 *4)) (-4 *4 (-1049)) (-4 *2 (-1241 *4)) - (-5 *1 (-446 *4 *2)))) - ((*1 *2 *3 *2 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+(((*1 *2 *3 *3 *3 *3 *4 *5) + (-12 (-5 *3 (-225)) (-5 *4 (-566)) + (-5 *5 (-3 (|:| |fn| (-390)) (|:| |fp| (-64 -1975)))) + (-5 *2 (-1035)) (-5 *1 (-746))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -1783 (-644 (-225))))) + (-2 (|:| |lfn| (-644 (-317 (-225)))) (|:| -1342 (-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)) @@ -2397,7 +1377,7 @@ (-5 *1 (-950 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-365) - (-10 -8 (-15 -1650 ($ *7)) (-15 -2499 (*7 $)) (-15 -2507 (*7 $))))))) + (-10 -8 (-15 -2725 ($ *7)) (-15 -2691 (*7 $)) (-15 -2702 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-973 *3 *4 *5)) (-4 *3 (-1049)) (-4 *4 (-792)) (-4 *5 (-850)) (-5 *2 (-644 *5)))) @@ -2407,42 +1387,53 @@ ((*1 *2 *3) (-12 (-5 *3 (-409 (-952 *4))) (-4 *4 (-558)) (-5 *2 (-644 (-1175))) (-5 *1 (-1043 *4))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-308)) (-4 *6 (-375 *5)) (-4 *4 (-375 *5)) - (-5 *2 - (-2 (|:| |particular| (-3 *4 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((*1 *1 *2 *3) @@ -2516,10 +1551,10 @@ (-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 (-4142 *4) (-771))) + (-4 *6 (-238 (-3991 *4) (-771))) (-14 *7 - (-1 (-112) (-2 (|:| -1351 *5) (|:| -3388 *6)) - (-2 (|:| -1351 *5) (|:| -3388 *6)))) + (-1 (-112) (-2 (|:| -2430 *5) (|:| -2576 *6)) + (-2 (|:| -2430 *5) (|:| -2576 *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) @@ -2549,364 +1584,449 @@ ((*1 *1 *1 *2 *3) (-12 (-4 *1 (-973 *4 *3 *2)) (-4 *4 (-1049)) (-4 *3 (-792)) (-4 *2 (-850))))) +(((*1 *1 *2 *3 *3 *3 *3) + (-12 (-5 *2 (-1 (-943 (-225)) (-225))) (-5 *3 (-1093 (-225))) + (-5 *1 (-926)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-943 (-225)) (-225))) (-5 *3 (-1093 (-225))) + (-5 *1 (-926)))) + ((*1 *1 *2 *3 *3 *3) + (-12 (-5 *2 (-1 (-943 (-225)) (-225))) (-5 *3 (-1093 (-225))) + (-5 *1 (-927)))) + ((*1 *1 *2 *3) + (-12 (-5 *2 (-1 (-943 (-225)) 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*4 (-13 (-29 *6) (-1200) (-959))) - (-5 *2 (-2 (|:| |particular| *4) (|:| -3781 (-644 *4)))) + (-5 *2 (-2 (|:| |particular| *4) (|:| -2091 (-644 *4)))) (-5 *1 (-652 *6 *4 *3)) (-4 *3 (-656 *4)))) ((*1 *2 *3 *2 *4 *2 *5) (|partial| -12 (-5 *4 (-1175)) (-5 *5 (-644 *2)) @@ -13922,40 +14637,40 @@ (-12 (-5 *3 (-689 *5)) (-4 *5 (-365)) (-5 *2 (-2 (|:| |particular| (-3 (-1265 *5) "failed")) - (|:| -3781 (-644 (-1265 *5))))) + (|:| -2091 (-644 (-1265 *5))))) (-5 *1 (-667 *5)) (-5 *4 (-1265 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-644 (-644 *5))) (-4 *5 (-365)) (-5 *2 (-2 (|:| |particular| (-3 (-1265 *5) "failed")) - (|:| -3781 (-644 (-1265 *5))))) + (|:| -2091 (-644 (-1265 *5))))) (-5 *1 (-667 *5)) (-5 *4 (-1265 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-689 *5)) (-4 *5 (-365)) (-5 *2 (-644 (-2 (|:| |particular| (-3 (-1265 *5) "failed")) - (|:| -3781 (-644 (-1265 *5)))))) + (|:| -2091 (-644 (-1265 *5)))))) (-5 *1 (-667 *5)) (-5 *4 (-644 (-1265 *5))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-644 (-644 *5))) (-4 *5 (-365)) (-5 *2 (-644 (-2 (|:| |particular| (-3 (-1265 *5) "failed")) - (|:| -3781 (-644 (-1265 *5)))))) + (|:| -2091 (-644 (-1265 *5)))))) (-5 *1 (-667 *5)) (-5 *4 (-644 (-1265 *5))))) ((*1 *2 *3 *4) (-12 (-4 *5 (-365)) (-4 *6 (-13 (-375 *5) (-10 -7 (-6 -4416)))) (-4 *4 (-13 (-375 *5) (-10 -7 (-6 -4416)))) (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3781 (-644 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2091 (-644 *4)))) (-5 *1 (-668 *5 *6 *4 *3)) (-4 *3 (-687 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-365)) (-4 *6 (-13 (-375 *5) (-10 -7 (-6 -4416)))) (-4 *7 (-13 (-375 *5) (-10 -7 (-6 -4416)))) (-5 *2 (-644 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -3781 (-644 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2091 (-644 *7))))) (-5 *1 (-668 *5 *6 *7 *3)) (-5 *4 (-644 *7)) (-4 *3 (-687 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -13973,7 +14688,7 @@ (-4 *7 (-13 (-29 *6) (-1200) (-959))) (-4 *6 (-13 (-308) (-1038 (-566)) (-639 (-566)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1265 *7)) (|:| -3781 (-644 (-1265 *7))))) + (-2 (|:| |particular| (-1265 *7)) (|:| -2091 (-644 (-1265 *7))))) (-5 *1 (-802 *6 *7)) (-5 *4 (-1265 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-689 *6)) (-5 *4 (-1175)) @@ -13985,27 +14700,27 @@ (-5 *5 (-1175)) (-4 *7 (-13 (-29 *6) (-1200) (-959))) (-4 *6 (-13 (-308) (-1038 (-566)) (-639 (-566)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1265 *7)) (|:| -3781 (-644 (-1265 *7))))) + (-2 (|:| |particular| (-1265 *7)) (|:| -2091 (-644 (-1265 *7))))) (-5 *1 (-802 *6 *7)))) ((*1 *2 *3 *4 *5) (|partial| -12 (-5 *3 (-644 *7)) (-5 *4 (-644 (-114))) (-5 *5 (-1175)) (-4 *7 (-13 (-29 *6) (-1200) (-959))) (-4 *6 (-13 (-308) (-1038 (-566)) (-639 (-566)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1265 *7)) (|:| -3781 (-644 (-1265 *7))))) + (-2 (|:| |particular| (-1265 *7)) (|:| -2091 (-644 (-1265 *7))))) (-5 *1 (-802 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-295 *7)) (-5 *4 (-114)) (-5 *5 (-1175)) (-4 *7 (-13 (-29 *6) (-1200) (-959))) (-4 *6 (-13 (-308) (-1038 (-566)) (-639 (-566)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *7) (|:| -3781 (-644 *7))) *7 "failed")) + (-3 (-2 (|:| |particular| *7) (|:| -2091 (-644 *7))) *7 "failed")) (-5 *1 (-802 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-114)) (-5 *5 (-1175)) (-4 *6 (-13 (-308) (-1038 (-566)) (-639 (-566)) (-147))) (-5 *2 - (-3 (-2 (|:| |particular| *3) (|:| -3781 (-644 *3))) *3 "failed")) + (-3 (-2 (|:| |particular| *3) (|:| -2091 (-644 *3))) *3 "failed")) (-5 *1 (-802 *6 *3)) (-4 *3 (-13 (-29 *6) (-1200) (-959))))) ((*1 *2 *3 *4 *3 *5) (|partial| -12 (-5 *3 (-295 *2)) (-5 *4 (-114)) (-5 *5 (-644 *2)) @@ -14041,10 +14756,10 @@ (|partial| -12 (-5 *5 (-1 - (-3 (-2 (|:| |particular| *6) (|:| -3781 (-644 *6))) "failed") + (-3 (-2 (|:| |particular| *6) (|:| -2091 (-644 *6))) "failed") *7 *6)) (-4 *6 (-365)) (-4 *7 (-656 *6)) - (-5 *2 (-2 (|:| |particular| (-1265 *6)) (|:| -3781 (-689 *6)))) + (-5 *2 (-2 (|:| |particular| (-1265 *6)) (|:| -2091 (-689 *6)))) (-5 *1 (-813 *6 *7)) 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\ No newline at end of file |