diff options
| -rw-r--r-- | src/share/algebra/browse.daase | 640 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1574 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1348 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9130 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27487 |
5 files changed, 20090 insertions, 20089 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 7e43c62b..1bdc25c0 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2294619 . 3508696571) +(2294602 . 3508766236) (-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 `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1633) +(-32 R -1610) ((|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 -1069) (QUOTE (-560))))) @@ -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 \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -1633 UP UPUP -2176) +(-40 -1610 UP UPUP -3100) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2216 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2216 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2216 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2216 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2216 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2216 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) -(-41 R -1633) +((|HasCategory| (-421 |#2|) (QUOTE (-147))) (|HasCategory| (-421 |#2|) (QUOTE (-149))) (|HasCategory| (-421 |#2|) (QUOTE (-363))) (-2191 (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))) (|HasCategory| (-421 |#2|) (QUOTE (-381))) (-2191 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2191 (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (QUOTE (-363)))) (-2191 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-363))))) (-2191 (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -660) (QUOTE (-560)))) (-2191 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 |#2|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-239))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (QUOTE (-240))) (|HasCategory| (-421 |#2|) (QUOTE (-376)))) (-12 (|HasCategory| (-421 |#2|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-421 |#2|) (QUOTE (-376))))) +(-41 R -1610) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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 (-466))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -435) (|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."))) ((-4509 . T) (-4510 . T)) -((-2216 (-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|))))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-871))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|))))))) +((-2191 (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|))))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1633) +(-54 |Base| R -1610) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -163,7 +163,7 @@ NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-59 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -171,64 +171,64 @@ NIL (-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's."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) -(-61 -3956) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +(-61 -3952) ((|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 -(-62 -3956) +(-62 -3952) ((|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 -(-63 -3956) +(-63 -3952) ((|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 -(-64 -3956) +(-64 -3952) ((|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 -(-65 -3956) +(-65 -3952) ((|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 -3956) +(-66 -3952) ((|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 -3956) +(-67 -3952) ((|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 -3956) +(-68 -3952) ((|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 -3956) +(-69 -3952) ((|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 -3956) +(-70 -3952) ((|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 -3956) +(-71 -3952) ((|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 -3956) +(-72 -3952) ((|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 -3956) +(-73 -3952) ((|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 -3956) +(-74 -3952) ((|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 -(-75 -3956) +(-75 -3952) ((|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 @@ -240,51 +240,51 @@ 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 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 -(-78 -3956) +(-78 -3952) ((|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 -(-79 -3956) +(-79 -3952) ((|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 -3956) +(-80 -3952) ((|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 -3956) +(-81 -3952) ((|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 -3956) +(-82 -3952) ((|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 -(-83 -3956) +(-83 -3952) ((|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 -(-84 -3956) +(-84 -3952) ((|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 -(-85 -3956) +(-85 -3952) ((|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 -(-86 -3956) +(-86 -3952) ((|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 -(-87 -3956) +(-87 -3952) ((|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 -(-88 -3956) +(-88 -3952) ((|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 -(-89 -3956) +(-89 -3952) ((|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}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2216 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-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 `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 @@ -396,7 +396,7 @@ NIL ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op, foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op, [foo1,...,foon])} attaches [\\spad{foo1},{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,...,fn]} then applying a derivation \\spad{D} to \\spad{op(a1,...,an)} returns \\spad{f1(a1,...,an) * D(a1) + ... + fn(a1,...,an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op, foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,...,an)} returns the result of \\spad{f(a1,...,an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op, [a1,...,an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,...,an)} is returned,{} and \"failed\" otherwise."))) NIL NIL -(-117 -1633 UP) +(-117 -1610 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 @@ -407,7 +407,7 @@ NIL (-119 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2216 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) +((|HasCategory| (-118 |#1|) (QUOTE (-939))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-149))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-118 |#1|) (QUOTE (-1051))) (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871))) (-2191 (|HasCategory| (-118 |#1|) (QUOTE (-842))) (|HasCategory| (-118 |#1|) (QUOTE (-871)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-1183))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-118 |#1|) (QUOTE (-239))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (QUOTE (-240))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -118) (|devaluate| |#1|)) (|%list| (QUOTE -118) (|devaluate| |#1|)))) (|HasCategory| (-118 |#1|) (QUOTE (-319))) (|HasCategory| (-118 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-118 |#1|) (QUOTE (-939)))) (|HasCategory| (-118 |#1|) (QUOTE (-147))))) (-120 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -423,7 +423,7 @@ NIL (-123 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"))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-124 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL @@ -443,11 +443,11 @@ NIL (-128 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-129 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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-130) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL @@ -455,7 +455,7 @@ NIL (-131) ((|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 `n'. The array can then store up to `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 `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."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2216 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2216 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) +((-2191 (-12 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-2191 (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130))))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-130) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-130) (QUOTE (-871))) (-2191 (|HasCategory| (-130) (QUOTE (-102))) (|HasCategory| (-130) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-130) (QUOTE (-102))) (-12 (|HasCategory| (-130) (QUOTE (-1132))) (|HasCategory| (-130) (|%list| (QUOTE -321) (QUOTE (-130)))))) (-132) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -476,11 +476,11 @@ 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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) (((-4511 "*") . T)) NIL -(-137 |minix| -4331 R) +(-137 |minix| -4350 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,...,t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,...,r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL -(-138 |minix| -4331 S T$) +(-138 |minix| -4350 S T$) ((|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 @@ -503,7 +503,7 @@ NIL (-143) ((|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}."))) ((-4509 . T) (-4499 . T) (-4510 . T)) -((-2216 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2191 (-12 (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-146) (QUOTE (-381))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-144 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}'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}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -517,7 +517,7 @@ NIL NIL NIL (-147) -((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) +((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) ((-4506 . T)) NIL (-148 R) @@ -528,7 +528,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4506 . T)) NIL -(-150 -1633 UP UPUP) +(-150 -1610 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 @@ -568,7 +568,7 @@ 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 -(-160 R -1633) +(-160 R -1610) ((|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})/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.} 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.} 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.} n!/(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 @@ -602,7 +602,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-559))) (|HasCategory| |#2| (QUOTE (-1033))) (|HasCategory| |#2| (QUOTE (-1234))) (|HasCategory| |#2| (QUOTE (-1091))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4505)) (|HasAttribute| |#2| (QUOTE -4508)) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571)))) (-168 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})"))) -((-4502 -2216 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-3011 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-4502 -2191 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-2953 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-169 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -614,8 +614,8 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4502 -2216 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-3011 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2216 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1234)))) (|HasCategory| |#1| (QUOTE (-1234))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1234)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4508)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) +((-4502 -2191 (|has| |#1| (-571)) (-12 (|has| |#1| (-319)) (|has| |#1| (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4505 |has| |#1| (-6 -4505)) (-4508 |has| |#1| (-6 -4508)) (-2953 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2191 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-363)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-939)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-939))))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1234)))) (|HasCategory| |#1| (QUOTE (-1234))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| |#1| (QUOTE (-1091))) (-12 (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-1234)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (-12 (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasAttribute| |#1| (QUOTE -4505)) (|HasAttribute| |#1| (QUOTE -4508)) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-363))))) (-172 R S) ((|constructor| (NIL "This package extends maps from underlying rings to maps between complex over those rings.")) (|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -692,7 +692,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-191 R -1633) +(-191 R -1610) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -804,23 +804,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-219 -1633 UP UPUP R) +(-219 -1610 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 -(-220 -1633 FP) +(-220 -1610 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 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 (-221) ((|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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2216 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-222) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `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|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-223 R -1633) +(-223 R -1610) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -835,18 +835,18 @@ NIL (-226 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-227 |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}."))) ((-4506 . T)) NIL -(-228 R -1633) +(-228 R -1610) ((|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 (-229) ((|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}."))) -((-3000 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-230) ((|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)}.}"))) @@ -855,7 +855,7 @@ NIL (-231 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}"))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-232 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 @@ -904,19 +904,19 @@ 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 -(-244 S -4331 R) +(-244 S -4350 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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 (-376))) (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (QUOTE (-871))) (|HasAttribute| |#3| (QUOTE -4506)) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (QUOTE (-1132)))) -(-245 -4331 R) +(-245 -4350 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|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"))) ((-4503 |has| |#2| (-1080)) (-4504 |has| |#2| (-1080)) (-4506 |has| |#2| (-6 -4506)) (-4509 . T)) NIL -(-246 -4331 R) +(-246 -4350 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."))) ((-4503 |has| |#2| (-1080)) (-4504 |has| |#2| (-1080)) (-4506 |has| |#2| (-6 -4506)) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-2216 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-1080)))) (-12 (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-376))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1080)))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-376)))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-815))) (-2216 (|HasCategory| |#2| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-381))) (-2216 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-175)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE 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(QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))))) +(-247 -4350 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 @@ -939,7 +939,7 @@ NIL (-252 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}"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-253 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'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 @@ -951,7 +951,7 @@ NIL (-255 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-256) ((|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain `d'.")) (|reflect| (($ (|ConstructorCall| (|DomainConstructor|))) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall| (|DomainConstructor|)) $) "\\spad{reify(d)} returns the abstract syntax for the domain `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|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object `d'."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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} := 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 @@ -1031,7 +1031,7 @@ NIL (-275 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"))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#3| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-276 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}.")) (|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 @@ -1076,11 +1076,11 @@ 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|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1'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 -(-287 R -1633) +(-287 R -1610) ((|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 -(-288 R -1633) +(-288 R -1610) ((|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 @@ -1132,7 +1132,7 @@ 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 -(-301 S R |Mod| -2695 -3550 |exactQuo|) +(-301 S R |Mod| -4452 -4246 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL @@ -1150,8 +1150,8 @@ NIL NIL (-305 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) -((-4506 -2216 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-1080)) (-4504 |has| |#1| (-1080))) -((|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2216 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2216 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2216 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) +((-4506 -2191 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4503 |has| |#1| (-1080)) (-4504 |has| |#1| (-1080))) +((|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-1080)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748)))) (|HasCategory| |#1| (QUOTE (-487))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1143)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-310))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-487)))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748)))) (-2191 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-748)))) (-306 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL @@ -1159,7 +1159,7 @@ NIL (-307 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) (-308) ((|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 @@ -1172,11 +1172,11 @@ NIL ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-311 -1633 S) +(-311 -1610 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-312 E -1633) +(-312 E -1610) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -1216,7 +1216,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|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 -(-322 -1633) +(-322 -1610) ((|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 @@ -1231,11 +1231,11 @@ NIL (-325 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))}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . 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(|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -321) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -298) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1285) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-319))) (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-559))) (-12 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-939))) (|HasCategory| $ (QUOTE (-147)))) (-2191 (|HasCategory| (-1285 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (-12 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(|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."))) -((-4506 -2216 (-12 (|has| |#1| (-571)) (-2216 (|has| |#1| (-1080)) (|has| |#1| (-487)))) (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) ((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-571)) (-4501 |has| |#1| (-571))) -((-2216 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE 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(QUOTE (-1080))) (|HasCategory| $ (|%list| (QUOTE -1069) (QUOTE (-560))))) (-327 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 @@ -1244,7 +1244,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-329 R -1633) +(-329 R -1610) ((|constructor| (NIL "Taylor series solutions of explicit ODE'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 @@ -1255,7 +1255,7 @@ NIL (-331 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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) (-332 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},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1287,12 +1287,12 @@ NIL (-339 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."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) -(-340 S -1633) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +(-340 S -1610) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-381)))) -(-341 -1633) +(-341 -1610) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL @@ -1312,7 +1312,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-346 -1633 UP UPUP R) +(-346 -1610 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}'s are integers and the \\spad{P}'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 @@ -1320,11 +1320,11 @@ 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 -(-348 S -1633 UP UPUP R) +(-348 S -1610 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}'s are integers and the \\spad{P}'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 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 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 -(-349 -1633 UP UPUP R) +(-349 -1610 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}'s are integers and the \\spad{P}'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 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 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 @@ -1343,12 +1343,12 @@ NIL (-353 |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}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) -(-354 S -1633 UP UPUP) +((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +(-354 S -1610 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 \\spad{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 (-381))) (|HasCategory| |#2| (QUOTE (-376)))) -(-355 -1633 UP UPUP) +(-355 -1610 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 \\spad{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."))) ((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL @@ -1359,15 +1359,15 @@ NIL (-357 |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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-358 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-359 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-360 GF) ((|constructor| (NIL "FiniteFieldFunctions(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 @@ -1384,42 +1384,42 @@ 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|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL -(-364 R UP -1633) +(-364 R UP -1610) ((|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 (-365 |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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) +((-2191 (|HasCategory| (-935 |#1|) (QUOTE (-147))) (|HasCategory| (-935 |#1|) (QUOTE (-381)))) (|HasCategory| (-935 |#1|) (QUOTE (-149))) (|HasCategory| (-935 |#1|) (QUOTE (-381))) (|HasCategory| (-935 |#1|) (QUOTE (-147)))) (-366 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-367 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-368 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-369 GF) ((|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(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(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(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(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(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(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 -(-370 -1633 GF) +(-370 -1610 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}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 -(-371 -1633 FP FPP) +(-371 -1610 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}'s exists."))) NIL NIL (-372 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) +((-2191 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-381)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-147)))) (-373 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{ls}."))) NIL @@ -1494,7 +1494,7 @@ NIL NIL (-391) ((|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}."))) -((-4492 . T) (-4500 . T) (-3000 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-4492 . T) (-4500 . T) (-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-392 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1552,7 +1552,7 @@ 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 -(-406 -1633 UP UPUP R) +(-406 -1610 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 @@ -1576,11 +1576,11 @@ NIL ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) NIL NIL -(-412 -3956 |returnType| -3421 |symbols|) +(-412 -3952 |returnType| -4118 |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 -(-413 -1633 UP) +(-413 -1610 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1602,12 +1602,12 @@ NIL ((|HasAttribute| |#1| (QUOTE -4492)) (|HasAttribute| |#1| (QUOTE -4500))) (-418) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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'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\"."))) -((-3000 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-419 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 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."))) ((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1253))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1253)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) +((|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -321) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -298) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-1253))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-1253)))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-466)))) (-420 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."))) NIL @@ -1615,7 +1615,7 @@ NIL (-421 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4496 -12 (|has| |#1| (-6 -4507)) (|has| |#1| (-466)) (|has| |#1| (-6 -4496))) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4496)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (QUOTE (-1051))) (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-842))) (|HasCategory| |#1| (QUOTE (-871)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843))))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-843)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-559))) (-12 (|HasAttribute| |#1| (QUOTE -4507)) (|HasAttribute| |#1| (QUOTE -4496)) (|HasCategory| |#1| (QUOTE (-466)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-422 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1636,7 +1636,7 @@ NIL ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-427 R -1633 UP A) +(-427 R -1610 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)}."))) ((-4506 . T)) NIL @@ -1644,7 +1644,7 @@ 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 -(-429 R -1633 UP A |ibasis|) +(-429 R -1610 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 -1069) (|devaluate| |#2|)))) @@ -1670,7 +1670,7 @@ NIL ((|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-1080))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-1143))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (-435 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|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}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4506 -2216 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) ((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-571)) (-4501 |has| |#1| (-571))) +((-4506 -2191 (|has| |#1| (-1080)) (|has| |#1| (-487))) (-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) ((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-571)) (-4501 |has| |#1| (-571))) NIL (-436 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1696,7 +1696,7 @@ NIL ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-442 R -1633) +(-442 R -1610) ((|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 @@ -1704,19 +1704,19 @@ 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"))) ((-4496 -12 (|has| |#1| (-6 -4496)) (|has| |#2| (-6 -4496))) (-4503 . T) (-4504 . T) (-4506 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4496)) (|HasAttribute| |#2| (QUOTE -4496)))) -(-444 R -1633) +(-444 R -1610) ((|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 -(-445 R -1633) +(-445 R -1610) ((|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 -(-446 R -1633) +(-446 R -1610) ((|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 \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{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)))) -(-447 R -1633) +(-447 R -1610) ((|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 @@ -1724,7 +1724,7 @@ 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 -(-449 R -1633 UP) +(-449 R -1610 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 -1069) (QUOTE (-48))))) @@ -1756,7 +1756,7 @@ 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's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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'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 -(-457 R UP -1633) +(-457 R UP -1610) ((|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 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'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'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's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri'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 @@ -1803,7 +1803,7 @@ NIL (-468 |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"))) (((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-469 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's conditional."))) NIL @@ -1868,7 +1868,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\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 -(-485 |lv| -1633 R) +(-485 |lv| -1610 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 @@ -1883,11 +1883,11 @@ NIL (-488 |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.")) (|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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . 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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)}"))) ((-4510 . T) (-4509 . T)) @@ -1903,7 +1903,7 @@ NIL (-493 |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."))) ((-4509 . T) (-4510 . 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Hall as given in Serre's book Lie Groups -- 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{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 @@ -1911,11 +1911,11 @@ NIL (-495 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1935,7 +1935,7 @@ NIL (-501) ((|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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2216 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-502 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|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1960,7 +1960,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-508 -1633 UP |AlExt| |AlPol|) +(-508 -1610 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP'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 @@ -1971,16 +1971,16 @@ NIL (-510 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-511 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'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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-512 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 -(-513 R UP -1633) +(-513 R UP -1610) ((|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 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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -2000,7 +2000,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-518 -1633 |Expon| |VarSet| |DPoly|) +(-518 -1610 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-1208))))) @@ -2051,7 +2051,7 @@ NIL (-530 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{June/91}} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|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}"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-531) ((|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 @@ -2059,15 +2059,15 @@ NIL (-532 |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}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((-2216 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) +((-2191 (|HasCategory| (-595 |#1|) (QUOTE (-147))) (|HasCategory| (-595 |#1|) (QUOTE (-381)))) (|HasCategory| (-595 |#1|) (QUOTE (-149))) (|HasCategory| (-595 |#1|) (QUOTE (-381))) (|HasCategory| (-595 |#1|) (QUOTE (-147)))) (-533 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-534 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."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-535 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,{} m*h and 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 @@ -2079,7 +2079,7 @@ NIL (-537 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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-538) ((|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 @@ -2112,7 +2112,7 @@ 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 ((-12 (|HasCategory| (-793) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132))))) -(-546 K -1633 |Par|) +(-546 K -1610 |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 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 @@ -2136,7 +2136,7 @@ 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 -(-552 K -1633 |Par|) +(-552 K -1610 |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 @@ -2191,12 +2191,12 @@ NIL (-565 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) -(-566 R -1633) +((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) +(-566 R -1610) ((|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 -(-567 R0 -1633 UP UPUP R) +(-567 R0 -1610 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 @@ -2206,7 +2206,7 @@ NIL NIL (-569 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3000 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-2941 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-570 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."))) @@ -2216,7 +2216,7 @@ 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."))) ((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL -(-572 R -1633) +(-572 R -1610) ((|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},{}...,{}kn (the \\spad{ki}'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}'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 @@ -2228,7 +2228,7 @@ 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 -(-575 R -1633 L) +(-575 R -1610 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}'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}'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 -680) (|devaluate| |#2|)))) @@ -2236,11 +2236,11 @@ 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 -(-577 -1633 UP UPUP R) +(-577 -1610 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 -(-578 -1633 UP) +(-578 -1610 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 @@ -2248,15 +2248,15 @@ 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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\tt \\spad{exp}},{} over a given range,{} {\\tt a} to {\\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 {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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,{} {\\tt \\spad{exp}},{} over a given range {\\tt a} to {\\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 -(-580 R -1633 L) +(-580 R -1610 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}'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 -680) (|devaluate| |#2|)))) -(-581 R -1633) +(-581 R -1610) ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1170)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-649))))) -(-582 -1633 UP) +(-582 -1610 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}'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 @@ -2264,27 +2264,27 @@ 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 -(-584 -1633) +(-584 -1610) ((|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}'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 (-585 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."))) -((-3000 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-2941 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-586) ((|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}'s exists."))) NIL NIL -(-587 R -1633) +(-587 R -1610) ((|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 -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-296))) (|HasCategory| |#2| (QUOTE (-649))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-296)))) (|HasCategory| |#1| (QUOTE (-571)))) -(-588 -1633 UP) +(-588 -1610 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 -(-589 R -1633) +(-589 R -1610) ((|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 @@ -2316,15 +2316,15 @@ 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 -(-597 -1633) +(-597 -1610) ((|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 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}."))) ((-4504 . T) (-4503 . T)) ((|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-1208))))) -(-598 E -1633) +(-598 E -1610) ((|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 -(-599 R -1633) +(-599 R -1610) ((|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},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL @@ -2359,7 +2359,7 @@ NIL (-607 |mn|) ((|constructor| (NIL "This domain implements low-level strings"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2216 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2216 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2191 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2191 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2191 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-608 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 @@ -2367,7 +2367,7 @@ NIL (-609 |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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-560)) (|devaluate| |#1|)))) (|HasCategory| (-560) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-560)))))) (-610 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) (((-4511 "*") |has| |#1| (-571)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) @@ -2384,7 +2384,7 @@ 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 -(-614 R -1633 FG) +(-614 R -1610 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and 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 @@ -2395,7 +2395,7 @@ NIL (-616 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-617 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2410,8 +2410,8 @@ NIL NIL (-620 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4506 -2216 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) -((-2216 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4506 -2191 (-1383 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) +((-2191 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-621) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL @@ -2439,7 +2439,7 @@ NIL (-627 |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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102)))) (-628 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 @@ -2464,7 +2464,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-634 -1633 UP) +(-634 -1610 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 @@ -2492,7 +2492,7 @@ NIL ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) ((-4506 . T)) NIL -(-641 R -1633) +(-641 R -1610) ((|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 @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-648 R -1633) +(-648 R -1610) ((|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 @@ -2528,18 +2528,18 @@ 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 -(-650 |lv| -1633) +(-650 |lv| -1610) ((|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 (-651) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2715) (QUOTE (-51))))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1190) (QUOTE (-871))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (QUOTE (-51))))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-1190) (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (QUOTE (-1132)))) (-652 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)."))) -((-4506 -2216 (-1384 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) -((-2216 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) +((-4506 -2191 (-1383 (|has| |#2| (-380 |#1|)) (|has| |#1| (-571))) (-12 (|has| |#2| (-432 |#1|)) (|has| |#1| (-571)))) (-4504 . T) (-4503 . T)) +((-2191 (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (|%list| (QUOTE -432) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -380) (|devaluate| |#1|)))) (-653 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{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2583,7 +2583,7 @@ NIL (-663 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-843))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-664 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL @@ -2607,7 +2607,7 @@ NIL (-669 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-670 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL @@ -2628,11 +2628,11 @@ NIL ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|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{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4504 . T) (-4503 . T)) ((|HasCategory| |#1| (QUOTE (-813)))) -(-675 R -1633 L) +(-675 R -1610 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 -(-676 A -3089) +(-676 A -2018) ((|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}}"))) ((-4503 . T) (-4504 . T) (-4506 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) @@ -2652,7 +2652,7 @@ 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}."))) ((-4503 . T) (-4504 . T) (-4506 . T)) NIL -(-681 -1633 UP) +(-681 -1610 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)))) @@ -2684,11 +2684,11 @@ 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}."))) ((-4510 . T) (-4509 . T)) NIL -(-689 -1633 |Row| |Col| M) +(-689 -1610 |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 -(-690 -1633) +(-690 -1610) ((|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'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 @@ -2699,7 +2699,7 @@ NIL (-692 |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."))) ((-4506 . T) (-4509 . T) (-4503 . T) (-4504 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2216 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-571))) (-2191 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-693) ((|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 @@ -2719,7 +2719,7 @@ NIL (-697 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 -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (QUOTE (-1080))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-698) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2775,7 +2775,7 @@ NIL (-711 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."))) ((-4509 . T) (-4510 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-319))) (|HasCategory| |#1| (QUOTE (-571))) (|HasAttribute| |#1| (QUOTE (-4511 "*"))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-712 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{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 @@ -2784,7 +2784,7 @@ 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 `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 `x' into \\%."))) NIL NIL -(-714 S -1633 FLAF FLAS) +(-714 S -1610 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,{} \\spad{kl+ku+1} being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions \\spad{kl+ku+1} by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row \\spad{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 @@ -2794,8 +2794,8 @@ NIL NIL (-716) ((|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"))) -((-4502 . T) (-4507 |has| (-721) (-376)) (-4501 |has| (-721) (-376)) (-3011 . T) (-4508 |has| (-721) (-6 -4508)) (-4505 |has| (-721) (-6 -4505)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2216 (|HasCategory| (-721) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2216 (-12 (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208))))) (-2216 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (|%list| (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-721) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2216 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1051))) (|HasCategory| (-721) (QUOTE (-1234))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1234)))) (-2216 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (-2216 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1234)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939))) (-2216 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2216 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2216 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4508)) (|HasAttribute| (-721) (QUOTE -4505)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-363))))) +((-4502 . T) (-4507 |has| (-721) (-376)) (-4501 |has| (-721) (-376)) (-2953 . T) (-4508 |has| (-721) (-6 -4508)) (-4505 |has| (-721) (-6 -4505)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((|HasCategory| (-721) (QUOTE (-149))) (|HasCategory| (-721) (QUOTE (-147))) (|HasCategory| (-721) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-381))) (|HasCategory| (-721) (QUOTE (-376))) (-2191 (|HasCategory| (-721) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-239))) (-2191 (-12 (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208))))) (-2191 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (|%list| (QUOTE -298) (QUOTE (-721)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -321) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-721)))) (|HasCategory| (-721) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-721) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-721) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (-2191 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-363)))) (|HasCategory| (-721) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-721) (QUOTE (-1051))) (|HasCategory| (-721) (QUOTE (-1234))) (-12 (|HasCategory| (-721) (QUOTE (-1033))) (|HasCategory| (-721) (QUOTE (-1234)))) (-2191 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (-2191 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-376))) (|HasCategory| (-721) (QUOTE (-939)))) (-12 (|HasCategory| (-721) (QUOTE (-363))) (|HasCategory| (-721) (QUOTE (-939))))) (|HasCategory| (-721) (QUOTE (-559))) (-12 (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-1234)))) (|HasCategory| (-721) (QUOTE (-1091))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939))) (-2191 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-376)))) (-2191 (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (QUOTE (-239)))) (-2191 (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-571)))) (-12 (|HasCategory| (-721) (QUOTE (-239))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (QUOTE (-240))) (|HasCategory| (-721) (QUOTE (-376)))) (-12 (|HasCategory| (-721) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-721) (QUOTE (-376)))) (|HasCategory| (-721) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-721) (QUOTE (-571))) (|HasAttribute| (-721) (QUOTE -4508)) (|HasAttribute| (-721) (QUOTE -4505)) (-12 (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (|%list| (QUOTE -929) (QUOTE (-1208)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-147)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-721) (QUOTE (-319))) (|HasCategory| (-721) (QUOTE (-939)))) (|HasCategory| (-721) (QUOTE (-363))))) (-717 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}."))) ((-4510 . T)) @@ -2808,13 +2808,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? 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 -(-720 OV E -1633 PG) +(-720 OV E -1610 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 (-721) ((|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}"))) -((-3000 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) +((-2941 . T) (-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-722 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."))) @@ -2840,7 +2840,7 @@ 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 \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-728 S -4306 I) +(-728 S -4324 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 @@ -2860,14 +2860,14 @@ 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 -(-733 R |Mod| -2695 -3550 |exactQuo|) +(-733 R |Mod| -4452 -4246 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-734 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4505 |has| |#1| (-376)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-1183))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-240))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-735 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2876,7 +2876,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4504 |has| |#1| (-175)) (-4503 |has| |#1| (-175)) (-4506 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149)))) -(-737 R |Mod| -2695 -3550 |exactQuo|) +(-737 R |Mod| -4452 -4246 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4506 . T)) NIL @@ -2888,7 +2888,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4504 . T) (-4503 . T)) NIL -(-740 -1633) +(-740 -1610) ((|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]]}."))) ((-4506 . T)) NIL @@ -2924,7 +2924,7 @@ 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 -(-749 -1633 UP) +(-749 -1610 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 @@ -2943,7 +2943,7 @@ NIL (-753 |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."))) (((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2191 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-888 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-754 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -3076,11 +3076,11 @@ 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 -(-787 -1633) +(-787 -1610) ((|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 -(-788 P -1633) +(-788 P -1610) ((|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''."))) NIL NIL @@ -3088,7 +3088,7 @@ NIL NIL NIL NIL -(-790 UP -1633) +(-790 UP -1610) ((|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 @@ -3104,7 +3104,7 @@ 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."))) (((-4511 "*") . T)) NIL -(-794 R -1633) +(-794 R -1610) ((|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 @@ -3124,7 +3124,7 @@ 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}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},{}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 -(-799 -1633 |ExtF| |SUEx| |ExtP| |n|) +(-799 -1610 |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 @@ -3139,11 +3139,11 @@ NIL (-802 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . 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((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) 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mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3211,8 +3211,8 @@ NIL (-820 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2216 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2216 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-821 -2216 R OS S) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (-2191 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1027 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-821 -2191 R OS S) ((|constructor| (NIL "\\spad{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 @@ -3220,11 +3220,11 @@ NIL ((|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 -(-823 R -1633 L) +(-823 R -1610 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}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-824 R -1633) +(-824 R -1610) ((|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 @@ -3232,7 +3232,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE'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 -(-826 R -1633) +(-826 R -1610) ((|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 @@ -3240,11 +3240,11 @@ 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'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'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'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'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'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'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'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's and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-828 -1633 UP UPUP R) +(-828 -1610 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 -(-829 -1633 UP L LQ) +(-829 -1610 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 @@ -3252,38 +3252,38 @@ 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 -(-831 -1633 UP L LQ) +(-831 -1610 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}'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)}'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}'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}'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 mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-832 -1633 UP) +(-832 -1610 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}'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}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-833 -1633 L UP A LO) +(-833 -1610 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 -(-834 -1633 UP) +(-834 -1610 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}'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 ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'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)))) -(-835 -1633 LO) +(-835 -1610 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 -(-836 -1633 LODO) +(-836 -1610 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op, g, [f1,...,fm], I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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(((-4511 "*") |has| |#2| (-376)) (-4502 |has| |#2| (-376)) (-4507 |has| |#2| (-376)) (-4501 |has| |#2| (-376)) (-4506 . T) (-4504 . T) (-4503 . T)) @@ -3347,7 +3347,7 @@ NIL (-854 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."))) ((-4506 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2216 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2216 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-855 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f, r, i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL @@ -3387,7 +3387,7 @@ NIL (-864 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4506 |has| |#1| (-870))) -((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2216 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2216 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (QUOTE (-21))) (-2191 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-870)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (-2191 (|HasCategory| |#1| (QUOTE (-870))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-559)))) (-865 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL @@ -3396,7 +3396,7 @@ NIL ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-867 -4331 S) +(-867 -4350 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 @@ -3440,11 +3440,11 @@ 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{\\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{\\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{\\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{\\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 (-376))) (|HasCategory| |#1| (QUOTE (-571)))) -(-878 R |sigma| -3057) +(-878 R |sigma| -3708) ((|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."))) ((-4503 . T) (-4504 . T) (-4506 . T)) ((|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-376)))) -(-879 |x| R |sigma| -3057) +(-879 |x| R |sigma| -3708) ((|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}."))) ((-4503 . T) (-4504 . T) (-4506 . T)) ((|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-376)))) @@ -3511,15 +3511,15 @@ NIL (-895 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2216 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1183))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) +((|HasCategory| (-893 |#1|) (QUOTE (-939))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-149))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-893 |#1|) (QUOTE (-1051))) (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871))) (-2191 (|HasCategory| (-893 |#1|) (QUOTE (-842))) (|HasCategory| (-893 |#1|) (QUOTE (-871)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-1183))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| (-893 |#1|) (QUOTE (-239))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (QUOTE (-240))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -528) (QUOTE (-1208)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -321) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (|%list| (QUOTE -298) (|%list| (QUOTE -893) (|devaluate| |#1|)) (|%list| (QUOTE -893) (|devaluate| |#1|)))) (|HasCategory| (-893 |#1|) (QUOTE (-319))) (|HasCategory| (-893 |#1|) (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-893 |#1|) (QUOTE (-939)))) (|HasCategory| (-893 |#1|) (QUOTE (-147))))) (-896 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2216 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) +((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-1051))) (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871))) (-2191 (|HasCategory| |#2| (QUOTE (-842))) (|HasCategory| |#2| (QUOTE (-871)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -298) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-559))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-897 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))))) (-898) ((|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'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's lowest value."))) NIL @@ -3592,7 +3592,7 @@ NIL ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a, b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p, v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,...,an], f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,...,an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x, [a1,...,an], f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,...,an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x, c?, o?, m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p, [p1,...,pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and pn to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,...,pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and pn.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form 's for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,...,an])} returns the pattern \\spad{[a1,...,an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op, [a1,...,an])} returns \\spad{op(a1,...,an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a, b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,...,an]} if \\spad{p = [a1,...,an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a, b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q, n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op, [a1,...,an]]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p, op)} returns \\spad{[a1,...,an]} if \\spad{p = op(a1,...,an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,...,an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-916 R -4306) +(-916 R -4324) ((|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 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 @@ -3620,7 +3620,7 @@ 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 -(-923 UP -1633) +(-923 UP -1610) ((|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 @@ -3651,11 +3651,11 @@ NIL (-930 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-931 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.")) (|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|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4506 . T)) -((-2216 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) +((-2191 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#1| (QUOTE (-871)))) (-932 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 @@ -3681,14 +3681,14 @@ NIL NIL NIL (-938 S) -((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) +((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-147)))) (-939) -((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) +((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\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}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} qnd \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) ((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL -(-940 R0 -1633 UP UPUP R) +(-940 R0 -1610 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 @@ -3716,7 +3716,7 @@ 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'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\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 -(-947 -1633) +(-947 -1610) ((|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 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 @@ -3732,11 +3732,11 @@ NIL ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,...,fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,...,fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL -(-951 |xx| -1633) +(-951 |xx| -1610) ((|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 -(-952 -1633 P) +(-952 -1610 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL @@ -3764,7 +3764,7 @@ NIL ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\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.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-959 R -1633) +(-959 R -1610) ((|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 '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 @@ -3772,7 +3772,7 @@ 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 -(-961 S R -1633) +(-961 S R -1610) ((|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 @@ -3792,11 +3792,11 @@ 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 -911) (|devaluate| |#1|)))) -(-966 -4306) +(-966 -4324) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-967 R -1633 -4306) +(-967 R -1610 -4324) ((|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 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 @@ -3819,7 +3819,7 @@ NIL (-972 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-973 |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 @@ -3831,7 +3831,7 @@ NIL (-975 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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1208) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-976 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f, p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL @@ -3848,7 +3848,7 @@ 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 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 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 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 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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) NIL -(-980 E V R P -1633) +(-980 E V R P -1610) ((|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},{}...,{}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 @@ -3856,7 +3856,7 @@ NIL ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap, coefmap, p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-982 E V R P -1633) +(-982 E V R P -1610) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-466)))) @@ -3871,7 +3871,7 @@ NIL (-985 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4507))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-133)))) (|HasAttribute| |#1| (QUOTE -4507))) (-986 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op, m)} returns the matrix A such that \\spad{A w = (W',W'',...,W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L), m}."))) NIL @@ -3879,7 +3879,7 @@ NIL (-987 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-988 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}."))) NIL @@ -3888,7 +3888,7 @@ NIL ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-990 -1633) +(-990 -1610) ((|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}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3903,7 +3903,7 @@ NIL (-993 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"))) ((-4506 -12 (|has| |#2| (-487)) (|has| |#1| (-487)))) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748))))) (-12 (|HasCategory| |#1| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-381)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-487))) (|HasCategory| |#2| (QUOTE (-487)))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-815))) (|HasCategory| |#2| (QUOTE (-815))))) (-12 (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#2| (QUOTE (-748)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-133)))) (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-871))))) (-994) ((|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 `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 @@ -3992,7 +3992,7 @@ 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 -(-1016 K R UP -1633) +(-1016 K R UP -1610) ((|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 @@ -4039,7 +4039,7 @@ NIL (-1027 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.}"))) ((-4502 |has| |#1| (-302)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-302))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -528) (QUOTE (-1208)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -298) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-1091))) (|HasCategory| |#1| (QUOTE (-559)))) (-1028 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,i,j,k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL @@ -4055,7 +4055,7 @@ NIL (-1031 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1032 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -4064,14 +4064,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-1034 -1633 UP UPUP |radicnd| |n|) +(-1034 -1610 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4502 |has| (-421 |#2|) (-376)) (-4507 |has| (-421 |#2|) (-376)) (-4501 |has| (-421 |#2|) (-376)) ((-4511 "*") . 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(|fractRadix| (($ (|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."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2216 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) +((|HasCategory| (-560) (QUOTE (-939))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-149))) (|HasCategory| (-560) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-1051))) (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871))) (-2191 (|HasCategory| (-560) (QUOTE (-842))) (|HasCategory| (-560) (QUOTE (-871)))) (|HasCategory| (-560) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-1183))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| (-560) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| (-560) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| (-560) (QUOTE (-239))) (|HasCategory| (-560) (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| (-560) (QUOTE (-240))) (|HasCategory| (-560) (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| (-560) (|%list| (QUOTE -528) (QUOTE (-1208)) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -321) (QUOTE (-560)))) (|HasCategory| (-560) (|%list| (QUOTE -298) (QUOTE (-560)) (QUOTE (-560)))) (|HasCategory| (-560) (QUOTE (-319))) (|HasCategory| (-560) (QUOTE (-559))) (|HasCategory| (-560) (|%list| (QUOTE -660) (QUOTE (-560)))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| (-560) (QUOTE (-939)))) (|HasCategory| (-560) (QUOTE (-147))))) (-1036) ((|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 @@ -4104,19 +4104,19 @@ 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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) ((-4502 . T) (-4507 . T) (-4501 . T) (-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4506 . T)) NIL -(-1044 R -1633) +(-1044 R -1610) ((|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 -(-1045 R -1633) +(-1045 R -1610) ((|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 -(-1046 -1633 UP) +(-1046 -1610 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 -(-1047 -1633 UP) +(-1047 -1610 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 @@ -4151,8 +4151,8 @@ NIL (-1055 |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"))) ((-4502 . T) (-4507 . T) (-4501 . T) (-4504 . T) (-4503 . T) ((-4511 "*") . T) (-4506 . T)) -((-2216 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) -(-1056 -1633 L) +((-2191 (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-421 (-560)) (|%list| (QUOTE -1069) (QUOTE (-560))))) +(-1056 -1610 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 @@ -4188,14 +4188,14 @@ 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 -(-1065 -1633 |Expon| |VarSet| |FPol| |LFPol|) +(-1065 -1610 |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"))) (((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL (-1066) ((|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.}"))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (QUOTE (-1208))) (|%list| (QUOTE |:|) (QUOTE -2715) (QUOTE (-51))))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-1132))) (|HasCategory| (-1208) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1208))) (|%list| (QUOTE |:|) (QUOTE -2660) (QUOTE (-51))))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| (-51) (QUOTE (-1132))) (|HasCategory| (-51) (|%list| (QUOTE -321) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-1132))) (|HasCategory| (-1208) (QUOTE (-871))) (|HasCategory| (-51) (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102))) (|HasCategory| (-51) (QUOTE (-102)))) (|HasCategory| (-51) (QUOTE (-102))) (|HasCategory| (-51) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (QUOTE (-102)))) (-1067) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4252,7 +4252,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4506 . T)) NIL -(-1081 |xx| -1633) +(-1081 |xx| -1610) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4271,7 +4271,7 @@ NIL (-1085 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4509 . T) (-4504 . T) (-4503 . T)) -((|HasCategory| |#3| (QUOTE (-175))) (-2216 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) +((|HasCategory| |#3| (QUOTE (-175))) (-2191 (-12 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (|HasCategory| |#3| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-376)))) (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (QUOTE (-319))) (|HasCategory| |#3| (QUOTE (-571))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-102))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887))))) (-1086 |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 @@ -4307,7 +4307,7 @@ NIL (-1094) ((|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| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE's")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE's")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4509 . T) (-4510 . 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When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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 @@ -4352,7 +4352,7 @@ NIL ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-1106 |Base| R -1633) +(-1106 |Base| R -1610) ((|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},{}...,{}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 @@ -4360,7 +4360,7 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1108 |Base| R -1633) +(-1108 |Base| R -1610) ((|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 @@ -4371,7 +4371,7 @@ NIL (-1110 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."))) ((-4502 |has| |#1| (-376)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) +((|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-363))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-381))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208)))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-12 (|HasCategory| |#1| (QUOTE (-239))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-240))) (|HasCategory| |#1| (QUOTE (-376)))) (-12 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (-1111 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4403,7 +4403,7 @@ NIL (-1118 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"))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . 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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 @@ -4443,7 +4443,7 @@ NIL (-1128 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)}}"))) ((-4509 . T) (-4499 . T) (-4510 . 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Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,y,...,z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |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 \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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|#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-376))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-381))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-748))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-815))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-871))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (|HasCategory| (-560) (QUOTE (-871))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-239))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -929) (QUOTE (-1208))))) (-2191 (|HasCategory| |#3| (QUOTE (-1080))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560)))))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -1069) (QUOTE (-560))))) (-12 (|HasCategory| |#3| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#3| (QUOTE (-1132)))) (|HasAttribute| |#3| (QUOTE -4506)) (-12 (|HasCategory| |#3| (QUOTE (-240))) (|HasCategory| |#3| (QUOTE (-1080)))) (-12 (|HasCategory| |#3| (QUOTE (-1080))) (|HasCategory| |#3| (|%list| (QUOTE -927) (QUOTE (-1208))))) (|HasCategory| |#3| (QUOTE (-175))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-133))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#3| (QUOTE (-102))) (-12 (|HasCategory| |#3| (QUOTE (-1132))) (|HasCategory| |#3| (|%list| (QUOTE -321) (|devaluate| |#3|))))) (-1145 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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{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 @@ -4520,7 +4520,7 @@ 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 `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1148 R -1633) +(-1148 R -1610) ((|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 @@ -4555,16 +4555,16 @@ NIL (-1156 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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-939))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2216 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) +((|HasCategory| |#1| (QUOTE (-939))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (|HasCategory| |#1| (QUOTE (-466))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#1| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-376))) (|HasAttribute| |#1| (QUOTE -4507)) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-939)))) (|HasCategory| |#1| (QUOTE (-147))))) (-1157 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1158 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}"))) ((-4510 . T) (-4509 . T)) NIL -(-1159 UP -1633) +(-1159 UP -1610) ((|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 @@ -4619,11 +4619,11 @@ NIL (-1172 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2216 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2216 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) +((-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))) (-2191 (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132)))) (-2191 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -321) (|%list| (QUOTE -1171) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-1132))))) (|HasCategory| (-1171 |#1| |#2|) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-1171 |#1| |#2|) (QUOTE (-102)))) (-1173 |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}."))) ((-4506 . T) (-4498 |has| |#2| (-6 (-4511 "*"))) (-4509 . T) (-4503 . T) (-4504 . T)) -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2216 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2216 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (QUOTE (-239))) (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -1069) (QUOTE (-560)))) (-2191 (-12 (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-240))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (QUOTE (-319))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-376))) (-2191 (|HasAttribute| |#2| (QUOTE (-4511 "*"))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-240)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-102))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-175)))) (-1174 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4647,7 +4647,7 @@ NIL (-1179 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1180 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 @@ -4659,7 +4659,7 @@ NIL (-1182 |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."))) ((-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132)))) +((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132)))) (-1183) ((|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}'s are never \\spad{nothing}.}")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4675,7 +4675,7 @@ NIL (-1186 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."))) ((-4510 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1187 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL @@ -4691,11 +4691,11 @@ NIL (-1190) ((|string| (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2216 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2216 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) +((-2191 (-12 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146))))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-2191 (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (|HasCategory| (-146) (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-146) (QUOTE (-871))) (-2191 (|HasCategory| (-146) (QUOTE (-102))) (|HasCategory| (-146) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-146) (QUOTE (-102))) (-12 (|HasCategory| (-146) (QUOTE (-1132))) (|HasCategory| (-146) (|%list| (QUOTE -321) (QUOTE (-146)))))) (-1191 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#1|)))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 (-1190)) (|:| -2715 |#1|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (QUOTE (-1190))) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#1|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-1132))) (|HasCategory| (-1190) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-102)))) (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 (-1190)) (|:| -2660 |#1|)) (QUOTE (-102)))) (-1192 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 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 @@ -4726,9 +4726,9 @@ NIL NIL (-1199 |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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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL @@ -4739,7 +4739,7 @@ NIL (-1202 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -4751,11 +4751,11 @@ NIL (-1205 |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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) (-1206 |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.")) (|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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) (-1207) ((|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 @@ -4771,7 +4771,7 @@ NIL (-1210 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-6 -4507)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2216 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4507))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-2191 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-466))) (-12 (|HasCategory| (-1002) (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasAttribute| |#1| (QUOTE -4507))) (-1211) ((|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 @@ -4811,7 +4811,7 @@ NIL (-1220 |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}"))) ((-4509 . T) (-4510 . T)) -((-12 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3830) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2715) (|devaluate| |#2|)))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2216 (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (QUOTE (-102)))) +((-12 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -321) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3818) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE -2660) (|devaluate| |#2|)))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-1132)))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -633) (QUOTE (-549)))) (-12 (|HasCategory| |#2| (QUOTE (-1132))) (|HasCategory| |#2| (|%list| (QUOTE -321) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1132))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887))))) (-2191 (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102))) (|HasCategory| |#2| (QUOTE (-102)))) (|HasCategory| |#2| (QUOTE (-102))) (|HasCategory| |#2| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (QUOTE (-102)))) (-1221 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL @@ -4871,7 +4871,7 @@ NIL (-1235 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4510 . T) (-4509 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) +((-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1132))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-1132)))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102)))) (-1236 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4880,7 +4880,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1238 R -1633) +(-1238 R -1610) ((|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 @@ -4888,14 +4888,14 @@ 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 -(-1240 R -1633) +(-1240 R -1610) ((|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 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 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 -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -911) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (|devaluate| |#1|))))) (-1241 |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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-149))) (|HasCategory| |#1| (QUOTE (-147))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-376)))) (-1242 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}Xn]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\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)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(ts,{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{ts},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{ts} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}ts,{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{ts} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}ts,{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL @@ -4916,7 +4916,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter'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 (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) -(-1247 -1633) +(-1247 -1610) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) (|generalTwoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalTwoFactor(p)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}."))) NIL NIL @@ -4962,8 +4962,8 @@ NIL NIL (-1258 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Laurent series in one variable \\indented{2}{\\spadtype{UnivariateLaurentSeries} 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{UnivariateLaurentSeries(Integer,x,3)} represents Laurent series in} \\indented{2}{\\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4511 "*") -2216 (-1384 (|has| |#1| (-376)) (|has| (-1288 |#1| |#2| |#3|) (-842))) (|has| |#1| (-175)) (-1384 (|has| |#1| (-376)) (|has| (-1288 |#1| |#2| |#3|) (-939)))) (-4502 -2216 (-1384 (|has| |#1| (-376)) (|has| (-1288 |#1| |#2| |#3|) (-842))) (|has| |#1| (-571)) (-1384 (|has| |#1| (-376)) (|has| (-1288 |#1| |#2| |#3|) (-939)))) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . 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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 @@ -4999,7 +4999,7 @@ NIL (-1267 |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}"))) (((-4511 "*") |has| |#2| (-175)) (-4502 |has| |#2| (-571)) (-4505 |has| |#2| (-376)) (-4507 |has| |#2| (-6 -4507)) (-4504 . T) (-4503 . T) (-4506 . T)) -((|HasCategory| |#2| (QUOTE (-939))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-175))) (-2216 (|HasCategory| |#2| (QUOTE (-175))) (|HasCategory| |#2| (QUOTE (-571)))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-391)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-391))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -911) (QUOTE (-560)))) (|HasCategory| |#2| (|%list| (QUOTE -911) (QUOTE (-560))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-391)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560))))) (|HasCategory| |#2| (|%list| (QUOTE -633) (|%list| (QUOTE -915) (QUOTE (-560)))))) (-12 (|HasCategory| (-1113) (|%list| (QUOTE -633) (QUOTE (-549)))) (|HasCategory| |#2| (|%list| (QUOTE -633) (QUOTE (-549))))) (|HasCategory| |#2| (|%list| (QUOTE -660) (QUOTE (-560)))) (|HasCategory| |#2| 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(-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-571))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-466))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-376))) (|HasCategory| |#2| (QUOTE (-1183))) (|HasCategory| |#2| (|%list| (QUOTE -929) (QUOTE (-1208)))) (|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-240))) (|HasAttribute| |#2| (QUOTE -4507)) (|HasCategory| |#2| (QUOTE (-466))) (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (-2191 (-12 (|HasCategory| $ (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-939)))) (|HasCategory| |#2| (QUOTE (-147))))) (-1268 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\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| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL @@ -5035,7 +5035,7 @@ NIL (-1276 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#2|) (QUOTE (-1208)))))) +((|HasCategory| |#2| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1143))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#2|) (QUOTE (-1208)))))) (-1277 |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{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) @@ -5047,7 +5047,7 @@ NIL (-1279 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) (-1280 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL @@ -5067,11 +5067,11 @@ NIL (-1284 |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)}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4507 |has| |#1| (-376)) (-4501 |has| |#1| (-376)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2216 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) +((|HasCategory| |#1| (QUOTE (-571))) (|HasCategory| |#1| (QUOTE (-175))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560))) (|devaluate| |#1|)))) (|HasCategory| (-421 (-560)) (QUOTE (-1143))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-2191 (|HasCategory| |#1| (QUOTE (-376))) (|HasCategory| |#1| (QUOTE (-571)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560)))))) (-1285 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))}."))) (((-4511 "*") |has| (-1279 |#2| |#3| |#4|) (-175)) (-4502 |has| (-1279 |#2| |#3| |#4|) (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-175))) (-2216 (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-571)))) +((|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-149))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-175))) (-2191 (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560)))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| (-1279 |#2| |#3| |#4|) (|%list| (QUOTE -1069) (QUOTE (-560)))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-376))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-466))) (|HasCategory| (-1279 |#2| |#3| |#4|) (QUOTE (-571)))) (-1286 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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 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| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -5083,7 +5083,7 @@ NIL (-1288 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|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}."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) -((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2216 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2587) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2216 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-571))) (-2191 (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-571)))) (|HasCategory| |#1| (QUOTE (-175))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-149))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -927) (QUOTE (-1208)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-793)) (|devaluate| |#1|)))) (|HasCategory| (-793) (QUOTE (-1143))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasSignature| |#1| (|%list| (QUOTE -2539) (|%list| (|devaluate| |#1|) (QUOTE (-1208)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-793))))) (|HasCategory| |#1| (QUOTE (-376))) (-2191 (-12 (|HasCategory| |#1| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#1| (QUOTE (-989))) (|HasCategory| |#1| (QUOTE (-1234)))) (-12 (|HasCategory| |#1| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasSignature| |#1| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1208))))) (|HasSignature| |#1| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#1|))))))) (-1289 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL @@ -5091,7 +5091,7 @@ NIL (-1290 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 (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1234))) (|HasSignature| |#2| (|%list| (QUOTE -3598) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -4318) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1208))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) +((|HasCategory| |#2| (|%list| (QUOTE -29) (QUOTE (-560)))) (|HasCategory| |#2| (QUOTE (-989))) (|HasCategory| |#2| (QUOTE (-1234))) (|HasSignature| |#2| (|%list| (QUOTE -3557) (|%list| (|%list| (QUOTE -663) (QUOTE (-1208))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3071) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1208))))) (|HasCategory| |#2| (|%list| (QUOTE -38) (|%list| (QUOTE -421) (QUOTE (-560))))) (|HasCategory| |#2| (QUOTE (-376)))) (-1291 |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."))) (((-4511 "*") |has| |#1| (-175)) (-4502 |has| |#1| (-571)) (-4503 . T) (-4504 . T) (-4506 . T)) @@ -5100,7 +5100,7 @@ NIL ((|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 -(-1293 -1633 UP L UTS) +(-1293 -1610 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 (-571)))) @@ -5123,7 +5123,7 @@ NIL (-1298 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."))) ((-4510 . T) (-4509 . T)) -((-2216 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2216 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2216 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2216 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) +((-2191 (-12 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-2191 (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887))))) (|HasCategory| |#1| (|%list| (QUOTE -633) (QUOTE (-549)))) (-2191 (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| |#1| (QUOTE (-871))) (-2191 (|HasCategory| |#1| (QUOTE (-102))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132)))) (|HasCategory| (-560) (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-748))) (|HasCategory| |#1| (QUOTE (-1080))) (-12 (|HasCategory| |#1| (QUOTE (-1033))) (|HasCategory| |#1| (QUOTE (-1080)))) (|HasCategory| |#1| (|%list| (QUOTE -632) (QUOTE (-887)))) (|HasCategory| |#1| (QUOTE (-102))) (-12 (|HasCategory| |#1| (QUOTE (-1132))) (|HasCategory| |#1| (|%list| (QUOTE -321) (|devaluate| |#1|))))) (-1299 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\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| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\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 @@ -5160,7 +5160,7 @@ 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]*v + A[2]\\spad{*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 -(-1308 K R UP -1633) +(-1308 K R UP -1610) ((|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 @@ -5192,11 +5192,11 @@ NIL ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1316 S -1633) +(-1316 S -1610) ((|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-381))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-149)))) -(-1317 -1633) +(-1317 -1610) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4501 . T) (-4507 . T) (-4502 . T) ((-4511 "*") . T) (-4503 . T) (-4504 . T) (-4506 . T)) NIL @@ -5260,4 +5260,4 @@ NIL NIL NIL NIL -((-3 NIL 2294599 2294604 2294609 2294614) (-2 NIL 2294579 2294584 2294589 2294594) (-1 NIL 2294559 2294564 2294569 2294574) (0 NIL 2294539 2294544 2294549 2294554) (-1328 "ZMOD.spad" 2294348 2294361 2294477 2294534) (-1327 "ZLINDEP.spad" 2293446 2293457 2294338 2294343) (-1326 "ZDSOLVE.spad" 2283406 2283428 2293436 2293441) (-1325 "YSTREAM.spad" 2282901 2282912 2283396 2283401) (-1324 "YDIAGRAM.spad" 2282535 2282544 2282891 2282896) (-1323 "XRPOLY.spad" 2281755 2281775 2282391 2282460) (-1322 "XPR.spad" 2279550 2279563 2281473 2281572) (-1321 "XPOLYC.spad" 2278869 2278885 2279476 2279545) (-1320 "XPOLY.spad" 2278424 2278435 2278725 2278794) (-1319 "XPBWPOLY.spad" 2276863 2276883 2278198 2278267) (-1318 "XFALG.spad" 2273911 2273927 2276789 2276858) (-1317 "XF.spad" 2272374 2272389 2273813 2273906) (-1316 "XF.spad" 2270817 2270834 2272258 2272263) (-1315 "XEXPPKG.spad" 2270076 2270102 2270807 2270812) (-1314 "XDPOLY.spad" 2269690 2269706 2269932 2270001) (-1313 "XALG.spad" 2269358 2269369 2269646 2269685) (-1312 "WUTSET.spad" 2265328 2265345 2268959 2268986) (-1311 "WP.spad" 2264535 2264579 2265186 2265253) (-1310 "WHILEAST.spad" 2264333 2264342 2264525 2264530) (-1309 "WHEREAST.spad" 2264004 2264013 2264323 2264328) (-1308 "WFFINTBS.spad" 2261667 2261689 2263994 2263999) (-1307 "WEIER.spad" 2259889 2259900 2261657 2261662) (-1306 "VSPACE.spad" 2259562 2259573 2259857 2259884) (-1305 "VSPACE.spad" 2259255 2259268 2259552 2259557) (-1304 "VOID.spad" 2258932 2258941 2259245 2259250) (-1303 "VIEWDEF.spad" 2254133 2254142 2258922 2258927) (-1302 "VIEW3D.spad" 2238094 2238103 2254123 2254128) (-1301 "VIEW2D.spad" 2225993 2226002 2238084 2238089) (-1300 "VIEW.spad" 2223713 2223722 2225983 2225988) (-1299 "VECTOR2.spad" 2222352 2222365 2223703 2223708) (-1298 "VECTOR.spad" 2220852 2220863 2221103 2221130) (-1297 "VECTCAT.spad" 2218764 2218775 2220820 2220847) (-1296 "VECTCAT.spad" 2216483 2216496 2218541 2218546) (-1295 "VARIABLE.spad" 2216263 2216278 2216473 2216478) (-1294 "UTYPE.spad" 2215907 2215916 2216253 2216258) (-1293 "UTSODETL.spad" 2215202 2215226 2215863 2215868) (-1292 "UTSODE.spad" 2213418 2213438 2215192 2215197) (-1291 "UTSCAT.spad" 2210897 2210913 2213316 2213413) (-1290 "UTSCAT.spad" 2207996 2208014 2210417 2210422) (-1289 "UTS2.spad" 2207591 2207626 2207986 2207991) (-1288 "UTS.spad" 2202469 2202497 2205989 2206086) (-1287 "URAGG.spad" 2197190 2197201 2202459 2202464) (-1286 "URAGG.spad" 2191875 2191888 2197146 2197151) (-1285 "UPXSSING.spad" 2189493 2189519 2190929 2191062) (-1284 "UPXSCONS.spad" 2187171 2187191 2187544 2187693) (-1283 "UPXSCCA.spad" 2185742 2185762 2187017 2187166) (-1282 "UPXSCCA.spad" 2184455 2184477 2185732 2185737) (-1281 "UPXSCAT.spad" 2183044 2183060 2184301 2184450) (-1280 "UPXS2.spad" 2182587 2182640 2183034 2183039) (-1279 "UPXS.spad" 2179802 2179830 2180638 2180787) (-1278 "UPSQFREE.spad" 2178216 2178230 2179792 2179797) (-1277 "UPSCAT.spad" 2176011 2176035 2178114 2178211) (-1276 "UPSCAT.spad" 2173491 2173517 2175596 2175601) (-1275 "UPOLYC2.spad" 2172962 2172981 2173481 2173486) (-1274 "UPOLYC.spad" 2168042 2168053 2172804 2172957) (-1273 "UPOLYC.spad" 2163008 2163021 2167772 2167777) (-1272 "UPMP.spad" 2161940 2161953 2162998 2163003) (-1271 "UPDIVP.spad" 2161505 2161519 2161930 2161935) (-1270 "UPDECOMP.spad" 2159766 2159780 2161495 2161500) (-1269 "UPCDEN.spad" 2158983 2158999 2159756 2159761) (-1268 "UP2.spad" 2158347 2158368 2158973 2158978) (-1267 "UP.spad" 2155375 2155390 2155762 2155915) (-1266 "UNISEG2.spad" 2154872 2154885 2155331 2155336) (-1265 "UNISEG.spad" 2154225 2154236 2154791 2154796) (-1264 "UNIFACT.spad" 2153328 2153340 2154215 2154220) (-1263 "ULSCONS.spad" 2144240 2144260 2144610 2144759) (-1262 "ULSCCAT.spad" 2141977 2141997 2144086 2144235) (-1261 "ULSCCAT.spad" 2139822 2139844 2141933 2141938) (-1260 "ULSCAT.spad" 2138062 2138078 2139668 2139817) (-1259 "ULS2.spad" 2137576 2137629 2138052 2138057) (-1258 "ULS.spad" 2127147 2127175 2128092 2128521) (-1257 "UINT8.spad" 2127024 2127033 2127137 2127142) (-1256 "UINT64.spad" 2126900 2126909 2127014 2127019) (-1255 "UINT32.spad" 2126776 2126785 2126890 2126895) (-1254 "UINT16.spad" 2126652 2126661 2126766 2126771) (-1253 "UFD.spad" 2125717 2125726 2126578 2126647) (-1252 "UFD.spad" 2124844 2124855 2125707 2125712) (-1251 "UDVO.spad" 2123725 2123734 2124834 2124839) (-1250 "UDPO.spad" 2121306 2121317 2123681 2123686) (-1249 "TYPEAST.spad" 2121225 2121234 2121296 2121301) (-1248 "TYPE.spad" 2121157 2121166 2121215 2121220) (-1247 "TWOFACT.spad" 2119809 2119824 2121147 2121152) (-1246 "TUPLE.spad" 2119300 2119311 2119705 2119710) (-1245 "TUBETOOL.spad" 2116167 2116176 2119290 2119295) (-1244 "TUBE.spad" 2114814 2114831 2116157 2116162) (-1243 "TSETCAT.spad" 2102885 2102902 2114782 2114809) (-1242 "TSETCAT.spad" 2090942 2090961 2102841 2102846) (-1241 "TS.spad" 2089535 2089551 2090501 2090598) (-1240 "TRMANIP.spad" 2083899 2083916 2089223 2089228) (-1239 "TRIMAT.spad" 2082862 2082887 2083889 2083894) (-1238 "TRIGMNIP.spad" 2081389 2081406 2082852 2082857) (-1237 "TRIGCAT.spad" 2080901 2080910 2081379 2081384) (-1236 "TRIGCAT.spad" 2080411 2080422 2080891 2080896) (-1235 "TREE.spad" 2078857 2078868 2079889 2079916) (-1234 "TRANFUN.spad" 2078696 2078705 2078847 2078852) (-1233 "TRANFUN.spad" 2078533 2078544 2078686 2078691) (-1232 "TOPSP.spad" 2078207 2078216 2078523 2078528) (-1231 "TOOLSIGN.spad" 2077870 2077881 2078197 2078202) (-1230 "TEXTFILE.spad" 2076431 2076440 2077860 2077865) (-1229 "TEX1.spad" 2075987 2075998 2076421 2076426) (-1228 "TEX.spad" 2073181 2073190 2075977 2075982) (-1227 "TEMUTL.spad" 2072736 2072745 2073171 2073176) (-1226 "TBCMPPK.spad" 2070837 2070860 2072726 2072731) (-1225 "TBAGG.spad" 2069895 2069918 2070817 2070832) (-1224 "TBAGG.spad" 2068961 2068986 2069885 2069890) (-1223 "TANEXP.spad" 2068369 2068380 2068951 2068956) (-1222 "TALGOP.spad" 2068093 2068104 2068359 2068364) (-1221 "TABLEAU.spad" 2067574 2067585 2068083 2068088) (-1220 "TABLE.spad" 2065507 2065530 2065777 2065804) (-1219 "TABLBUMP.spad" 2062286 2062297 2065497 2065502) (-1218 "SYSTEM.spad" 2061514 2061523 2062276 2062281) (-1217 "SYSSOLP.spad" 2058997 2059008 2061504 2061509) (-1216 "SYSPTR.spad" 2058896 2058905 2058987 2058992) (-1215 "SYSNNI.spad" 2058119 2058130 2058886 2058891) (-1214 "SYSINT.spad" 2057523 2057534 2058109 2058114) (-1213 "SYNTAX.spad" 2053857 2053866 2057513 2057518) (-1212 "SYMTAB.spad" 2051925 2051934 2053847 2053852) (-1211 "SYMS.spad" 2047948 2047957 2051915 2051920) (-1210 "SYMPOLY.spad" 2046927 2046938 2047009 2047136) (-1209 "SYMFUNC.spad" 2046428 2046439 2046917 2046922) (-1208 "SYMBOL.spad" 2043923 2043932 2046418 2046423) (-1207 "SWITCH.spad" 2040694 2040703 2043913 2043918) (-1206 "SUTS.spad" 2037673 2037701 2039092 2039189) (-1205 "SUPXS.spad" 2034875 2034903 2035724 2035873) (-1204 "SUPFRACF.spad" 2033980 2033998 2034865 2034870) (-1203 "SUP2.spad" 2033372 2033385 2033970 2033975) (-1202 "SUP.spad" 2030014 2030025 2030787 2030940) (-1201 "SUMRF.spad" 2028988 2028999 2030004 2030009) (-1200 "SUMFS.spad" 2028617 2028634 2028978 2028983) (-1199 "SULS.spad" 2018175 2018203 2019133 2019562) (-1198 "SUCHTAST.spad" 2017944 2017953 2018165 2018170) (-1197 "SUCH.spad" 2017634 2017649 2017934 2017939) (-1196 "SUBSPACE.spad" 2009765 2009780 2017624 2017629) (-1195 "SUBRESP.spad" 2008935 2008949 2009721 2009726) (-1194 "STTFNC.spad" 2005403 2005419 2008925 2008930) (-1193 "STTF.spad" 2001502 2001518 2005393 2005398) (-1192 "STTAYLOR.spad" 1994147 1994158 2001377 2001382) (-1191 "STRTBL.spad" 1992162 1992179 1992311 1992338) (-1190 "STRING.spad" 1990928 1990937 1991149 1991176) (-1189 "STREAM3.spad" 1990501 1990516 1990918 1990923) (-1188 "STREAM2.spad" 1989629 1989642 1990491 1990496) (-1187 "STREAM1.spad" 1989335 1989346 1989619 1989624) (-1186 "STREAM.spad" 1986121 1986132 1988728 1988743) (-1185 "STINPROD.spad" 1985057 1985073 1986111 1986116) (-1184 "STEPAST.spad" 1984291 1984300 1985047 1985052) (-1183 "STEP.spad" 1983500 1983509 1984281 1984286) (-1182 "STBL.spad" 1981548 1981576 1981715 1981730) (-1181 "STAGG.spad" 1980623 1980634 1981538 1981543) (-1180 "STAGG.spad" 1979696 1979709 1980613 1980618) (-1179 "STACK.spad" 1978924 1978935 1979174 1979201) (-1178 "SRING.spad" 1978684 1978693 1978914 1978919) (-1177 "SREGSET.spad" 1976383 1976400 1978285 1978312) (-1176 "SRDCMPK.spad" 1974960 1974980 1976373 1976378) (-1175 "SRAGG.spad" 1970143 1970152 1974928 1974955) (-1174 "SRAGG.spad" 1965346 1965357 1970133 1970138) (-1173 "SQMATRIX.spad" 1962841 1962859 1963757 1963844) (-1172 "SPLTREE.spad" 1957307 1957320 1962103 1962130) (-1171 "SPLNODE.spad" 1953927 1953940 1957297 1957302) (-1170 "SPFCAT.spad" 1952736 1952745 1953917 1953922) (-1169 "SPECOUT.spad" 1951288 1951297 1952726 1952731) (-1168 "SPADXPT.spad" 1943379 1943388 1951278 1951283) (-1167 "spad-parser.spad" 1942844 1942853 1943369 1943374) (-1166 "SPADAST.spad" 1942545 1942554 1942834 1942839) (-1165 "SPACEC.spad" 1926760 1926771 1942535 1942540) (-1164 "SPACE3.spad" 1926536 1926547 1926750 1926755) (-1163 "SORTPAK.spad" 1926085 1926098 1926492 1926497) (-1162 "SOLVETRA.spad" 1923848 1923859 1926075 1926080) (-1161 "SOLVESER.spad" 1922304 1922315 1923838 1923843) (-1160 "SOLVERAD.spad" 1918330 1918341 1922294 1922299) (-1159 "SOLVEFOR.spad" 1916792 1916810 1918320 1918325) (-1158 "SNTSCAT.spad" 1916392 1916409 1916760 1916787) (-1157 "SMTS.spad" 1914674 1914700 1915951 1916048) (-1156 "SMP.spad" 1912077 1912097 1912467 1912594) (-1155 "SMITH.spad" 1910922 1910947 1912067 1912072) (-1154 "SMATCAT.spad" 1909040 1909070 1910866 1910917) (-1153 "SMATCAT.spad" 1907090 1907122 1908918 1908923) (-1152 "SKAGG.spad" 1906059 1906070 1907058 1907085) (-1151 "SINT.spad" 1904999 1905008 1905925 1906054) (-1150 "SIMPAN.spad" 1904727 1904736 1904989 1904994) (-1149 "SIGNRF.spad" 1903845 1903856 1904717 1904722) (-1148 "SIGNEF.spad" 1903124 1903141 1903835 1903840) (-1147 "SIGAST.spad" 1902541 1902550 1903114 1903119) (-1146 "SIG.spad" 1901903 1901912 1902531 1902536) (-1145 "SHP.spad" 1899847 1899862 1901859 1901864) (-1144 "SHDP.spad" 1887202 1887229 1887719 1887818) (-1143 "SGROUP.spad" 1886810 1886819 1887192 1887197) (-1142 "SGROUP.spad" 1886416 1886427 1886800 1886805) (-1141 "SGCF.spad" 1879555 1879564 1886406 1886411) (-1140 "SFRTCAT.spad" 1878501 1878518 1879523 1879550) (-1139 "SFRGCD.spad" 1877564 1877584 1878491 1878496) (-1138 "SFQCMPK.spad" 1872377 1872397 1877554 1877559) (-1137 "SFORT.spad" 1871816 1871830 1872367 1872372) (-1136 "SEXOF.spad" 1871659 1871699 1871806 1871811) (-1135 "SEXCAT.spad" 1869487 1869527 1871649 1871654) (-1134 "SEX.spad" 1869379 1869388 1869477 1869482) (-1133 "SETMN.spad" 1867837 1867854 1869369 1869374) (-1132 "SETCAT.spad" 1867322 1867331 1867827 1867832) (-1131 "SETCAT.spad" 1866805 1866816 1867312 1867317) (-1130 "SETAGG.spad" 1863354 1863365 1866785 1866800) (-1129 "SETAGG.spad" 1859911 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225393) (-193 "CYCLES.spad" 221696 221704 224894 224899) (-192 "CVMP.spad" 221113 221123 221686 221691) (-191 "CTRIGMNP.spad" 219613 219629 221103 221108) (-190 "CTORKIND.spad" 219216 219224 219603 219608) (-189 "CTORCAT.spad" 218457 218465 219206 219211) (-188 "CTORCAT.spad" 217696 217706 218447 218452) (-187 "CTORCALL.spad" 217285 217295 217686 217691) (-186 "CTOR.spad" 216976 216984 217275 217280) (-185 "CSTTOOLS.spad" 216221 216234 216966 216971) (-184 "CRFP.spad" 209993 210006 216211 216216) (-183 "CRCEAST.spad" 209713 209721 209983 209988) (-182 "CRAPACK.spad" 208780 208790 209703 209708) (-181 "CPMATCH.spad" 208281 208296 208702 208707) (-180 "CPIMA.spad" 207986 208005 208271 208276) (-179 "COORDSYS.spad" 202995 203005 207976 207981) (-178 "CONTOUR.spad" 202422 202430 202985 202990) (-177 "CONTFRAC.spad" 198172 198182 202324 202417) (-176 "CONDUIT.spad" 197930 197938 198162 198167) (-175 "COMRING.spad" 197604 197612 197868 197925) (-174 "COMPPROP.spad" 197122 197130 197594 197599) (-173 "COMPLPAT.spad" 196889 196904 197112 197117) (-172 "COMPLEX2.spad" 196604 196616 196879 196884) (-171 "COMPLEX.spad" 191915 191925 192159 192420) (-170 "COMPILER.spad" 191464 191472 191905 191910) (-169 "COMPFACT.spad" 191066 191080 191454 191459) (-168 "COMPCAT.spad" 189138 189148 190800 191061) (-167 "COMPCAT.spad" 186935 186947 188599 188604) (-166 "COMMUPC.spad" 186683 186701 186925 186930) (-165 "COMMONOP.spad" 186216 186224 186673 186678) (-164 "COMMAAST.spad" 185979 185987 186206 186211) (-163 "COMM.spad" 185790 185798 185969 185974) (-162 "COMBOPC.spad" 184713 184721 185780 185785) (-161 "COMBINAT.spad" 183480 183490 184703 184708) (-160 "COMBF.spad" 180902 180918 183470 183475) (-159 "COLOR.spad" 179739 179747 180892 180897) (-158 "COLONAST.spad" 179405 179413 179729 179734) (-157 "CMPLXRT.spad" 179116 179133 179395 179400) (-156 "CLLCTAST.spad" 178778 178786 179106 179111) (-155 "CLIP.spad" 174886 174894 178768 178773) (-154 "CLIF.spad" 173541 173557 174842 174881) (-153 "CLAGG.spad" 170078 170088 173531 173536) (-152 "CLAGG.spad" 166483 166495 169938 169943) (-151 "CINTSLPE.spad" 165838 165851 166473 166478) (-150 "CHVAR.spad" 163976 163998 165828 165833) (-149 "CHARZ.spad" 163891 163899 163956 163971) (-148 "CHARPOL.spad" 163417 163427 163881 163886) (-147 "CHARNZ.spad" 163170 163178 163397 163412) (-146 "CHAR.spad" 160538 160546 163160 163165) (-145 "CFCAT.spad" 159866 159874 160528 160533) (-144 "CDEN.spad" 159086 159100 159856 159861) (-143 "CCLASS.spad" 157182 157190 158444 158483) (-142 "CATEGORY.spad" 156256 156264 157172 157177) (-141 "CATCTOR.spad" 156147 156155 156246 156251) (-140 "CATAST.spad" 155773 155781 156137 156142) (-139 "CASEAST.spad" 155487 155495 155763 155768) (-138 "CARTEN2.spad" 154877 154904 155477 155482) (-137 "CARTEN.spad" 150244 150268 154867 154872) (-136 "CARD.spad" 147539 147547 150218 150239) (-135 "CAPSLAST.spad" 147321 147329 147529 147534) (-134 "CACHSET.spad" 146945 146953 147311 147316) (-133 "CABMON.spad" 146500 146508 146935 146940) (-132 "BYTEORD.spad" 146175 146183 146490 146495) (-131 "BYTEBUF.spad" 143876 143884 145162 145189) (-130 "BYTE.spad" 143351 143359 143866 143871) (-129 "BTREE.spad" 142295 142305 142829 142856) (-128 "BTOURN.spad" 141171 141181 141773 141800) (-127 "BTCAT.spad" 140563 140573 141139 141166) (-126 "BTCAT.spad" 139975 139987 140553 140558) (-125 "BTAGG.spad" 139441 139449 139943 139970) (-124 "BTAGG.spad" 138927 138937 139431 139436) (-123 "BSTREE.spad" 137539 137549 138405 138432) (-122 "BRILL.spad" 135744 135755 137529 137534) (-121 "BRAGG.spad" 134700 134710 135734 135739) (-120 "BRAGG.spad" 133620 133632 134656 134661) (-119 "BPADICRT.spad" 131445 131457 131692 131785) (-118 "BPADIC.spad" 131117 131129 131371 131440) (-117 "BOUNDZRO.spad" 130773 130790 131107 131112) (-116 "BOP1.spad" 128231 128241 130763 130768) (-115 "BOP.spad" 123365 123373 128221 128226) (-114 "BOOLEAN.spad" 122803 122811 123355 123360) (-113 "BOOLE.spad" 122453 122461 122793 122798) (-112 "BOOLE.spad" 122101 122111 122443 122448) (-111 "BMODULE.spad" 121813 121825 122069 122096) (-110 "BITS.spad" 121187 121195 121402 121429) (-109 "BINDING.spad" 120608 120616 121177 121182) (-108 "BINARY.spad" 118577 118585 118933 119026) (-107 "BGAGG.spad" 117782 117792 118557 118572) (-106 "BGAGG.spad" 116995 117007 117772 117777) (-105 "BFUNCT.spad" 116559 116567 116975 116990) (-104 "BEZOUT.spad" 115699 115726 116509 116514) (-103 "BBTREE.spad" 112447 112457 115177 115204) (-102 "BASTYPE.spad" 111946 111954 112437 112442) (-101 "BASTYPE.spad" 111443 111453 111936 111941) (-100 "BALFACT.spad" 110902 110915 111433 111438) (-99 "AUTOMOR.spad" 110353 110362 110882 110897) (-98 "ATTREG.spad" 107076 107083 110105 110348) (-97 "ATTRBUT.spad" 103099 103106 107056 107071) (-96 "ATTRAST.spad" 102816 102823 103089 103094) (-95 "ATRIG.spad" 102286 102293 102806 102811) (-94 "ATRIG.spad" 101754 101763 102276 102281) (-93 "ASTCAT.spad" 101658 101665 101744 101749) (-92 "ASTCAT.spad" 101560 101569 101648 101653) (-91 "ASTACK.spad" 100770 100779 101038 101065) (-90 "ASSOCEQ.spad" 99604 99615 100726 100731) (-89 "ASP9.spad" 98685 98698 99594 99599) (-88 "ASP80.spad" 98007 98020 98675 98680) (-87 "ASP8.spad" 97050 97063 97997 98002) (-86 "ASP78.spad" 96501 96514 97040 97045) (-85 "ASP77.spad" 95870 95883 96491 96496) (-84 "ASP74.spad" 94962 94975 95860 95865) (-83 "ASP73.spad" 94233 94246 94952 94957) (-82 "ASP7.spad" 93393 93406 94223 94228) (-81 "ASP6.spad" 92260 92273 93383 93388) (-80 "ASP55.spad" 90769 90782 92250 92255) (-79 "ASP50.spad" 88586 88599 90759 90764) (-78 "ASP49.spad" 87585 87598 88576 88581) (-77 "ASP42.spad" 86000 86039 87575 87580) (-76 "ASP41.spad" 84587 84626 85990 85995) (-75 "ASP4.spad" 83882 83895 84577 84582) (-74 "ASP35.spad" 82870 82883 83872 83877) (-73 "ASP34.spad" 82171 82184 82860 82865) (-72 "ASP33.spad" 81731 81744 82161 82166) (-71 "ASP31.spad" 80871 80884 81721 81726) (-70 "ASP30.spad" 79763 79776 80861 80866) (-69 "ASP29.spad" 79229 79242 79753 79758) (-68 "ASP28.spad" 70502 70515 79219 79224) (-67 "ASP27.spad" 69399 69412 70492 70497) (-66 "ASP24.spad" 68486 68499 69389 69394) (-65 "ASP20.spad" 67950 67963 68476 68481) (-64 "ASP19.spad" 62636 62649 67940 67945) (-63 "ASP12.spad" 62050 62063 62626 62631) (-62 "ASP10.spad" 61321 61334 62040 62045) (-61 "ASP1.spad" 60702 60715 61311 61316) (-60 "ARRAY2.spad" 59941 59950 60180 60207) (-59 "ARRAY12.spad" 58654 58665 59931 59936) (-58 "ARRAY1.spad" 57317 57326 57663 57690) (-57 "ARR2CAT.spad" 53099 53120 57285 57312) (-56 "ARR2CAT.spad" 48901 48924 53089 53094) (-55 "ARITY.spad" 48273 48280 48891 48896) (-54 "APPRULE.spad" 47557 47579 48263 48268) (-53 "APPLYORE.spad" 47176 47189 47547 47552) (-52 "ANY1.spad" 46247 46256 47166 47171) (-51 "ANY.spad" 45098 45105 46237 46242) (-50 "ANTISYM.spad" 43543 43559 45078 45093) (-49 "ANON.spad" 43252 43259 43533 43538) (-48 "AN.spad" 41558 41565 43065 43158) (-47 "AMR.spad" 39743 39754 41456 41553) (-46 "AMR.spad" 37759 37772 39474 39479) (-45 "ALIST.spad" 34599 34620 34949 34976) (-44 "ALGSC.spad" 33734 33760 34471 34524) (-43 "ALGPKG.spad" 29517 29528 33690 33695) (-42 "ALGMFACT.spad" 28710 28724 29507 29512) (-41 "ALGMANIP.spad" 26194 26209 28537 28542) (-40 "ALGFF.spad" 23799 23826 24016 24172) (-39 "ALGFACT.spad" 22918 22928 23789 23794) (-38 "ALGEBRA.spad" 22751 22760 22874 22913) (-37 "ALGEBRA.spad" 22616 22627 22741 22746) (-36 "ALAGG.spad" 22128 22149 22584 22611) (-35 "AHYP.spad" 21509 21516 22118 22123) (-34 "AGG.spad" 19842 19849 21499 21504) (-33 "AGG.spad" 18139 18148 19798 19803) (-32 "AF.spad" 16567 16582 18071 18076) (-31 "ADDAST.spad" 16253 16260 16557 16562) (-30 "ACPLOT.spad" 14844 14851 16243 16248) (-29 "ACFS.spad" 12701 12710 14746 14839) (-28 "ACFS.spad" 10644 10655 12691 12696) (-27 "ACF.spad" 7398 7405 10546 10639) (-26 "ACF.spad" 4238 4247 7388 7393) (-25 "ABELSG.spad" 3779 3786 4228 4233) (-24 "ABELSG.spad" 3318 3327 3769 3774) (-23 "ABELMON.spad" 2861 2868 3308 3313) (-22 "ABELMON.spad" 2402 2411 2851 2856) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2294582 2294587 2294592 2294597) (-2 NIL 2294562 2294567 2294572 2294577) (-1 NIL 2294542 2294547 2294552 2294557) (0 NIL 2294522 2294527 2294532 2294537) (-1328 "ZMOD.spad" 2294331 2294344 2294460 2294517) (-1327 "ZLINDEP.spad" 2293429 2293440 2294321 2294326) (-1326 "ZDSOLVE.spad" 2283389 2283411 2293419 2293424) (-1325 "YSTREAM.spad" 2282884 2282895 2283379 2283384) (-1324 "YDIAGRAM.spad" 2282518 2282527 2282874 2282879) (-1323 "XRPOLY.spad" 2281738 2281758 2282374 2282443) (-1322 "XPR.spad" 2279533 2279546 2281456 2281555) (-1321 "XPOLYC.spad" 2278852 2278868 2279459 2279528) (-1320 "XPOLY.spad" 2278407 2278418 2278708 2278777) (-1319 "XPBWPOLY.spad" 2276846 2276866 2278181 2278250) (-1318 "XFALG.spad" 2273894 2273910 2276772 2276841) (-1317 "XF.spad" 2272357 2272372 2273796 2273889) (-1316 "XF.spad" 2270800 2270817 2272241 2272246) (-1315 "XEXPPKG.spad" 2270059 2270085 2270790 2270795) (-1314 "XDPOLY.spad" 2269673 2269689 2269915 2269984) (-1313 "XALG.spad" 2269341 2269352 2269629 2269668) (-1312 "WUTSET.spad" 2265311 2265328 2268942 2268969) (-1311 "WP.spad" 2264518 2264562 2265169 2265236) (-1310 "WHILEAST.spad" 2264316 2264325 2264508 2264513) (-1309 "WHEREAST.spad" 2263987 2263996 2264306 2264311) (-1308 "WFFINTBS.spad" 2261650 2261672 2263977 2263982) (-1307 "WEIER.spad" 2259872 2259883 2261640 2261645) (-1306 "VSPACE.spad" 2259545 2259556 2259840 2259867) (-1305 "VSPACE.spad" 2259238 2259251 2259535 2259540) (-1304 "VOID.spad" 2258915 2258924 2259228 2259233) (-1303 "VIEWDEF.spad" 2254116 2254125 2258905 2258910) (-1302 "VIEW3D.spad" 2238077 2238086 2254106 2254111) (-1301 "VIEW2D.spad" 2225976 2225985 2238067 2238072) (-1300 "VIEW.spad" 2223696 2223705 2225966 2225971) (-1299 "VECTOR2.spad" 2222335 2222348 2223686 2223691) (-1298 "VECTOR.spad" 2220835 2220846 2221086 2221113) (-1297 "VECTCAT.spad" 2218747 2218758 2220803 2220830) (-1296 "VECTCAT.spad" 2216466 2216479 2218524 2218529) (-1295 "VARIABLE.spad" 2216246 2216261 2216456 2216461) (-1294 "UTYPE.spad" 2215890 2215899 2216236 2216241) (-1293 "UTSODETL.spad" 2215185 2215209 2215846 2215851) (-1292 "UTSODE.spad" 2213401 2213421 2215175 2215180) (-1291 "UTSCAT.spad" 2210880 2210896 2213299 2213396) (-1290 "UTSCAT.spad" 2207979 2207997 2210400 2210405) (-1289 "UTS2.spad" 2207574 2207609 2207969 2207974) (-1288 "UTS.spad" 2202452 2202480 2205972 2206069) (-1287 "URAGG.spad" 2197173 2197184 2202442 2202447) (-1286 "URAGG.spad" 2191858 2191871 2197129 2197134) (-1285 "UPXSSING.spad" 2189476 2189502 2190912 2191045) (-1284 "UPXSCONS.spad" 2187154 2187174 2187527 2187676) (-1283 "UPXSCCA.spad" 2185725 2185745 2187000 2187149) (-1282 "UPXSCCA.spad" 2184438 2184460 2185715 2185720) (-1281 "UPXSCAT.spad" 2183027 2183043 2184284 2184433) (-1280 "UPXS2.spad" 2182570 2182623 2183017 2183022) (-1279 "UPXS.spad" 2179785 2179813 2180621 2180770) (-1278 "UPSQFREE.spad" 2178199 2178213 2179775 2179780) (-1277 "UPSCAT.spad" 2175994 2176018 2178097 2178194) (-1276 "UPSCAT.spad" 2173474 2173500 2175579 2175584) (-1275 "UPOLYC2.spad" 2172945 2172964 2173464 2173469) (-1274 "UPOLYC.spad" 2168025 2168036 2172787 2172940) (-1273 "UPOLYC.spad" 2162991 2163004 2167755 2167760) (-1272 "UPMP.spad" 2161923 2161936 2162981 2162986) (-1271 "UPDIVP.spad" 2161488 2161502 2161913 2161918) (-1270 "UPDECOMP.spad" 2159749 2159763 2161478 2161483) (-1269 "UPCDEN.spad" 2158966 2158982 2159739 2159744) (-1268 "UP2.spad" 2158330 2158351 2158956 2158961) (-1267 "UP.spad" 2155358 2155373 2155745 2155898) (-1266 "UNISEG2.spad" 2154855 2154868 2155314 2155319) (-1265 "UNISEG.spad" 2154208 2154219 2154774 2154779) (-1264 "UNIFACT.spad" 2153311 2153323 2154198 2154203) (-1263 "ULSCONS.spad" 2144223 2144243 2144593 2144742) (-1262 "ULSCCAT.spad" 2141960 2141980 2144069 2144218) (-1261 "ULSCCAT.spad" 2139805 2139827 2141916 2141921) (-1260 "ULSCAT.spad" 2138045 2138061 2139651 2139800) (-1259 "ULS2.spad" 2137559 2137612 2138035 2138040) (-1258 "ULS.spad" 2127130 2127158 2128075 2128504) (-1257 "UINT8.spad" 2127007 2127016 2127120 2127125) (-1256 "UINT64.spad" 2126883 2126892 2126997 2127002) (-1255 "UINT32.spad" 2126759 2126768 2126873 2126878) (-1254 "UINT16.spad" 2126635 2126644 2126749 2126754) (-1253 "UFD.spad" 2125700 2125709 2126561 2126630) (-1252 "UFD.spad" 2124827 2124838 2125690 2125695) (-1251 "UDVO.spad" 2123708 2123717 2124817 2124822) (-1250 "UDPO.spad" 2121289 2121300 2123664 2123669) (-1249 "TYPEAST.spad" 2121208 2121217 2121279 2121284) (-1248 "TYPE.spad" 2121140 2121149 2121198 2121203) (-1247 "TWOFACT.spad" 2119792 2119807 2121130 2121135) (-1246 "TUPLE.spad" 2119283 2119294 2119688 2119693) (-1245 "TUBETOOL.spad" 2116150 2116159 2119273 2119278) (-1244 "TUBE.spad" 2114797 2114814 2116140 2116145) (-1243 "TSETCAT.spad" 2102868 2102885 2114765 2114792) (-1242 "TSETCAT.spad" 2090925 2090944 2102824 2102829) (-1241 "TS.spad" 2089518 2089534 2090484 2090581) (-1240 "TRMANIP.spad" 2083882 2083899 2089206 2089211) (-1239 "TRIMAT.spad" 2082845 2082870 2083872 2083877) (-1238 "TRIGMNIP.spad" 2081372 2081389 2082835 2082840) (-1237 "TRIGCAT.spad" 2080884 2080893 2081362 2081367) (-1236 "TRIGCAT.spad" 2080394 2080405 2080874 2080879) (-1235 "TREE.spad" 2078840 2078851 2079872 2079899) (-1234 "TRANFUN.spad" 2078679 2078688 2078830 2078835) (-1233 "TRANFUN.spad" 2078516 2078527 2078669 2078674) (-1232 "TOPSP.spad" 2078190 2078199 2078506 2078511) (-1231 "TOOLSIGN.spad" 2077853 2077864 2078180 2078185) (-1230 "TEXTFILE.spad" 2076414 2076423 2077843 2077848) (-1229 "TEX1.spad" 2075970 2075981 2076404 2076409) (-1228 "TEX.spad" 2073164 2073173 2075960 2075965) (-1227 "TEMUTL.spad" 2072719 2072728 2073154 2073159) (-1226 "TBCMPPK.spad" 2070820 2070843 2072709 2072714) (-1225 "TBAGG.spad" 2069878 2069901 2070800 2070815) (-1224 "TBAGG.spad" 2068944 2068969 2069868 2069873) (-1223 "TANEXP.spad" 2068352 2068363 2068934 2068939) (-1222 "TALGOP.spad" 2068076 2068087 2068342 2068347) (-1221 "TABLEAU.spad" 2067557 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(-1091 "RNS.spad" 1760952 1760961 1761951 1762044) (-1090 "RNS.spad" 1759941 1759952 1760942 1760947) (-1089 "RNGBIND.spad" 1759101 1759115 1759896 1759901) (-1088 "RNG.spad" 1758836 1758845 1759091 1759096) (-1087 "RMODULE.spad" 1758617 1758628 1758826 1758831) (-1086 "RMCAT2.spad" 1758037 1758094 1758607 1758612) (-1085 "RMATRIX.spad" 1756807 1756826 1757150 1757189) (-1084 "RMATCAT.spad" 1752386 1752417 1756763 1756802) (-1083 "RMATCAT.spad" 1747855 1747888 1752234 1752239) (-1082 "RLINSET.spad" 1747559 1747570 1747845 1747850) (-1081 "RINTERP.spad" 1747447 1747467 1747549 1747554) (-1080 "RING.spad" 1746917 1746926 1747427 1747442) (-1079 "RING.spad" 1746395 1746406 1746907 1746912) (-1078 "RIDIST.spad" 1745787 1745796 1746385 1746390) (-1077 "RGCHAIN.spad" 1744308 1744324 1745202 1745229) (-1076 "RGBCSPC.spad" 1744097 1744109 1744298 1744303) (-1075 "RGBCMDL.spad" 1743659 1743671 1744087 1744092) (-1074 "RFFACTOR.spad" 1743121 1743132 1743649 1743654) (-1073 "RFFACT.spad" 1742856 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(-980 "POLYCATQ.spad" 1583556 1583578 1585420 1585425) (-979 "POLYCAT.spad" 1577058 1577079 1583424 1583551) (-978 "POLYCAT.spad" 1569856 1569879 1576224 1576229) (-977 "POLY2UP.spad" 1569308 1569322 1569846 1569851) (-976 "POLY2.spad" 1568905 1568917 1569298 1569303) (-975 "POLY.spad" 1566168 1566178 1566683 1566810) (-974 "POLUTIL.spad" 1565133 1565162 1566124 1566129) (-973 "POLTOPOL.spad" 1563881 1563896 1565123 1565128) (-972 "POINT.spad" 1562545 1562555 1562632 1562659) (-971 "PNTHEORY.spad" 1559247 1559255 1562535 1562540) (-970 "PMTOOLS.spad" 1558022 1558036 1559237 1559242) (-969 "PMSYM.spad" 1557571 1557581 1558012 1558017) (-968 "PMQFCAT.spad" 1557162 1557176 1557561 1557566) (-967 "PMPREDFS.spad" 1556624 1556646 1557152 1557157) (-966 "PMPRED.spad" 1556111 1556125 1556614 1556619) (-965 "PMPLCAT.spad" 1555188 1555206 1556040 1556045) (-964 "PMLSAGG.spad" 1554773 1554787 1555178 1555183) (-963 "PMKERNEL.spad" 1554352 1554364 1554763 1554768) (-962 "PMINS.spad" 1553932 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 4c82ba30..2ab83e9f 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(205732 . 3508696576) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))))) -((((-560)) . T) (($) -2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +(205732 . 3508766241) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) #0#) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))))) +((((-560)) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) (|has| |#1| (-939)) ((((-887)) . T)) ((((-887)) . T)) @@ -23,23 +23,23 @@ ((((-549)) . T) (((-1190)) . T) (((-229)) . T) (((-391)) . T) (((-915 (-391))) . T)) (((|#1|) . T)) ((((-229)) . T) (((-887)) . T)) -(-2216 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2216 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) +(-2191 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2191 (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (-12 (|has| |#1| (-871)) (|has| |#2| (-871)))) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-870))) -((($ $) . T) ((#0=(-421 (-560)) #0#) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1| |#1|) . 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T)) @@ -52,14 +52,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1213)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -(-2216 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(((|#2| (-496 (-2340 |#1|) (-793))) . T)) -((((-1208)) -2216 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) +(-2191 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(((|#2| (-496 (-2305 |#1|) (-793))) . T)) +((((-1208)) -2191 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) (((|#1| (-545 (-1208))) . T)) ((((-1190)) . T) (((-987 (-130))) . T) (((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((#0=(-893 |#1|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (|has| |#4| (-381)) (|has| |#3| (-381)) @@ -75,14 +75,14 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-571)) -((((-560)) . T) (((-421 (-560))) -2216 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) -((((-2 (|:| -4001 |#1|) (|:| -2440 |#2|))) . T)) +((((-560)) . T) (((-421 (-560))) -2191 (|has| |#2| (-38 (-421 (-560)))) (|has| |#2| (-1069 (-421 (-560))))) ((|#2|) . T) (($) -2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((-888 |#1|)) . T)) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) +((((-2 (|:| -3998 |#1|) (|:| -3881 |#2|))) . T)) ((($) . T)) ((((-887)) |has| |#1| (-632 (-887))) ((|#1|) . T)) -((((-560)) . T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1208)) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-560)) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T) (($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((-1208)) . T)) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-1208)) . T)) (((|#1|) . T)) @@ -103,12 +103,12 @@ ((((-887)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2216 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . 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T) (((-560)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) (((|#2|) . T) (((-560)) . T) ((|#6|) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2216 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2191 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((($) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) ((($ $) . T)) ((($) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) @@ -132,30 +132,30 @@ (|has| |#1| (-381)) (((|#1|) . T)) ((((-887)) . T)) -((((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) (((|#1|) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) -(((|#1|) . 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T)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) (|has| |#1| (-1132)) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) (|has| |#1| (-1132)) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) (|has| |#1| (-870)) (((|#1| |#1|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -170,12 +170,12 @@ (|has| |#3| (-815)) (|has| |#3| (-815)) (((|#1| |#2|) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-1213)) . T)) (((|#1| |#2|) . T)) (((|#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) (((-1208) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1208) |#2|)))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1| (-1208) (-1119 (-1208)) (-545 (-1119 (-1208)))) . T)) ((((-560) |#1|) . T)) @@ -195,29 +195,29 @@ ((((-1190) |#1|) . T)) ((((-1265 (-560)) $) . T) (((-560) (-130)) . T)) (((|#1|) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#3| (-793)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . 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T)) ((((-421 (-560))) . T) (($) . T)) @@ -228,7 +228,7 @@ (((|#1|) . T)) (|has| |#2| (-376)) ((((-1265 (-560)) $) . T) (((-560) |#1|) . T)) -((($) -2216 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2191 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -241,13 +241,13 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#1| |#1|) . T)) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . 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T) (($) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080)))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -258,10 +258,10 @@ ((((-171 (-229))) |has| |#1| (-1051)) (((-171 (-391))) |has| |#1| (-1051)) (((-549)) |has| |#1| (-633 (-549))) (((-1202 |#1|)) . T) (((-915 (-560))) |has| |#1| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#1| (-633 (-915 (-391))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1|) . 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T)) -((((-2 (|:| -4001 |#1|) (|:| -2440 |#2|))) . T) (((-887)) . T)) +((((-2 (|:| -3998 |#1|) (|:| -3881 |#2|))) . T) (((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549))) (((-915 (-391))) |has| |#1| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#1| (-633 (-915 (-560))))) -(((|#4|) -2216 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080)))) -(((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080)))) -((((-2 (|:| -4001 |#1|) (|:| -2440 |#2|))) . T)) +(((|#4|) -2191 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080)))) +(((|#3|) -2191 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080)))) +((((-2 (|:| -3998 |#1|) (|:| -3881 |#2|))) . T)) ((((-887)) . T)) ((((-887)) . T)) ((((-549)) . T) (((-560)) . T) (((-915 (-560))) . T) (((-391)) . T) (((-229)) . T)) @@ -326,15 +326,15 @@ (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) ((($) . 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T)) @@ -349,15 +349,15 @@ (|has| |#1| (-1132)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) ((((-887)) . T) (((-1213)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((((-1213)) . 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T)) (((|#1| (-1002)) . T)) ((((-560)) . T) ((|#2|) . T)) @@ -369,7 +369,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1183)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) +((((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) (|has| (-1285 |#1| |#2| |#3| |#4|) (-147)) (|has| (-1285 |#1| |#2| |#3| |#4|) (-149)) (|has| |#1| (-147)) @@ -381,28 +381,28 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) -((((-1156 |#1| (-1208))) . T) (((-560)) . T) (((-840 (-1208))) . T) (($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1208)) . T)) +((((-1156 |#1| (-1208))) . T) (((-560)) . T) (((-840 (-1208))) . T) (($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1208)) . 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T)) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-887)) . T)) ((((-887)) . T)) (|has| (-1279 |#2| |#3| |#4|) (-149)) @@ -415,18 +415,18 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) (((|#1|) . T)) ((($) . T)) ((((-560) |#1|) . T)) (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-870))) ((((-887)) |has| |#1| (-1132))) -((($) -2216 (|has| |#1| (-240)) (|has| |#1| (-239)))) -(-2216 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-363))) +((($) -2191 (|has| |#1| (-240)) (|has| |#1| (-239)))) +(-2191 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-363))) ((((-935 |#1|)) . T)) ((((-421 |#2|) |#3|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) @@ -437,7 +437,7 @@ ((((-887)) . T)) ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) (|has| |#1| (-376)) -(-2216 (-12 (|has| (-1288 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2191 (-12 (|has| (-1288 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-793) |#1|))) @@ -451,23 +451,23 @@ ((((-1265 (-560)) $) . T) (((-560) |#1|) . T)) ((((-887)) . T)) (((|#2|) . T)) -(-2216 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571)) (((-560)) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) -((((-1288 |#1| |#2| |#3|)) . 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T) (($) -2191 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T)) (((|#1|) . T)) ((((-1208)) -12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842))) -(-2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) -(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-571)))) +(-2191 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560)))) ((|#1| |#1|) . T) (($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($ $) |has| |#1| (-571)) ((|#1| |#1|) . T)) -((($ (-1208)) -2216 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) +((($ (-1208)) -2191 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) (((#0=(-721) (-1202 #0#)) . T)) ((((-595 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-421 (-560))) . T) (($) . T)) @@ -475,18 +475,18 @@ ((((-887)) . T) (((-1298 |#3|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((($) . T) (((-421 (-560))) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2216 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2191 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((((-887)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((($) . T)) -((($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((#1=(-1288 |#1| |#2| |#3|) #1#) |has| |#1| (-376)) ((|#1| |#1|) . T)) -(((|#1| |#1|) . T) (($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((#0=(-421 (-560)) #0#) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . T)) -(((|#1|) . 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T) (($) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376)))) (((|#3|) |has| |#3| (-1080))) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (|has| (-1120 |#1|) (-1132)) (((|#2| (-841 |#1|)) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T)) @@ -494,20 +494,20 @@ (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . 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T)) -((($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-421 $) (-421 $)) |has| |#1| (-571)) (($ $) . T) ((|#1| |#1|) . T)) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((#0=(-1113) |#2|) . T) ((#0# $) . T) (($ $) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) @@ -516,22 +516,22 @@ ((((-246 |#1| |#2|) |#2|) . T)) ((((-887)) . T)) (((|#3|) |has| |#3| (-1132)) (((-560)) -12 (|has| |#3| (-1069 (-560))) (|has| |#3| (-1132))) (((-421 (-560))) -12 (|has| |#3| (-1069 (-421 (-560)))) (|has| |#3| (-1132)))) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#1|) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-549)) |has| |#1| (-633 (-549)))) (((|#1|) |has| |#1| (-175))) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) (|has| |#1| (-376)) ((((-1213)) . T)) (((|#1|) . T)) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-870))) ((($) . T)) ((((-1208) |#1|) |has| |#1| (-528 (-1208) |#1|)) ((|#1| |#1|) |has| |#1| (-321 |#1|))) (|has| |#2| (-842)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-870)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1| |#2| |#3| (-545 |#3|)) . T)) ((((-887)) . T)) @@ -540,15 +540,15 @@ (|has| |#1| (-381)) ((((-421 (-560))) . T)) (((|#1|) . T)) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((((-421 (-560))) . T)) ((((-1190) |#1|) . T)) (|has| |#1| (-381)) ((((-560)) . T)) ((((-560)) . T)) (((|#1|) . T) (((-560)) . T)) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-1208)) -12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1208))))) @@ -562,12 +562,12 @@ ((((-560) |#3|) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) (|has| |#2| (-1080)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) -(-2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) +(-2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((((-887)) . T)) ((((-1285 |#1| |#2| |#3| |#4|)) . T)) ((((-421 (-560))) . T) (((-560)) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -576,9 +576,9 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T)) ((((-560)) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#1|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) -((((-560)) -2216 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) +((((-560)) -2191 (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (|has| |#2| (-1080))) ((|#2|) |has| |#2| (-1132)) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -595,7 +595,7 @@ ((((-887)) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . 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T)) (((|#1|) . T)) @@ -1116,8 +1116,8 @@ (((|#1|) . T)) ((((-1208)) . T)) (|has| |#1| (-571)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-571)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -1129,7 +1129,7 @@ (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-149)) -(((|#2| (-246 (-2340 |#1|) (-793)) (-888 |#1|)) . T)) +(((|#2| (-246 (-2305 |#1|) (-793)) (-888 |#1|)) . T)) (((|#1| (-545 |#3|) |#3|) . T)) (|has| |#1| (-147)) (((#0=(-421 (-560)) #0#) |has| |#2| (-376)) (($ $) . T)) @@ -1143,12 +1143,12 @@ (|has| |#1| (-147)) ((((-421 (-560))) |has| |#2| (-376)) (($) . 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T)) -((((-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) +((((-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) (((|#3|) . T)) ((($ $) . T) ((#0=(-888 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-843)) @@ -1211,10 +1211,10 @@ ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) . T) (($) . T) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| (-1120 |#1|) (-1132)) -(((|#2| |#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)))) -((((-560) (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2| |#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)))) +((((-560) (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) ((((-560)) . T)) ((((-1213)) . T)) ((((-793)) . T)) @@ -1233,34 +1233,34 @@ (((|#1|) . T)) ((((-421 (-560))) . T) (($) . T)) ((($) . T) (((-421 (-560))) . T)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-571))) ((((-1213)) . T)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((((-560)) . T)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-571))) (|has| |#1| (-147)) ((((-560)) . 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T)) -((($) -2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) -((($) -2216 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) +((($) -2191 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2191 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) -2191 (|has| (-421 |#2|) (-240)) (|has| (-421 |#2|) (-239)))) ((((-560) |#2|) . T)) -((($ (-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((($ (-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-381)) @@ -1280,46 +1280,46 @@ ((((-887)) . 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T)) (((|#1|) |has| |#1| (-321 |#1|))) @@ -1329,21 +1329,21 @@ (|has| |#1| (-381)) ((((-1208) $) |has| |#1| (-528 (-1208) $)) (($ $) |has| |#1| (-321 $)) ((|#1| |#1|) |has| |#1| (-321 |#1|)) (((-1208) |#1|) |has| |#1| (-528 (-1208) |#1|))) ((((-1208)) |has| |#1| (-927 (-1208)))) -(-2216 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2191 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((($) . T)) ((((-402) |#1|) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#2|) . T) (((-887)) . T)) ((((-887)) . T)) (((|#2|) . T)) ((((-935 |#1|)) . T)) ((((-887)) . T) (((-1213)) . T)) ((((-1213)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1352,7 +1352,7 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) (((|#1| |#1|) . T)) (((#0=(-893 |#1|)) |has| #0# (-321 #0#))) -((((-560)) . T) (($) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) +((((-560)) . T) (($) -2191 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2191 (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-1069 (-421 (-560))))) ((|#1|) . T)) (((|#1| |#2|) . T)) (|has| |#2| (-815)) (|has| |#2| (-815)) @@ -1361,7 +1361,7 @@ (-12 (|has| |#1| (-815)) (|has| |#2| (-815))) (|has| |#2| (-1080)) ((($) . T) (((-560)) . T) ((|#2|) . T)) -(((|#2|) . T) (((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#2|) . T) (($) . T)) (|has| |#1| (-1234)) (((#0=(-560) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) @@ -1375,7 +1375,7 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-421 (-560)) #0#) . T)) (|has| |#1| (-376)) ((((-560)) . T) (((-421 (-560))) . T) (($) . 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T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) +((($) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-38 (-421 (-560))))) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T)) ((($) . T) (((-560)) . T)) ((((-560) (-146)) . T)) -((((-560) (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T) ((|#1| |#2|) . T)) +((((-560) (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T) ((|#1| |#2|) . T)) ((((-421 (-560))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-887)) . T)) ((((-935 |#1|)) . T)) (|has| |#1| (-376)) @@ -1423,11 +1423,11 @@ (|has| |#1| (-376)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-870)) -((($) -2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) -(((#0=(-421 (-560)) #0#) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1| |#1|) . T)) +(((#0=(-421 (-560)) #0#) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1| |#1|) . T)) ((((-421 (-560))) |has| |#1| (-1069 (-560))) (((-560)) |has| |#1| (-1069 (-560))) (((-1208)) |has| |#1| (-1069 (-1208))) ((|#1|) . T)) ((($) . T)) ((($) . T)) @@ -1485,7 +1485,7 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) ((((-560)) |has| |#1| (-911 (-560))) (((-391)) |has| |#1| (-911 (-391)))) -((((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) ((|#1|) . 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T)) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) -(((|#2| |#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(((|#2| |#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (((|#2|) . T) (((-560)) . T)) ((((-887)) . T)) ((((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T) ((|#2|) . T)) ((((-887)) . T)) ((((-887)) . T)) ((((-1190) (-1208) (-560) (-229) (-887)) . T)) @@ -1559,9 +1559,9 @@ ((((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((($) . T) (((-421 (-560))) . T)) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080)))) (|has| $ (-149)) ((((-421 |#2|)) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1069 (-421 (-560)))) (((-560)) |has| #0# (-1069 (-560))) ((#0#) . T)) @@ -1570,11 +1570,11 @@ (|has| |#2| (-149)) (|has| |#1| (-149)) (|has| |#1| (-147)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) (((|#1|) . T)) (|has| |#2| (-240)) @@ -1611,9 +1611,9 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-1027 |#1|)) . T) ((|#1|) . T)) -((((-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208)))) (((-840 (-1208))) . T)) +((((-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208)))) (((-840 (-1208))) . T)) ((((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-421 (-560))) . T) (((-421 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1202 |#1|)) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) @@ -1622,8 +1622,8 @@ (((|#1|) . T) (((-560)) . T) (($) . T)) (((|#2|) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#2|) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) @@ -1636,30 +1636,30 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) ((((-1288 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1288 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((#0=(-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) #0#) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))))) (((|#2| |#2|) . T)) -(-2216 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) +(-2191 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (-12 (|has| |#1| (-376)) (|has| |#2| (-239)))) (|has| |#2| (-376)) (((|#2|) . T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1|) |has| |#1| (-175))) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) -((($) -2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939)))) +((($) -2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#1| (-1132)) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-38 (-421 (-560)))) ((((-1190) (-51)) . T)) (((|#1|) . 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T)) -((((-560)) -2216 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) ((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080))) +((((-560)) -2191 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) ((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080))) (($) |has| |#2| (-1080))) (((|#1|) . T)) ((((-560) |#3|) . T)) ((((-560) (-146)) . T)) @@ -1675,7 +1675,7 @@ ((((-560)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1|) . T)) -((($ (-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) +((($ (-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) ((((-146)) . T)) ((((-887)) . T)) @@ -1686,26 +1686,26 @@ (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) -(-2216 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2191 (|has| |#2| (-240)) (|has| |#2| (-239))) ((((-560) (-146)) . T) (((-1265 (-560)) $) . T)) -(((#0=(-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) #0#) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) -((($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +(((#0=(-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) #0#) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (|has| |#1| (-871)) (((|#2| (-793) (-1113)) . T)) (((|#1| |#2|) . T)) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) (|has| |#1| (-813)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-571))) -((((-1208)) -2216 (-12 (|has| (-1288 |#1| |#2| |#3|) (-927 (-1208))) (|has| |#1| (-376))) (-12 (|has| (-1288 |#1| |#2| |#3|) (-929 (-1208))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-571))) +((((-1208)) -2191 (-12 (|has| (-1288 |#1| |#2| |#3|) (-927 (-1208))) (|has| |#1| (-376))) (-12 (|has| (-1288 |#1| |#2| |#3|) (-929 (-1208))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))))) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208))))) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208))))) (((|#1|) |has| |#1| (-175))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2216 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) +(-2191 (|has| |#1| (-149)) (-12 (|has| |#1| (-376)) (|has| |#2| (-149)))) (((|#4|) . T)) -(-2216 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) +(-2191 (|has| |#1| (-147)) (-12 (|has| |#1| (-376)) (|has| |#2| (-147)))) ((((-1190) |#1|) . T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1719,24 +1719,24 @@ (((|#3|) . T)) ((((-1288 |#1| |#2| |#3|)) |has| |#1| (-376))) ((($) . T) (((-560)) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T)) -((((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1206 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) +((((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1206 |#1| |#2| |#3|)) |has| |#1| (-376)) (((-560)) . T) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-560)) . T) (($) . T)) ((((-887)) . T)) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) (((-560)) . T) (($) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132))) (((-987 |#1|)) . T)) (|has| |#1| (-870)) (|has| |#1| (-870)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-987 |#1|)) . T)) -(((|#4|) -2216 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) -(((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) +(((|#4|) -2191 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)))) +(((|#3|) -2191 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)))) (|has| |#2| (-376)) (((|#1|) |has| |#1| (-175))) -(((|#4|) -2216 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) -(((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) +(((|#4|) -2191 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-748)) (|has| |#4| (-1080)))) +(((|#3|) -2191 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080)))) (((|#2|) |has| |#2| (-1080))) (((|#2|) |has| |#2| (-1080))) ((((-1190) |#1|) . T)) @@ -1748,8 +1748,8 @@ ((((-402) (-1190)) . T)) ((($ (-1208)) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((((-887)) -2216 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1298 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -3830 (-1190)) (|:| -2715 #0#))) . T)) +((((-887)) -2191 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-632 (-887))) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-381)) (|has| |#2| (-748)) (|has| |#2| (-815)) (|has| |#2| (-871)) (|has| |#2| (-1080)) (|has| |#2| (-1132))) (((-1298 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3818 (-1190)) (|:| -2660 #0#))) . T)) (((|#1|) . T)) ((((-887)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) @@ -1758,7 +1758,7 @@ ((((-560)) . T)) (|has| |#2| (-149)) (|has| |#1| (-487)) -(-2216 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) +(-2191 (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) (|has| |#1| (-376)) ((((-887)) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -1769,8 +1769,8 @@ (|has| |#1| (-870)) ((((-887)) . T)) (((|#2|) . T)) -((((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2216 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) -(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2216 (|has| |#1| (-376)) (|has| |#1| (-571)))) +((((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) |has| |#1| (-175))) +(((|#1|) |has| |#1| (-175)) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) -2191 (|has| |#1| (-376)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . T) (((-560)) . T) (((-841 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1779,8 +1779,8 @@ ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-887)) . T)) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2340 |#1|) (-793)) (-888 |#1|)) . T)) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2305 |#1|) (-793)) (-888 |#1|)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1| (-545 (-1208)) (-1208)) . T)) (((|#1|) . T)) @@ -1801,19 +1801,19 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +(((|#1|) . T) (((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-1208) (-51)) . 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T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) (|has| |#1| (-871)) (|has| |#1| (-871)) @@ -1834,15 +1834,15 @@ (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#1|) |has| |#1| (-175))) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)))) -((($) -2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -(-2216 (|has| |#2| (-376)) (|has| |#2| (-466)) (|has| |#2| (-939))) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . 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T)) @@ -1851,7 +1851,7 @@ (|has| |#1| (-842)) (|has| |#1| (-842)) (((|#1|) . T)) -(-2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-870)) (|has| |#1| (-870)) (|has| |#1| (-870)) @@ -1860,14 +1860,14 @@ ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-1208)) |has| |#1| (-927 (-1208))) (((-1113)) . T)) (((|#1|) . T)) (|has| |#1| (-870)) -(((#0=(-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) #0#) |has| (-2 (|:| -3830 (-1190)) (|:| -2715 (-51))) (-321 (-2 (|:| -3830 (-1190)) (|:| -2715 (-51)))))) +(((#0=(-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) #0#) |has| (-2 (|:| -3818 (-1190)) (|:| -2660 (-51))) (-321 (-2 (|:| -3818 (-1190)) (|:| -2660 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#1| (-1132)) ((((-887)) . T) (((-1213)) . T)) @@ -1891,14 +1891,14 @@ (((|#3|) . T)) (((|#1| (-793) (-1113)) . T)) ((((-146)) . T)) -((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2216 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) +((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2191 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) (((|#1|) . T)) (((|#2|) . T)) ((((-146)) . 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T)) (|has| |#1| (-147)) (|has| |#1| (-149)) @@ -1917,31 +1917,31 @@ ((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571))) ((($) |has| |#1| (-571))) (((|#2|) . T)) -((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2216 (|has| |#1| (-175)) (|has| |#1| (-571)))) +((((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (($) -2191 (|has| |#1| (-175)) (|has| |#1| (-571)))) ((($) |has| |#1| (-571)) ((|#1|) . T)) ((($) |has| |#1| (-870))) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) (|has| |#1| (-939)) ((((-1208)) . T)) ((((-887)) . T)) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-571))) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (((-1288 |#1| |#2| |#3|)) |has| |#1| (-376)) ((|#1|) . 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T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) ((((-694 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1975,7 +1975,7 @@ ((((-887)) . T)) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-887)) . T)) -((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) |has| |#2| (-175)) (($) -2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) ((((-1213)) . T)) ((((-421 (-560))) . T) (($) . T) (((-421 |#1|)) . T) ((|#1|) . T) (((-560)) . T)) (((|#3|) . T) (((-560)) . T) (((-630 $)) . T)) @@ -1983,12 +1983,12 @@ ((((-887)) . T)) ((((-887)) . T)) (((|#2|) . T)) -(-2216 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-381)) (|has| |#3| (-748)) (|has| |#3| (-815)) (|has| |#3| (-871)) (|has| |#3| (-1080)) (|has| |#3| (-1132))) +(-2191 (|has| |#3| (-21)) (|has| |#3| (-23)) (|has| |#3| (-25)) (|has| |#3| (-133)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-381)) (|has| |#3| (-748)) (|has| |#3| (-815)) (|has| |#3| (-871)) (|has| |#3| (-1080)) (|has| |#3| (-1132))) (|has| |#2| (-1080)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . 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T)) ((($) |has| |#1| (-240))) @@ -2243,12 +2243,12 @@ (|has| |#1| (-147)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) |has| |#1| (-175))) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-560)) . T) ((|#1|) . T) (($) . T) (((-421 (-560))) . T) (((-1208)) |has| |#1| (-1069 (-1208)))) (((|#1| |#2|) . T)) -((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2216 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) -(-2216 (-12 (|has| |#4| (-240)) (|has| |#4| (-1080))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1080)))) -(-2216 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) -2191 (|has| |#1| (-870)) (|has| |#1| (-1069 (-560)))) ((|#1|) . T)) +(-2191 (-12 (|has| |#4| (-240)) (|has| |#4| (-1080))) (-12 (|has| |#4| (-239)) (|has| |#4| (-1080)))) +(-2191 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((((-146)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2259,13 +2259,13 @@ ((((-887)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . 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T) (($ (-1208)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208))))) (|has| |#1| (-939)) @@ -2273,7 +2273,7 @@ (((|#2|) |has| |#2| (-1080))) (|has| |#1| (-376)) ((($) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))))) (((|#1|) |has| |#1| (-175))) ((($ (-888 |#1|)) . T)) (((|#1| |#1|) . T)) @@ -2284,7 +2284,7 @@ (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-663 $)) . T) (((-1190)) . T) (((-1208)) . T) (((-560)) . T) (((-229)) . T) (((-887)) . T)) -((((-560)) -2216 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) ((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080))) +((((-560)) -2191 (|has| |#3| (-21)) (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) ((|#3|) -2191 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-748)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080))) ((((-421 (-560))) . T) (((-560)) . T) (((-630 $)) . T)) (((|#1|) . T)) ((((-887)) . T)) @@ -2300,7 +2300,7 @@ (((|#1| (-793) (-1113)) . T)) ((((-887)) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-560)) -2216 (|has| (-421 (-560)) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) . T)) +(((|#1|) . T) (((-560)) -2191 (|has| (-421 (-560)) (-1069 (-560))) (|has| |#1| (-1069 (-560)))) (((-421 (-560))) . T)) (((|#1| (-616 |#1| |#3|) (-616 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) @@ -2320,37 +2320,37 @@ ((((-721)) . T)) ((((-721)) . T)) (((|#2|) |has| |#2| (-175))) -(-2216 (|has| |#1| (-240)) (|has| |#1| (-239))) +(-2191 (|has| |#1| (-240)) (|has| |#1| (-239))) ((((-560)) . T) ((|#2|) . T) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) -((((-114)) |has| |#1| (-1132)) (((-887)) -2216 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132)))) +((((-114)) |has| |#1| (-1132)) (((-887)) -2191 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1190)) (|:| -2660 (-51)))) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . T)) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) -((((-1208)) -2216 (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))))) +((((-1208)) -2191 (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))))) ((((-560)) . T) (((-421 (-560))) . T) (($) . T)) ((((-887)) . T)) ((((-721)) . T) (((-421 (-560))) . T) (((-560)) . T)) (((|#1| |#1|) |has| |#1| (-175))) (((|#2|) . T)) -((($) . T) (((-560)) . T) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) +((($) . T) (((-560)) . T) (((-421 (-560))) -2191 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . T)) ((((-560) |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|))))) +(((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) (((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|))))) ((((-391)) . T)) ((((-721)) . T)) ((((-421 (-560))) . #0=(|has| |#2| (-376))) (($) . #0#)) (((|#1|) |has| |#1| (-175))) ((((-421 (-975 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#1|) . T)) (((|#2|) . T)) (((|#3|) |has| |#3| (-1080))) @@ -2362,7 +2362,7 @@ ((((-1208)) |has| |#2| (-927 (-1208)))) (|has| |#1| (-871)) ((((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (|has| |#1| (-813)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-487)) @@ -2370,8 +2370,8 @@ (|has| |#1| (-381)) (|has| |#1| (-381)) (|has| |#1| (-376)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) -((($) -2216 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-175)) (|has| |#1| (-487)) (|has| |#1| (-571)) (|has| |#1| (-1080)) (|has| |#1| (-1143))) +((($) -2191 (|has| |#1| (-240)) (|has| |#1| (-239)) (|has| |#1| (-363)))) ((((-118 |#1|)) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-363)) @@ -2383,7 +2383,7 @@ (|has| |#1| (-38 (-421 (-560)))) (((|#2|) . T) (((-887)) . T)) (((|#2|) . T) (((-887)) . T)) -((($ (-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) +((($ (-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2393,18 +2393,18 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-871)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) +((((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (|has| |#1| (-149)) (|has| |#1| (-147)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) |has| (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)) (-321 (-2 (|:| -3830 |#1|) (|:| -2715 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) |has| (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)) (-321 (-2 (|:| -3818 |#1|) (|:| -2660 |#2|)))) ((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) (((|#2|) . T)) (|has| |#1| (-15 * (|#1| (-560) |#1|))) (((|#3|) . T)) ((((-118 |#1|)) . T)) (|has| |#1| (-381)) -(-2216 (-12 (|has| (-1288 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1288 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) +(-2191 (-12 (|has| (-1288 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1288 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-871)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T)) @@ -2423,17 +2423,17 @@ (((|#1|) |has| |#1| (-376))) (((|#1|) |has| |#1| (-376))) ((((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((($ $) . T) (((-630 $) $) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) ((($) . 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T)) -((((-1208)) -2216 (-12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1208))) (|has| |#3| (-1080))))) +((((-1208)) -2191 (-12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1208))) (|has| |#3| (-1080))))) ((((-663 (-802 |#1| (-888 |#2|)))) . T) (((-887)) . T)) ((((-549)) |has| (-802 |#1| (-888 |#2|)) (-633 (-549)))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -2442,17 +2442,17 @@ (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) (((|#1|) |has| |#1| (-175))) ((((-887)) . T)) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-939))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-939))) (((|#1|) . T)) ((($) . T)) ((($) |has| |#1| (-571)) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) -2216 (|has| |#1| (-175)) (|has| |#1| (-571))) ((|#1|) . 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T)) ((((-560)) -12 (|has| |#1| (-21)) (|has| |#2| (-21)))) @@ -2460,13 +2460,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((((-560)) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (((#0=(-1279 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560)))) (($) . T)) ((((-560)) . T)) ((($) . 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T)) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) (((|#3|) -12 (|has| |#3| (-321 |#3|)) (|has| |#3| (-1132)))) ((((-1265 (-560)) $) . T) (((-560) |#1|) . T)) (((|#1|) . T)) @@ -2544,16 +2544,16 @@ ((((-421 (-560))) . T) (($) . T)) ((((-421 (-560))) . T) (($) . T)) ((((-421 (-560))) . T) (($) . T)) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-1253))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-1253))) ((($) . T)) ((((-421 (-560))) |has| #0=(-421 |#2|) (-1069 (-421 (-560)))) (((-560)) |has| #0# (-1069 (-560))) ((#0#) . T)) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| (-793)) . T)) (|has| |#1| (-871)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) -((($) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) (((-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-363))) ((|#1|) . 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T)) @@ -2642,13 +2642,13 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (|has| |#2| (-147)) (|has| |#2| (-149)) -(-2216 (|has| |#2| (-842)) (|has| |#2| (-871))) +(-2191 (|has| |#2| (-842)) (|has| |#2| (-871))) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) ((((-560)) . T) ((|#1|) . T)) (((|#2|) . T) (($) . T) (((-560)) . T)) (((|#2|) . T)) -((((-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((((-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-376))) ((((-421 |#2|)) . T)) @@ -2657,10 +2657,10 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-560)) . T) (($) . T) (((-421 (-560))) . 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T)) (((|#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132)))) -((($ (-1208)) -2216 (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))))) +((($ (-1208)) -2191 (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))))) ((((-421 (-560))) . T) (((-560)) . T) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (|has| |#1| (-38 (-421 (-560)))) @@ -2695,13 +2695,13 @@ (|has| |#1| (-147)) (|has| |#1| (-149)) ((($ $) . 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T)) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) -(((|#2|) -2216 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) -((($ (-1208)) -2216 (-12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1208))) (|has| |#3| (-1080))))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)))) +(((|#2|) -2191 (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-748)) (|has| |#2| (-1080)))) +((($ (-1208)) -2191 (-12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080))) (-12 (|has| |#3| (-929 (-1208))) (|has| |#3| (-1080))))) ((($ $) . T) ((#0=(-1279 |#2| |#3| |#4|) #0#) . T) ((#1=(-421 (-560)) #1#) |has| #0# (-38 (-421 (-560))))) ((((-935 |#1|)) . T)) (-12 (|has| |#1| (-376)) (|has| |#2| (-842))) @@ -2787,14 +2787,14 @@ ((((-887)) . T)) ((($) . T) (((-560)) . T)) ((($) . T)) -(-2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-376)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1279 |#2| |#3| |#4|)) . T) (((-421 (-560))) |has| #0# (-38 (-421 (-560))))) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) -(-2216 (-12 (|has| |#1| (-319)) (|has| |#1| (-939))) (|has| |#1| (-376)) (|has| |#1| (-363))) -(-2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) +(-2191 (-12 (|has| |#1| (-319)) (|has| |#1| (-939))) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) ((((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-887)) . T)) @@ -2832,7 +2832,7 @@ ((($) . T)) (((|#4|) . T)) ((($) . T)) -((($ (-1208)) -2216 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1208)))))) +((($ (-1208)) -2191 (-12 (|has| |#1| (-376)) (|has| |#1| (-927 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#1| (-929 (-1208)))))) ((((-887)) . T)) (((|#1| (-545 (-1208))) . T)) ((($ $) . T)) @@ -2842,29 +2842,29 @@ (((|#2|) . T)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) (((|#2|) . 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T) (((-560)) . T)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1190)) (|:| -2660 (-51)))) . T)) (((|#1|) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((((-887)) . T)) (((|#1| |#2|) . T)) ((($) . T) (((-560)) . T)) (((|#1| (-421 (-560))) . T)) (((|#1|) . T)) -(-2216 (|has| |#1| (-302)) (|has| |#1| (-376))) +(-2191 (|has| |#1| (-302)) (|has| |#1| (-376))) ((((-146)) . T)) ((((-560)) |has| #0=(-421 |#2|) (-660 (-560))) ((#0#) . T) (((-421 (-560))) . T) (($) . T)) (|has| |#1| (-870)) @@ -2880,7 +2880,7 @@ ((((-887)) . T)) ((((-887)) . T)) ((((-186)) . T) (((-887)) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -2897,8 +2897,8 @@ (|has| |#1| (-871)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) -((($) -2216 (-12 (|has| (-1206 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1206 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) +((((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) +((($) -2191 (-12 (|has| (-1206 |#1| |#2| |#3|) (-240)) (|has| |#1| (-376))) (-12 (|has| (-1206 |#1| |#2| |#3|) (-239)) (|has| |#1| (-376))) (|has| |#1| (-15 * (|#1| (-560) |#1|))))) ((((-887)) . T)) (((|#2|) |has| |#2| (-376))) ((((-887)) . T)) @@ -2913,19 +2913,19 @@ (|has| |#3| (-1080)) (|has| |#1| (-1132)) ((((-1208) (-51)) . T)) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . 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T) (($ $) . T)) ((((-560)) . T)) (((|#1|) . T)) @@ -2937,12 +2937,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (|has| |#1| (-842)) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) ((((-421 |#2|)) . T)) (|has| |#1| (-870)) -((((-1235 |#1|)) . T) (((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-1235 |#1|)) . T) (((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) . T) ((#1=(-560) #1#) . T) (($ $) . T)) ((((-935 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) (((|#2|) |has| |#2| (-1080)) (((-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080)))) @@ -2961,36 +2961,36 @@ (((|#2|) |has| |#2| (-175))) (((|#1|) . T)) (((|#2|) . 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T)) (((#0=(-1285 |#1| |#2| |#3| |#4|) $) |has| #0# (-298 #0# #0#))) (|has| |#1| (-376)) -(-2216 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) -(((|#1|) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) (((-560)) -2216 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)))) +(-2191 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(((|#1|) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080))) (($) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080))) (((-560)) -2191 (|has| |#1| (-21)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)))) (((#0=(-1113) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-363))) (((#0=(-421 (-560)) #0#) . T) ((#1=(-721) #1#) . T) (($ $) . T)) ((((-326 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) |has| |#1| (-376))) ((((-887)) . T)) (|has| |#1| (-1132)) (((|#1|) . T)) -(((|#1|) -2216 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) -(((|#1|) -2216 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2191 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) +(((|#1|) -2191 (|has| |#2| (-380 |#1|)) (|has| |#2| (-432 |#1|)))) (((|#2|) . T)) ((((-421 (-560))) . T) (((-721)) . T) (($) . T)) ((((-593)) . T)) (((|#3| |#3|) . T)) -((($ (-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((($ (-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) (|has| |#1| (-871)) (|has| |#2| (-240)) ((((-888 |#1|)) . T)) @@ -3011,10 +3011,10 @@ (|has| |#1| (-1132)) (((|#2|) . T)) (((|#1|) . T)) -((($) -2216 (|has| |#1| (-240)) (|has| |#1| (-239)))) +((($) -2191 (|has| |#1| (-240)) (|has| |#1| (-239)))) ((((-560)) . T)) (((|#2|) . T) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (($) . T) (((-560)) . T)) -(-2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) (((|#2|) . T) (((-560)) |has| |#2| (-660 (-560)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -3057,7 +3057,7 @@ (|has| |#2| (-1051)) ((($) . T)) (|has| |#1| (-939)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#4|) . T)) ((($) . T)) (((|#2|) . T)) @@ -3067,32 +3067,32 @@ (|has| |#1| (-376)) ((((-935 |#1|)) . T)) ((($) . T) (((-560)) . T) ((|#1|) . T) (((-421 (-560))) . T)) -((($) -2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) -((($) |has| |#1| (-870)) (((-560)) -2216 (|has| |#1| (-21)) (|has| |#1| (-870)))) +((($) -2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) |has| |#1| (-870)) (((-560)) -2191 (|has| |#1| (-21)) (|has| |#1| (-870)))) ((($ $) . T) ((#0=(-421 (-560)) #0#) . T)) -(-2216 (|has| |#1| (-381)) (|has| |#1| (-871))) +(-2191 (|has| |#1| (-381)) (|has| |#1| (-871))) (((|#1|) . T)) ((((-793)) . T)) ((((-887)) . T)) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208))))) ((((-421 |#2|) |#3|) . T)) -(-2216 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) +(-2191 (-12 (|has| |#3| (-240)) (|has| |#3| (-1080))) (-12 (|has| |#3| (-239)) (|has| |#3| (-1080)))) ((($) . T) (((-421 (-560))) . T)) ((($) . T) (((-560)) . T) (((-421 (-560))) . T) (((-630 $)) . T)) ((((-560)) . T) (($) . T)) ((((-560)) . T) (($) . T)) ((((-793) |#1|) . T)) -(((|#2| (-246 (-2340 |#1|) (-793))) . T)) +(((|#2| (-246 (-2305 |#1|) (-793))) . T)) (((|#1| (-545 |#3|)) . T)) ((((-421 (-560))) . T)) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((((-1190)) . T) (((-887)) . T)) -(((#0=(-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) #0#) |has| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (-321 (-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))))) +(((#0=(-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) #0#) |has| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (-321 (-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))))) ((((-1190)) . T)) (|has| |#1| (-939)) (|has| |#2| (-376)) (((|#1|) . T) (($) . T) (((-560)) . T)) -(-2216 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2191 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -3109,12 +3109,12 @@ (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -(-2216 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-319)) (|has| |#1| (-376)) (|has| |#1| (-363))) (|has| |#1| (-38 (-421 (-560)))) (-12 (|has| |#1| (-559)) (|has| |#1| (-843))) ((((-887)) . T)) (|has| |#1| (-376)) -((((-1208)) -2216 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))))) +((((-1208)) -2191 (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))))) (|has| |#1| (-376)) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208))))) ((((-421 (-560))) . T) (($) . T)) @@ -3126,13 +3126,13 @@ ((((-560) |#1|) . T)) ((((-1208)) |has| |#1| (-927 (-1208)))) (((|#1|) . T)) -(-2216 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) +(-2191 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363))) (((|#2|) |has| |#1| (-376))) (((|#2|) |has| |#1| (-376))) -(-2216 (|has| |#4| (-815)) (|has| |#4| (-871))) -(-2216 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2191 (|has| |#4| (-815)) (|has| |#4| (-871))) +(-2191 (|has| |#3| (-815)) (|has| |#3| (-871))) ((((-560)) . T) (($) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-175))) @@ -3167,7 +3167,7 @@ (|has| |#1| (-871)) ((((-887)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (((|#1|) . T)) ((($) . T) (((-560)) . T) ((|#2|) . T)) @@ -3176,27 +3176,27 @@ (((|#3|) . T)) ((((-1190)) . T) (((-520)) . T) (((-229)) . T) (((-560)) . T)) (((|#1|) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) (((|#4| |#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) -(-2216 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2191 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#2|) . T)) (((|#2|) . T)) (|has| |#2| (-1080)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) -((((-2 (|:| -3830 (-1190)) (|:| -2715 |#1|))) . T)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) +((((-2 (|:| -3818 (-1190)) (|:| -2660 |#1|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (|has| |#1| (-38 (-421 (-560)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-421 (-560)))) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) ((($) . T)) (|has| |#1| (-149)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-381))) (|has| |#1| (-149)) ((($) . T)) ((((-595 |#1|)) . T)) @@ -3212,7 +3212,7 @@ ((((-421 (-560))) |has| |#2| (-1069 (-560))) (((-560)) |has| |#2| (-1069 (-560))) (((-1208)) |has| |#2| (-1069 (-1208))) ((|#2|) . T)) (((#0=(-421 |#2|) #0#) . T) ((#1=(-421 (-560)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(-2216 (|has| |#1| (-147)) (|has| |#1| (-363))) +(-2191 (|has| |#1| (-147)) (|has| |#1| (-363))) (|has| |#1| (-149)) ((((-887)) . T)) ((($) . T)) @@ -3232,15 +3232,15 @@ ((((-421 |#2|)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +((((-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208))))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) (|has| |#1| (-813)) (|has| |#1| (-813)) ((((-887)) . T)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T) (((-560)) . T)) ((((-887)) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-115)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -3250,7 +3250,7 @@ (((|#1|) |has| |#1| (-175)) (($) |has| |#1| (-571)) (((-421 (-560))) |has| |#1| (-571))) ((((-887)) . T)) ((((-887)) . T)) -(-2216 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) +(-2191 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080)))) (((#0=(-935 |#1|) #0#) . T) (($ $) . T) ((#1=(-421 (-560)) #1#) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -3262,10 +3262,10 @@ ((((-887)) . T)) (((|#2|) . T)) ((((-560)) . T)) -((((-1208)) -2216 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) +((((-1208)) -2191 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) ((((-887)) . T)) ((((-560)) . T)) -(-2216 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2191 (|has| |#2| (-815)) (|has| |#2| (-871))) ((((-171 (-391))) . T) (((-229)) . T) (((-391)) . T)) ((((-887)) . T)) ((((-887)) . T)) @@ -3277,11 +3277,11 @@ (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (|has| |#1| (-376)) (|has| |#1| (-376)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-887)) . T)) ((((-560) $) . T) (((-663 (-560)) $) . T)) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-487)) (|has| |#1| (-748)) (|has| |#1| (-927 (-1208))) (|has| |#1| (-1080)) (|has| |#1| (-1143)) (|has| |#1| (-1132))) (|has| |#1| (-1183)) ((((-935 |#1|)) . T) (((-421 (-560))) . T) (($) . T)) ((($) . T)) @@ -3291,22 +3291,22 @@ (((#0=(-118 |#1|) $) |has| #0# (-298 #0# #0#))) (((|#1|) |has| |#1| (-175))) ((((-326 |#1|)) . T) (((-560)) . T)) -(-2216 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2191 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1| |#1|) . T)) ((((-887)) . T)) (((|#1|) . T)) ((((-115)) . T) ((|#1|) . T)) ((((-887)) . T)) -((((-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((((-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) (((|#1|) |has| |#1| (-321 |#1|))) ((((-560) |#1|) . T) (((-1265 (-560)) $) . T)) (((|#1| |#2|) . T)) ((((-1208) |#1|) . T)) -(((|#1|) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)))) +(((|#1|) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)))) (((|#1|) . T)) ((($ (-1208)) . T)) -(((|#1|) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) +(((|#1|) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-1080)))) ((((-560)) . T) (((-421 (-560))) . T)) (((|#1|) . T)) (|has| |#1| (-571)) @@ -3315,15 +3315,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-421 |#2|)) . T) (((-421 (-560))) . T) (($) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) (|has| |#1| (-376)) (|has| |#1| (-571)) ((($) . T)) (|has| |#1| (-1132)) ((((-802 |#1| (-888 |#2|))) |has| (-802 |#1| (-888 |#2|)) (-321 (-802 |#1| (-888 |#2|))))) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -3332,17 +3332,17 @@ (((|#1| (-793)) . T)) (|has| |#1| (-240)) (((|#1| (-545 (-1119 (-1208)))) . 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T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1208)) . T)) +((((-1156 |#1| (-1208))) . T) (((-560)) . T) (((-1119 (-1208))) . T) (($) -2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1069 (-421 (-560))))) (((-1208)) . T)) (((|#1|) |has| |#1| (-175))) (((|#1| (-1298 |#1|) (-1298 |#1|)) . T)) ((((-595 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) @@ -3375,7 +3375,7 @@ ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((|#1|) . T) (((-560)) . T)) (((|#1|) . T)) ((((-887)) . T)) -(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2216 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +(((#0=(-421 (-560)) #0#) |has| |#2| (-38 (-421 (-560)))) ((|#2| |#2|) . T) (($ $) -2191 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) ((((-305 |#3|)) . T)) (((|#1|) . T)) @@ -3384,30 +3384,30 @@ (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) (((|#1|) . T) (((-421 (-560))) . T) (($) . T)) -((($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) -((($ $) -2216 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) +((($ $) -2191 (|has| |#1| (-175)) (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1| |#1|) . T) ((#0=(-421 (-560)) #0#) |has| |#1| (-38 (-421 (-560))))) (((|#2|) . 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T)) -(-2216 (|has| |#2| (-815)) (|has| |#2| (-871))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#2| (-815)) (|has| |#2| (-871))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) ((((-1208)) . T) ((|#1|) . T)) @@ -3419,15 +3419,15 @@ (((#0=(-421 (-560)) #0#) . T)) ((((-421 (-560))) . T)) (((|#1|) |has| |#1| (-175))) -(-2216 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) +(-2191 (|has| |#2| (-21)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-1080))) (((|#1|) . T)) (((|#1|) . T)) -(-2216 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2191 (|has| |#2| (-21)) (|has| |#2| (-23)) (|has| |#2| (-25)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) (((|#1|) . T)) ((((-421 (-560))) . T) (((-560)) . 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T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) ((((-1113)) . T) ((|#2|) . T) (((-560)) |has| |#2| (-1069 (-560))) (((-421 (-560))) |has| |#2| (-1069 (-421 (-560))))) (((|#1|) . T)) @@ -3477,11 +3477,11 @@ ((($) |has| |#1| (-381))) (|has| |#2| (-842)) (|has| |#2| (-842)) -((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) +((((-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) ((|#2|) |has| |#1| (-376)) (($) . T) ((|#1|) . T)) ((($ (-1208)) |has| |#1| (-927 (-1208)))) (((|#1|) . T) (((-560)) |has| |#1| (-1069 (-560))) (((-421 (-560))) |has| |#1| (-1069 (-421 (-560))))) -((($) -2216 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) -(((|#1|) . T) (((-421 (-560))) -2216 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) +((($) -2191 (-12 (|has| |#1| (-240)) (|has| |#1| (-376))) (-12 (|has| |#1| (-239)) (|has| |#1| (-376))) (|has| |#1| (-363)))) +(((|#1|) . T) (((-421 (-560))) -2191 (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-376))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) ((((-560)) |has| |#1| (-911 (-560))) (((-391)) |has| |#1| (-911 (-391)))) (((|#1|) . T)) @@ -3496,7 +3496,7 @@ (-12 (|has| |#1| (-376)) (|has| |#2| (-939))) (|has| |#1| (-376)) (((|#4|) -12 (|has| |#4| (-321 |#4|)) (|has| |#4| (-1132)))) -(((|#2|) -2216 (|has| |#2| (-6 (-4511 "*"))) (|has| |#2| (-175)))) +(((|#2|) -2191 (|has| |#2| (-6 (-4511 "*"))) (|has| |#2| (-175)))) (((|#2|) . T)) (|has| |#1| (-376)) (((|#2|) . T)) @@ -3510,12 +3510,12 @@ (((|#2| (-793)) . T)) ((((-1208)) . T)) ((((-893 |#1|)) . 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T) (((-421 (-560))) . T) (((-560)) |has| |#2| (-660 (-560)))) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) (((|#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) (((|#1| |#1|) -12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132)))) @@ -3542,7 +3542,7 @@ (((|#1|) . T)) ((((-887)) . T)) (|has| |#2| (-939)) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560))))) ((((-887)) . T)) ((((-887)) . T)) @@ -3553,7 +3553,7 @@ ((((-1202 |#1|)) . T) (((-887)) . T)) ((((-887)) . T)) ((((-421 (-560))) |has| |#2| (-1069 (-421 (-560)))) (((-560)) |has| |#2| (-1069 (-560))) ((|#2|) . T) (((-888 |#1|)) . T)) -((((-1208)) -2216 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208)))) (((-1113)) . T)) +((((-1208)) -2191 (|has| |#1| (-927 (-1208))) (|has| |#1| (-929 (-1208)))) (((-1113)) . T)) ((((-118 |#1|)) . T) (($) . T) (((-421 (-560))) . T)) ((((-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) (((-560)) |has| |#1| (-1069 (-560))) ((|#1|) . T) (((-1208)) . T)) ((((-887)) . T)) @@ -3573,10 +3573,10 @@ ((((-663 |#1|)) . T)) ((($) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|)))) ((($) . T) (((-560)) . T) (((-1285 |#1| |#2| |#3| |#4|)) . T) (((-421 (-560))) . 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T)) @@ -3591,16 +3591,16 @@ ((((-421 |#2|) |#3|) . T)) (((|#1|) . T)) ((((-887)) . T)) -(-2216 (|has| |#1| (-102)) (|has| |#1| (-1132))) -(((|#2| (-496 (-2340 |#1|) (-793))) . T)) +(-2191 (|has| |#1| (-102)) (|has| |#1| (-1132))) +(((|#2| (-496 (-2305 |#1|) (-793))) . T)) ((((-560) |#1|) . T)) ((((-1190)) . T) (((-887)) . T)) (((|#2| |#2|) . T)) (((|#1| (-545 (-1208))) . T)) -(-2216 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) +(-2191 (|has| |#2| (-21)) (|has| |#2| (-133)) (|has| |#2| (-175)) (|has| |#2| (-376)) (|has| |#2| (-815)) (|has| |#2| (-1080))) ((((-560)) . T)) (((|#2|) . T)) -((($) -2216 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) +((($) -2191 (-12 (|has| |#2| (-240)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))))) (((|#2|) . T)) ((((-1208)) |has| |#1| (-927 (-1208))) (((-1113)) . T)) (((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) @@ -3609,9 +3609,9 @@ ((($) . T) (((-421 (-560))) . T)) ((($) . T)) ((($) . T)) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) (((|#1|) . T)) -((($) -2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((($) -2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) |has| |#1| (-175)) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) ((((-887)) . T)) ((((-146)) . T)) (((|#1|) . T) (((-421 (-560))) . T)) @@ -3620,7 +3620,7 @@ ((((-887)) . T)) (((|#1|) . T)) (|has| |#1| (-1183)) -((($ (-1208)) -2216 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) +((($ (-1208)) -2191 (|has| (-421 |#2|) (-927 (-1208))) (|has| (-421 |#2|) (-929 (-1208))))) (((|#1|) . T)) (((|#1| (-545 (-888 |#2|)) (-888 |#2|) (-802 |#1| (-888 |#2|))) . T)) ((((-421 $) (-421 $)) |has| |#1| (-571)) (($ $) . T) ((|#1| |#1|) . T)) @@ -3645,44 +3645,44 @@ (|has| |#1| (-1132)) (|has| |#1| (-1132)) (|has| |#2| (-376)) -(((|#1|) . T) (($) -2216 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) +(((|#1|) . T) (($) -2191 (|has| |#1| (-302)) (|has| |#1| (-376))) (((-421 (-560))) |has| |#1| (-376))) (|has| |#1| (-376)) (|has| |#1| (-376)) -((($) -2216 (|has| |#2| (-240)) (|has| |#2| (-239)))) +((($) -2191 (|has| |#2| (-240)) (|has| |#2| (-239)))) ((((-560)) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-1132)) -((($ (-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((($ (-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) ((((-1208)) -12 (|has| |#4| (-927 (-1208))) (|has| |#4| (-1080)))) ((((-1208)) -12 (|has| |#3| (-927 (-1208))) (|has| |#3| (-1080)))) (((|#1|) . T)) (|has| |#1| (-240)) -(((|#2| (-246 (-2340 |#1|) (-793))) . T)) +(((|#2| (-246 (-2305 |#1|) (-793))) . 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T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) +((((-421 (-560))) |has| |#2| (-38 (-421 (-560)))) ((|#2|) . T) (($) -2191 (|has| |#2| (-175)) (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939)))) +((($) -2191 (|has| |#1| (-175)) (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) (((|#1|) . T) (($) . T) (((-421 (-560))) . T)) @@ -3724,11 +3724,11 @@ (((|#1|) . 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T)) ((((-887)) . T) (((-1213)) . T)) -((((-663 |#1|)) . T) (((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-663 |#1|)) . T) (((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-1213)) . T)) ((((-1213)) . T)) ((((-1213)) . T)) @@ -3752,19 +3752,19 @@ ((((-1213)) . T)) ((((-887)) . T) (((-1213)) . T)) ((((-1213)) . T)) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) |has| (-2 (|:| -3830 (-1208)) (|:| -2715 (-51))) (-321 (-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))))) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) |has| (-2 (|:| -3818 (-1208)) (|:| -2660 (-51))) (-321 (-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) ((((-560) |#1|) . T)) ((((-560) |#1|) . T)) ((((-560) |#1|) . 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T)) ((((-1208)) -12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080)))) (|has| |#2| (-1080)) -(-2216 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) +(-2191 (-12 (|has| |#1| (-487)) (|has| |#2| (-487))) (-12 (|has| |#1| (-748)) (|has| |#2| (-748)))) (|has| |#1| (-147)) (|has| |#1| (-149)) (|has| |#1| (-376)) @@ -4010,7 +4010,7 @@ (((|#1| |#2|) . T)) ((((-560)) . T) ((|#2|) |has| |#2| (-175))) ((((-115)) . T) ((|#1|) . T) (((-560)) . T)) -(-2216 (|has| |#1| (-363)) (|has| |#1| (-381))) +(-2191 (|has| |#1| (-363)) (|has| |#1| (-381))) (((|#1| |#2|) . T)) ((((-229)) . T)) ((((-421 (-560))) . T) (($) . T) (((-560)) . T)) @@ -4019,11 +4019,11 @@ ((($) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((|#1|) . T) (((-560)) |has| |#1| (-660 (-560)))) ((($) . T) (((-560)) |has| |#1| (-660 (-560))) ((|#1|) . T) (((-421 (-560))) |has| |#1| (-38 (-421 (-560))))) (((|#2|) |has| |#2| (-1132)) (((-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) (((-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132)))) -(-2216 (|has| |#2| (-240)) (|has| |#2| (-239))) +(-2191 (|has| |#2| (-240)) (|has| |#2| (-239))) (((|#1|) . T)) (((|#1|) . T)) ((((-549)) |has| |#1| (-633 (-549)))) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-871)) (|has| |#1| (-1132)))) ((((-560) $) . T) (((-663 (-560)) $) . T)) ((($) . T) (((-421 (-560))) . T)) (|has| |#1| (-939)) @@ -4035,14 +4035,14 @@ (((|#1| |#1|) |has| |#1| (-175))) (((|#1|) . T) (((-560)) . T)) ((((-1213)) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-571))) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-571))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#2|) . T)) -(-2216 (|has| |#1| (-21)) (|has| |#1| (-870))) +(-2191 (|has| |#1| (-21)) (|has| |#1| (-870))) (((|#1|) |has| |#1| (-175))) (((|#1|) . T)) (((|#1|) . T)) -((((-887)) -2216 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) +((((-887)) -2191 (-12 (|has| |#1| (-632 (-887))) (|has| |#2| (-632 (-887)))) (-12 (|has| |#1| (-1132)) (|has| |#2| (-1132))))) ((((-421 |#2|) |#3|) . T)) ((((-421 (-560))) . T) (($) . T)) (|has| |#1| (-38 (-421 (-560)))) @@ -4051,7 +4051,7 @@ ((($) . T) (((-560)) . T)) (|has| (-421 |#2|) (-149)) (|has| (-421 |#2|) (-147)) -(-2216 (|has| |#3| (-815)) (|has| |#3| (-871))) +(-2191 (|has| |#3| (-815)) (|has| |#3| (-871))) ((($) . T)) ((((-721)) . T)) (((|#1|) . T) (((-421 (-560))) . T) (((-560)) . T) (($) . T)) @@ -4067,7 +4067,7 @@ ((((-1213)) . T)) ((((-560)) . T)) (((|#2|) . T)) -((((-1208)) -2216 (-12 (|has| (-1206 |#1| |#2| |#3|) (-927 (-1208))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))))) +((((-1208)) -2191 (-12 (|has| (-1206 |#1| |#2| |#3|) (-927 (-1208))) (|has| |#1| (-376))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208)))))) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208))))) ((((-1208)) -12 (|has| |#1| (-15 * (|#1| (-793) |#1|))) (|has| |#1| (-927 (-1208))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -4083,11 +4083,11 @@ ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) ((((-1171 |#1| |#2|)) . T)) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) -(((|#2|) . T) (((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) ((($) . T)) (|has| |#1| (-1051)) -(((|#2|) . T) (((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) ((($) . T)) ((((-887)) . T)) ((((-549)) |has| |#2| (-633 (-549))) (((-915 (-560))) |has| |#2| (-633 (-915 (-560)))) (((-915 (-391))) |has| |#2| (-633 (-915 (-391)))) (((-391)) . #0=(|has| |#2| (-1051))) (((-229)) . #0#)) @@ -4096,7 +4096,7 @@ (((|#1|) . T)) (|has| |#1| (-38 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560)))) -((((-1208)) -2216 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) +((((-1208)) -2191 (|has| |#2| (-927 (-1208))) (|has| |#2| (-929 (-1208))))) ((((-887)) . T)) (((|#2|) . T)) ((((-887)) . T)) @@ -4106,15 +4106,15 @@ ((((-1206 |#1| |#2| |#3|)) . T)) ((((-1206 |#1| |#2| |#3|)) . T) (((-1199 |#1| |#2| |#3|)) . T)) ((((-887)) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T)) ((((-1206 |#1| |#2| |#3|)) |has| |#1| (-376))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-376)) -(((|#3|) . T) ((|#2|) . T) ((|#4|) -2216 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) -(((|#2|) . T) ((|#3|) -2216 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) +(((|#3|) . T) ((|#2|) . T) ((|#4|) -2191 (|has| |#4| (-175)) (|has| |#4| (-376)) (|has| |#4| (-1080))) (($) |has| |#4| (-1080)) (((-560)) -12 (|has| |#4| (-660 (-560))) (|has| |#4| (-1080)))) +(((|#2|) . T) ((|#3|) -2191 (|has| |#3| (-175)) (|has| |#3| (-376)) (|has| |#3| (-1080))) (($) |has| |#3| (-1080)) (((-560)) -12 (|has| |#3| (-660 (-560))) (|has| |#3| (-1080)))) (((|#1|) . T)) (((|#1|) . T)) ((((-118 |#1|)) . T)) @@ -4128,7 +4128,7 @@ ((((-186)) . T) (((-887)) . T)) ((((-887)) . T)) (((|#1|) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) ((((-560) |#1|) . T) (((-1265 (-560)) $) . T)) ((((-887)) . T)) (((|#1|) . T)) @@ -4136,14 +4136,14 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) (($ $) . T) (((-560) |#1|) . T)) ((($ $) . T) (((-421 (-560)) |#1|) . T)) -(-2216 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) +(-2191 (|has| |#1| (-376)) (|has| |#1| (-466)) (|has| |#1| (-939))) ((($ (-1208)) |has| |#1| (-1080))) -(-2216 (|has| |#1| (-871)) (|has| |#1| (-1132))) +(-2191 (|has| |#1| (-871)) (|has| |#1| (-1132))) ((((-887)) . T)) ((((-887)) . T)) ((((-887)) . T)) (((|#1| (-545 |#2|)) . T)) -((((-2 (|:| -3830 (-1208)) (|:| -2715 (-51)))) . T)) +((((-2 (|:| -3818 (-1208)) (|:| -2660 (-51)))) . T)) ((((-560) (-130)) . T)) (((|#1| (-560)) . T)) (((|#1| (-421 (-560))) . T)) @@ -4158,8 +4158,8 @@ ((((-1213)) . T)) ((((-887)) . T) (((-1213)) . T)) ((((-887)) . T) (((-1213)) . T)) -(-2216 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) -(-2216 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) +(-2191 (|has| |#2| (-466)) (|has| |#2| (-571)) (|has| |#2| (-939))) +(-2191 (|has| |#1| (-466)) (|has| |#1| (-571)) (|has| |#1| (-939))) ((($) . T)) (((|#2| (-545 (-888 |#1|))) . T)) ((((-1213)) . T)) @@ -4174,7 +4174,7 @@ ((((-1213)) . T)) ((((-887)) . T) (((-1213)) . T)) ((((-1213)) . T)) -((((-887)) -2216 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) +((((-887)) -2191 (|has| |#1| (-632 (-887))) (|has| |#1| (-1132)))) (((|#1| |#2|) . T)) (((|#1|) . T)) ((((-1190) |#1|) . T)) @@ -4182,7 +4182,7 @@ ((((-421 |#2|)) . T)) (|has| |#1| (-571)) (|has| |#1| (-571)) -((((-2 (|:| -3830 |#1|) (|:| -2715 |#2|))) . T)) +((((-2 (|:| -3818 |#1|) (|:| -2660 |#2|))) . T)) (((|#2| (-793)) . T)) ((($) . T) ((|#2|) . T)) ((($) . T) (((-421 (-560))) . T)) @@ -4192,14 +4192,14 @@ ((((-560)) . T) (($) . 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-1248) T) ((-534 . -1248) T) ((-1199 . -351) 199571) ((-1172 . -503) 199542) ((-1199 . -390) 199494) ((-1118 . -1088) T) ((-450 . -102) T) ((-187 . -1132) T) ((-260 . -34) T) ((-259 . -34) T) ((-1190 . -874) T) ((-872 . -635) 199478) ((-803 . -1088) T) ((-802 . -1088) T) ((-753 . -927) 199455) ((-468 . -1088) T) ((-58 . -503) 199439) ((-1065 . -1087) 199413) ((-533 . -503) 199397) ((-530 . -503) 199381) ((-511 . -503) 199365) ((-510 . -503) 199349) ((-252 . -528) 199282) ((-1065 . -111) 199249) ((-1206 . -927) 199162) ((-1205 . -927) 199068) ((-692 . -1143) T) ((-1199 . -927) 198901) ((-667 . -93) T) ((-1157 . -927) 198885) ((-353 . -1183) T) ((-334 . -1087) 198867) ((-31 . -504) 198848) ((-260 . -816) 198827) ((-260 . -815) 198806) ((-259 . -816) 198785) ((-259 . -815) 198764) ((-31 . -632) 198730) ((-50 . -1088) T) ((-260 . -748) 198708) ((-259 . -748) 198686) ((-1241 . -1132) T) ((-692 . -23) T) ((-595 . -1088) T) ((-532 . -1088) T) ((-391 . -1087) 198651) ((-334 . -111) 198626) 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196913) ((-1202 . -670) 196802) ((-1156 . -670) 196691) ((-878 . -670) 196665) ((-740 . -632) 196647) ((-561 . -381) T) ((-1320 . -23) T) ((-716 . -929) NIL) ((-1319 . -23) T) ((-505 . -1132) T) ((-391 . -635) 196597) ((-391 . -637) 196579) ((-1065 . -1080) T) ((-889 . -102) T) ((-1220 . -298) 196558) ((-171 . -381) 196509) ((-1035 . -1248) T) ((-1002 . -1248) T) ((-943 . -1248) T) ((-856 . -635) 196463) ((-850 . -635) 196418) ((-44 . -23) T) ((-1328 . -102) T) ((-493 . -298) 196397) ((-597 . -1132) T) ((-1177 . -1140) 196366) ((-443 . -1248) T) ((-1134 . -1135) 196318) ((-404 . -21) T) ((-404 . -25) T) ((-154 . -1143) T) ((-1241 . -739) 196215) ((-1228 . -1132) T) ((-1035 . -909) 196197) ((-1035 . -911) 196179) ((-642 . -234) 196163) ((-642 . -274) 196147) ((-638 . -21) T) ((-301 . -571) T) ((-638 . -25) T) ((-1035 . -1069) 196107) ((-733 . -739) 196072) ((-246 . -390) 196041) ((-391 . -1080) T) ((-227 . -1088) T) ((-119 . -274) 196018) ((-119 . -234) 195995) ((-58 . -298) 195947) 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T) ((-530 . -19) 194521) ((-510 . -19) 194505) ((-58 . -618) 194482) ((-1034 . -239) 194419) ((-930 . -102) 194369) ((-878 . -748) T) ((-803 . -1132) T) ((-530 . -618) 194346) ((-510 . -618) 194323) ((-802 . -1132) T) ((-802 . -1096) 194290) ((-475 . -1132) T) ((-468 . -1132) T) ((-597 . -739) 194265) ((-671 . -1132) T) ((-1288 . -47) 194242) ((-1285 . -102) T) ((-1279 . -47) 194212) ((-1258 . -47) 194189) ((-1241 . -175) 194140) ((-1205 . -319) 194119) ((-1199 . -319) 194098) ((-1127 . -635) 194079) ((-1122 . -635) 194060) ((-1110 . -571) 194011) ((-1110 . -1253) 193962) ((-1104 . -635) 193943) ((-1035 . -927) NIL) ((-1097 . -635) 193924) ((-692 . -133) T) ((-646 . -1143) T) ((-1067 . -635) 193905) ((-1050 . -635) 193886) ((-736 . -1087) 193856) ((-734 . -921) 193759) ((-721 . -668) 193709) ((-286 . -1132) T) ((-86 . -455) T) ((-86 . -410) T) ((-733 . -175) T) ((-659 . -1087) 193693) ((-50 . -1132) T) ((-609 . -47) 193670) ((-229 . -670) 193635) ((-595 . -1132) T) ((-532 . -1132) T) 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T) ((-492 . -93) T) ((-421 . -239) 191161) ((-368 . -632) 191143) ((-366 . -632) 191125) ((-358 . -632) 191107) ((-275 . -633) 190855) ((-275 . -632) 190837) ((-255 . -632) 190819) ((-255 . -633) 190680) ((-140 . -93) T) ((-139 . -93) T) ((-135 . -93) T) ((-1172 . -632) 190662) ((-1151 . -662) 190649) ((-1151 . -1082) 190636) ((-841 . -748) T) ((-841 . -881) T) ((-616 . -300) 190613) ((-595 . -739) 190578) ((-493 . -633) NIL) ((-493 . -632) 190560) ((-532 . -739) 190505) ((-326 . -102) T) ((-325 . -102) T) ((-301 . -23) T) ((-154 . -133) T) ((-935 . -632) 190487) ((-935 . -633) 190469) ((-400 . -748) T) ((-896 . -1087) 190421) ((-896 . -111) 190359) ((-736 . -1080) T) ((-734 . -1274) 190343) ((-716 . -363) NIL) ((-115 . -102) T) ((-141 . -102) T) ((-137 . -102) T) ((-533 . -632) 190275) ((-391 . -819) T) ((-170 . -1248) T) ((-227 . -1132) T) ((-391 . -814) T) ((-58 . -633) 190236) ((-229 . -816) T) ((-229 . -813) T) ((-58 . -632) 190148) ((-229 . -748) T) ((-530 . -633) 190109) ((-530 . -632) 190021) ((-511 . -632) 189953) ((-510 . -633) 189914) ((-510 . -632) 189826) ((-1110 . -376) 189777) ((-40 . -426) 189754) ((-78 . -1248) T) ((-895 . -939) NIL) ((-372 . -341) 189738) ((-372 . -376) T) ((-367 . -341) 189722) ((-367 . -376) T) ((-359 . -341) 189706) ((-359 . -376) T) ((-326 . -296) 189685) ((-108 . -376) T) ((-70 . -1248) T) ((-661 . -1132) T) ((-1258 . -351) 189637) ((-895 . -670) 189582) ((-1258 . -390) 189534) ((-993 . -133) 189389) ((-837 . -133) 189260) ((-45 . -874) NIL) ((-987 . -673) 189244) ((-1257 . -684) T) ((-1118 . -175) 189155) ((-987 . -385) 189139) ((-1093 . -816) T) ((-1093 . -813) T) ((-896 . -635) 189037) ((-803 . -175) 188928) ((-802 . -175) 188839) ((-838 . -47) 188801) ((-1093 . -748) T) ((-339 . -503) 188785) ((-975 . -748) T) ((-1312 . -321) 188723) ((-1288 . -927) 188636) ((-468 . -175) 188547) ((-252 . -298) 188499) ((-1284 . -1087) 188334) ((-1279 . -927) 188240) ((-1263 . -1087) 188048) ((-495 . -748) T) ((-1258 . -927) 187881) ((-1241 . -302) 187860) ((-1218 . -1248) T) ((-1215 . -381) T) ((-1214 . -381) T) ((-1177 . -153) 187844) ((-1151 . -102) T) ((-1146 . -1132) T) ((-1110 . -23) T) ((-1110 . -1143) T) ((-1107 . -102) T) ((-1089 . -632) 187811) ((-1034 . -424) 187783) ((-954 . -984) T) ((-758 . -321) 187721) ((-76 . -1248) T) ((-686 . -397) 187693) ((-171 . -939) 187646) ((-30 . -984) T) ((-114 . -866) T) ((-1 . -632) 187628) ((-1027 . -921) 187549) ((-131 . -673) 187531) ((-50 . -640) 187515) ((-716 . -668) 187450) ((-609 . -927) 187363) ((-452 . -102) T) ((-143 . -321) NIL) ((-131 . -385) 187345) ((-896 . -1080) T) ((-854 . -871) 187324) ((-81 . -1248) T) ((-733 . -302) T) ((-40 . -1088) T) ((-595 . -175) T) ((-532 . -175) T) ((-526 . -632) 187306) ((-171 . -670) 187180) ((-521 . -632) 187162) ((-365 . -149) 187144) ((-365 . -147) T) ((-372 . -1143) T) ((-367 . -1143) T) ((-359 . -1143) T) ((-1035 . -319) T) ((-943 . -319) T) ((-896 . -250) T) ((-108 . -1143) T) ((-896 . -240) 187123) ((-1284 . -111) 186944) ((-1263 . -111) 186733) ((-252 . -1287) 186717) ((-560 . -870) T) ((-372 . -23) T) ((-353 . -363) T) ((-326 . -321) 186704) ((-325 . -321) 186645) ((-367 . -23) T) ((-331 . -133) T) ((-359 . -23) T) ((-1035 . -1051) T) ((-31 . -635) 186626) ((-108 . -23) T) ((-678 . -1082) 186610) ((-252 . -618) 186587) ((-661 . -739) 186571) ((-345 . -1132) T) ((-678 . -662) 186541) ((-1285 . -38) 186433) ((-1267 . -939) 186412) ((-114 . -1132) T) ((-838 . -1248) T) ((-427 . -1248) T) ((-1066 . -102) T) ((-1267 . -670) 186301) ((-895 . -816) NIL) ((-879 . -670) 186275) ((-895 . -813) NIL) ((-838 . -911) NIL) ((-895 . -748) T) ((-1118 . -528) 186148) ((-803 . -528) 186095) ((-802 . -528) 186047) ((-585 . -670) 186034) ((-838 . -1069) 185862) ((-468 . -528) 185805) ((-402 . -403) T) ((-1284 . -635) 185618) ((-1263 . -635) 185366) ((-60 . -1248) T) ((-638 . -871) 185345) ((-514 . -684) T) ((-1177 . -1007) 185314) ((-1055 . -668) 185251) ((-1034 . -466) T) ((-721 . -870) T) ((-525 . -814) T) 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-1132) T) ((-918 . -102) T) ((-803 . -302) 183568) ((-339 . -19) 183552) ((-58 . -300) 183529) ((-802 . -302) 183460) ((-879 . -748) T) ((-119 . -870) NIL) ((-530 . -300) 183437) ((-339 . -618) 183414) ((-510 . -300) 183391) ((-468 . -302) 183322) ((-1066 . -321) 183173) ((-900 . -504) 183154) ((-900 . -632) 183120) ((-703 . -504) 183101) ((-585 . -748) T) ((-698 . -504) 183082) ((-703 . -632) 183032) ((-698 . -632) 182998) ((-674 . -632) 182980) ((-492 . -504) 182961) ((-492 . -632) 182927) ((-252 . -633) 182888) ((-252 . -504) 182865) ((-140 . -504) 182846) ((-139 . -504) 182827) ((-135 . -504) 182808) ((-252 . -632) 182700) ((-216 . -102) T) ((-140 . -632) 182666) ((-139 . -632) 182632) ((-135 . -632) 182598) ((-1179 . -34) T) ((-972 . -1248) T) ((-357 . -739) 182543) ((-692 . -25) T) ((-692 . -21) T) ((-1208 . -635) 182524) ((-343 . -1248) T) ((-488 . -1080) T) ((-652 . -432) 182489) ((-620 . -432) 182454) ((-1151 . -1183) T) ((-1279 . -319) 182433) ((-734 . -1082) 182256) ((-595 . -302) T) ((-532 . -302) T) ((-1258 . -319) 182235) ((-488 . -240) 182187) ((-488 . -250) 182166) ((-453 . -1248) T) ((-734 . -662) 181995) ((-1258 . -1051) NIL) ((-1110 . -133) T) ((-896 . -819) 181974) ((-146 . -102) T) ((-40 . -1132) T) ((-896 . -814) 181953) ((-663 . -1041) 181937) ((-594 . -1088) T) ((-560 . -1088) T) ((-509 . -1088) T) ((-421 . -466) T) ((-372 . -133) T) ((-326 . -414) 181921) ((-325 . -414) 181882) ((-367 . -133) T) ((-359 . -133) T) ((-1213 . -1132) T) ((-1151 . -38) 181869) ((-1120 . -632) 181836) ((-108 . -133) T) ((-983 . -1132) T) ((-948 . -1132) T) ((-793 . -1132) T) ((-694 . -1132) T) ((-723 . -149) T) ((-623 . -102) T) ((-118 . -149) T) ((-1320 . -21) T) ((-1320 . -25) T) ((-1319 . -21) T) ((-1319 . -25) T) ((-686 . -1087) 181820) ((-545 . -871) T) ((-514 . -871) T) ((-377 . -1248) T) ((-368 . -1087) 181772) ((-366 . -1087) 181724) ((-358 . -1087) 181676) ((-260 . -1248) T) ((-259 . -1248) T) ((-275 . -1087) 181519) ((-255 . -1087) 181362) ((-686 . -111) 181341) ((-839 . -1253) 181320) ((-562 . -866) T) ((-326 . -929) 181286) ((-368 . -111) 181224) ((-366 . -111) 181162) ((-358 . -111) 181100) ((-275 . -111) 180929) ((-255 . -111) 180758) ((-325 . -929) NIL) ((-642 . -426) 180742) ((-44 . -21) T) ((-44 . -25) T) ((-931 . -874) 180693) ((-130 . -684) T) ((-837 . -660) 180599) ((-839 . -571) 180578) ((-501 . -874) T) ((-260 . -1069) 180405) ((-259 . -1069) 180232) ((-128 . -121) 180216) ((-221 . -874) T) ((-935 . -1087) 180181) ((-734 . -102) T) ((-721 . -1088) T) ((-611 . -635) 180162) ((-600 . -635) 180143) ((-549 . -637) 180046) ((-357 . -175) T) ((-154 . -21) T) ((-154 . -25) T) ((-87 . -632) 180028) ((-935 . -111) 179984) ((-40 . -739) 179929) ((-893 . -1132) T) ((-686 . -635) 179906) ((-667 . -635) 179887) ((-368 . -635) 179824) ((-366 . -635) 179761) ((-358 . -635) 179698) ((-562 . -1132) T) ((-339 . -633) 179659) ((-339 . -632) 179571) ((-275 . -635) 179324) ((-255 . -635) 179109) ((-190 . -1248) T) ((-1263 . -814) 179062) 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177526) ((-1085 . -23) T) ((-1055 . -870) T) ((-935 . -1080) T) ((-334 . -670) 177508) ((-723 . -239) T) ((-692 . -236) 177453) ((-1205 . -950) 177432) ((-1199 . -950) 177411) ((-1199 . -842) NIL) ((-1027 . -1082) 177307) ((-996 . -1248) T) ((-935 . -250) T) ((-839 . -376) 177286) ((-218 . -1132) T) ((-394 . -23) T) ((-129 . -1132) 177264) ((-123 . -1132) 177242) ((-935 . -240) T) ((-131 . -34) T) ((-391 . -670) 177207) ((-1027 . -662) 177155) ((-893 . -739) 177142) ((-1328 . -668) 177114) ((-1077 . -153) 177079) ((-1024 . -1248) T) ((-887 . -1248) T) ((-40 . -175) T) ((-716 . -426) 177061) ((-734 . -321) 177048) ((-856 . -670) 177008) ((-850 . -670) 176982) ((-331 . -25) T) ((-331 . -21) T) ((-676 . -298) 176961) ((-594 . -1132) T) ((-560 . -1132) T) ((-509 . -1132) T) ((-1202 . -1248) T) ((-252 . -300) 176938) ((-1156 . -1248) T) ((-878 . -1248) T) ((-325 . -274) 176899) ((-325 . -234) 176860) ((-1254 . -874) T) ((-1202 . -911) NIL) ((-55 . -1132) T) ((-1156 . -911) 176719) ((-130 . -871) T) ((-1202 . -1069) 176599) ((-1156 . -1069) 176482) ((-187 . -632) 176464) ((-878 . -1069) 176360) ((-803 . -298) 176287) ((-839 . -1143) T) ((-1065 . -748) T) ((-1077 . -1007) 176216) ((-616 . -673) 176200) ((-1034 . -921) 176107) ((-1027 . -102) T) ((-839 . -23) T) ((-734 . -1183) 176085) ((-716 . -1088) T) ((-616 . -385) 176069) ((-365 . -466) T) ((-357 . -302) T) ((-1301 . -1132) T) ((-256 . -1132) T) ((-413 . -102) T) ((-301 . -21) T) ((-301 . -25) T) ((-374 . -748) T) ((-732 . -1132) T) ((-721 . -1132) T) ((-374 . -487) T) ((-1241 . -632) 176051) ((-1202 . -390) 176035) ((-1156 . -390) 176019) ((-1055 . -426) 175981) ((-143 . -233) 175963) ((-391 . -816) T) ((-391 . -813) T) ((-893 . -175) T) ((-391 . -748) T) ((-733 . -632) 175945) ((-734 . -38) 175774) ((-1298 . -1297) 175758) ((-365 . -416) T) ((-1298 . -1132) 175708) ((-1222 . -1132) T) ((-594 . -739) 175695) ((-560 . -739) 175682) ((-509 . -739) 175647) ((-1285 . -668) 175537) ((-326 . -649) 175516) ((-856 . -748) T) 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T) ((-900 . -635) 174698) ((-736 . -670) 174658) ((-501 . -1253) T) ((-703 . -635) 174639) ((-698 . -635) 174620) ((-659 . -670) 174604) ((-221 . -1253) T) ((-421 . -921) 174525) ((-229 . -1069) 174485) ((-40 . -302) T) ((-501 . -571) T) ((-492 . -635) 174466) ((-372 . -25) T) ((-326 . -668) 174121) ((-325 . -668) 174035) ((-372 . -21) T) ((-367 . -25) T) ((-367 . -21) T) ((-221 . -571) T) ((-359 . -25) T) ((-359 . -21) T) ((-331 . -236) 173981) ((-252 . -635) 173958) ((-140 . -635) 173939) ((-139 . -635) 173920) ((-135 . -635) 173901) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1088) T) ((-594 . -175) T) ((-560 . -175) T) ((-509 . -175) T) ((-1093 . -1248) T) ((-975 . -1248) T) ((-735 . -1248) T) ((-661 . -298) 173868) ((-676 . -632) 173850) ((-495 . -1248) T) ((-758 . -759) 173834) ((-346 . -632) 173816) ((-68 . -396) T) ((-68 . -410) T) ((-1128 . -107) 173800) ((-1093 . -911) 173782) ((-975 . -911) 173707) ((-677 . -1143) T) ((-642 . -739) 173694) ((-495 . -911) NIL) ((-1177 . -102) T) ((-1120 . -637) 173678) ((-1093 . -1069) 173660) ((-97 . -632) 173642) ((-491 . -149) T) ((-975 . -1069) 173522) ((-119 . -739) 173467) ((-734 . -929) 173374) ((-677 . -23) T) ((-495 . -1069) 173250) ((-1118 . -633) NIL) ((-1118 . -632) 173232) ((-803 . -633) NIL) ((-803 . -632) 173193) ((-802 . -633) 172827) ((-802 . -632) 172741) ((-1144 . -660) 172647) ((-820 . -874) 172626) ((-475 . -632) 172608) ((-468 . -632) 172590) ((-468 . -633) 172451) ((-1066 . -233) 172397) ((-896 . -939) 172376) ((-128 . -34) T) ((-839 . -133) T) ((-671 . -632) 172358) ((-592 . -102) T) ((-368 . -1317) 172342) ((-366 . -1317) 172326) ((-358 . -1317) 172310) ((-123 . -528) 172243) ((-129 . -528) 172176) ((-526 . -814) T) ((-526 . -819) T) ((-525 . -816) T) ((-103 . -321) 172114) ((-226 . -102) 172064) ((-721 . -175) T) ((-716 . -1132) T) ((-896 . -670) 171980) ((-65 . -398) T) ((-286 . -632) 171962) ((-65 . -410) T) ((-975 . -390) 171946) ((-893 . -302) T) ((-50 . -632) 171928) ((-1151 . -668) 171900) ((-1027 . -38) 171848) ((-626 . -1132) T) ((-621 . -1132) T) ((-595 . -632) 171830) ((-495 . -390) 171814) ((-595 . -633) 171796) ((-532 . -632) 171778) ((-935 . -1317) 171765) ((-895 . -1248) T) ((-723 . -466) T) ((-509 . -528) 171731) ((-1310 . -1248) T) ((-1309 . -1248) T) ((-501 . -376) T) ((-368 . -381) 171710) ((-366 . -381) 171689) ((-358 . -381) 171668) ((-736 . -748) T) ((-221 . -376) T) ((-118 . -466) T) ((-1322 . -1313) 171652) ((-895 . -909) 171629) ((-895 . -911) NIL) ((-993 . -871) 171528) ((-837 . -871) 171479) ((-1256 . -102) T) ((-678 . -680) 171463) ((-1235 . -34) T) ((-174 . -632) 171445) ((-1144 . -25) 171278) ((-1144 . -21) 171189) ((-895 . -1069) 171166) ((-975 . -927) 171147) ((-1267 . -47) 171124) ((-935 . -381) T) ((-607 . -874) T) ((-58 . -673) 171108) ((-530 . -673) 171092) ((-495 . -927) 171069) ((-71 . -455) T) ((-71 . -410) T) ((-510 . -673) 171053) ((-58 . -385) 171037) ((-642 . -175) T) ((-530 . -385) 171021) ((-510 . -385) 171005) ((-561 . -1248) T) 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169722) ((-359 . -236) 169695) ((-177 . -466) T) ((-82 . -455) T) ((-226 . -321) 169633) ((-82 . -410) T) ((-227 . -632) 169615) ((-108 . -236) 169602) ((-221 . -23) T) ((-1323 . -1318) 169581) ((-699 . -1069) 169565) ((-594 . -302) T) ((-560 . -302) T) ((-509 . -302) T) ((-1267 . -1248) T) ((-137 . -484) 169520) ((-879 . -1248) T) ((-678 . -668) 169479) ((-48 . -1132) T) ((-734 . -274) 169463) ((-734 . -234) 169447) ((-895 . -927) NIL) ((-585 . -1248) T) ((-1267 . -911) NIL) ((-913 . -102) T) ((-910 . -102) T) ((-661 . -632) 169429) ((-402 . -1132) T) ((-171 . -390) 169413) ((-171 . -351) 169397) ((-1267 . -1069) 169277) ((-879 . -1069) 169173) ((-1173 . -102) T) ((-1027 . -929) 169096) ((-677 . -133) T) ((-674 . -814) 169075) ((-674 . -819) 169054) ((-119 . -528) 168962) ((-585 . -1069) 168944) ((-305 . -1306) 168914) ((-1199 . -874) NIL) ((-890 . -102) T) ((-985 . -571) 168893) ((-1241 . -1087) 168776) ((-1034 . -1082) 168721) ((-496 . -660) 168627) ((-934 . -1132) T) ((-1055 . -739) 168564) ((-733 . -1087) 168529) ((-1034 . -662) 168474) ((-636 . -102) T) ((-616 . -34) T) ((-1179 . -1248) T) ((-1241 . -111) 168343) ((-488 . -670) 168240) ((-353 . -739) 168185) ((-171 . -927) 168144) ((-721 . -302) T) ((-716 . -175) T) ((-733 . -111) 168100) ((-1328 . -1088) T) ((-1267 . -390) 168084) ((-419 . -1253) 168062) ((-1146 . -632) 168044) ((-325 . -870) NIL) ((-419 . -571) T) ((-229 . -319) T) ((-1263 . -813) 167997) ((-1263 . -816) 167950) ((-1284 . -748) T) ((-1263 . -748) T) ((-48 . -739) 167915) ((-229 . -1051) T) ((-1285 . -426) 167881) ((-1267 . -927) 167824) ((-365 . -1306) 167801) ((-1241 . -635) 167683) ((-740 . -748) T) ((-345 . -632) 167665) ((-534 . -874) 167644) ((-1144 . -236) 167535) ((-114 . -632) 167517) ((-114 . -633) 167499) ((-740 . -487) T) ((-733 . -635) 167449) ((-1322 . -1082) 167433) ((-496 . -25) 167266) ((-129 . -503) 167250) ((-123 . -503) 167234) ((-496 . -21) 167145) ((-1322 . -662) 167115) ((-642 . -302) T) ((-597 . -1087) 167090) 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-1248) T) ((-48 . -175) T) ((-723 . -401) T) ((-723 . -145) T) ((-1322 . -102) T) ((-1230 . -1248) T) ((-1228 . -635) 166423) ((-1119 . -1248) T) ((-1118 . -1087) 166266) ((-1106 . -1248) T) ((-275 . -939) 166245) ((-255 . -939) 166224) ((-803 . -1087) 166047) ((-802 . -1087) 165890) ((-627 . -1248) T) ((-1196 . -632) 165872) ((-1118 . -111) 165701) ((-1077 . -102) T) ((-489 . -1248) T) ((-475 . -1087) 165672) ((-468 . -1087) 165515) ((-686 . -670) 165499) ((-895 . -319) T) ((-803 . -111) 165308) ((-802 . -111) 165137) ((-368 . -670) 165089) ((-366 . -670) 165041) ((-358 . -670) 164993) ((-275 . -670) 164882) ((-255 . -670) 164771) ((-1190 . -871) T) ((-1119 . -1069) 164755) ((-1106 . -1069) 164732) ((-1035 . -874) T) ((-1031 . -34) T) ((-475 . -111) 164693) ((-468 . -111) 164522) ((-1002 . -874) T) ((-995 . -632) 164504) ((-987 . -1248) T) ((-985 . -1143) T) ((-128 . -1041) 164488) ((-872 . -1248) T) ((-895 . -1051) NIL) ((-757 . -1143) T) ((-737 . -1143) T) ((-676 . -635) 164406) ((-1298 . -503) 164390) ((-1216 . -1248) T) ((-1215 . -1248) T) ((-1173 . -38) 164350) ((-985 . -23) T) ((-935 . -670) 164315) ((-889 . -1132) T) ((-864 . -102) T) ((-839 . -21) T) ((-652 . -1082) 164299) ((-620 . -1082) 164283) ((-839 . -25) T) ((-757 . -23) T) ((-737 . -23) T) ((-652 . -662) 164267) ((-110 . -684) T) ((-620 . -662) 164251) ((-595 . -1087) 164216) ((-532 . -1087) 164161) ((-231 . -57) 164119) ((-467 . -23) T) ((-421 . -102) T) ((-1214 . -1248) T) ((-270 . -102) T) ((-110 . -113) T) ((-716 . -302) T) ((-890 . -38) 164089) ((-1118 . -635) 163825) ((-595 . -111) 163781) ((-532 . -111) 163710) ((-419 . -1143) T) ((-326 . -1088) 163600) ((-325 . -1088) T) ((-132 . -1248) T) ((-131 . -1248) T) ((-803 . -635) 163348) ((-802 . -635) 163114) ((-676 . -1080) T) ((-1328 . -1132) T) ((-468 . -635) 162899) ((-171 . -319) 162830) ((-419 . -23) T) ((-40 . -632) 162812) ((-40 . -633) 162796) ((-108 . -1022) 162778) ((-118 . -894) 162762) ((-671 . -635) 162746) ((-48 . -528) 162712) 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-1132) 146013) ((-1256 . -866) T) ((-331 . -1004) 145975) ((-105 . -102) T) ((-48 . -1087) 145940) ((-895 . -874) NIL) ((-1323 . -102) T) ((-395 . -102) T) ((-1285 . -632) 145922) ((-1164 . -1165) 145906) ((-1035 . -660) 145888) ((-900 . -1248) T) ((-48 . -111) 145844) ((-703 . -1248) T) ((-698 . -1248) T) ((-674 . -1248) T) ((-837 . -921) 145711) ((-492 . -1248) T) ((-252 . -1248) T) ((-545 . -102) T) ((-514 . -102) T) ((-154 . -1306) 145695) ((-140 . -1248) T) ((-139 . -1248) T) ((-135 . -1248) T) ((-1249 . -102) T) ((-1055 . -635) 145632) ((-839 . -239) T) ((-1202 . -1253) 145611) ((-218 . -381) T) ((-353 . -635) 145541) ((-1156 . -1253) 145520) ((-246 . -25) 145353) ((-246 . -21) 145264) ((-129 . -121) 145248) ((-123 . -121) 145232) ((-44 . -766) 145216) ((-1202 . -571) 145127) ((-1156 . -571) 145058) ((-1256 . -1132) T) ((-561 . -874) T) ((-1066 . -298) 145033) ((-1198 . -1114) T) ((-1025 . -1114) T) ((-838 . -133) T) ((-119 . -819) NIL) ((-119 . -814) NIL) ((-368 . -319) T) 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143042) ((-1220 . -107) 142992) ((-669 . -153) 142976) ((-651 . -153) 142922) ((-118 . -668) 142894) ((-493 . -1225) 142873) ((-501 . -149) T) ((-501 . -147) NIL) ((-1151 . -633) 142788) ((-452 . -632) 142770) ((-221 . -149) T) ((-221 . -147) NIL) ((-1151 . -632) 142752) ((-130 . -102) T) ((-51 . -102) T) ((-1258 . -660) 142704) ((-493 . -107) 142654) ((-1024 . -23) T) ((-1323 . -38) 142624) ((-1202 . -1143) T) ((-1156 . -1143) T) ((-1093 . -1253) T) ((-246 . -236) 142515) ((-324 . -102) T) ((-878 . -1143) T) ((-975 . -1253) 142494) ((-495 . -1253) 142473) ((-1093 . -571) T) ((-975 . -571) 142404) ((-1202 . -23) T) ((-1184 . -1114) T) ((-1156 . -23) T) ((-878 . -23) T) ((-495 . -571) 142335) ((-1173 . -739) 142267) ((-692 . -1082) 142251) ((-1177 . -528) 142184) ((-692 . -662) 142168) ((-1066 . -633) NIL) ((-1066 . -632) 142150) ((-96 . -1114) T) ((-1328 . -1087) 142137) ((-890 . -739) 142107) ((-1328 . -111) 142092) ((-1241 . -47) 142061) ((-1199 . -871) NIL) ((-260 . -133) T) ((-259 . -133) T) ((-1134 . -1132) T) ((-1034 . -1132) T) ((-63 . -632) 142043) ((-1110 . -921) 141912) ((-1055 . -814) T) ((-1055 . -819) T) ((-1288 . -25) T) ((-1288 . -21) T) ((-1279 . -21) T) ((-1279 . -25) T) ((-893 . -670) 141899) ((-1258 . -21) T) ((-1258 . -25) T) ((-1058 . -153) 141883) ((-1035 . -236) 141870) ((-896 . -842) 141849) ((-896 . -950) T) ((-734 . -298) 141776) ((-610 . -21) T) ((-352 . -668) 141735) ((-108 . -921) NIL) ((-610 . -25) T) ((-609 . -21) T) ((-177 . -668) 141652) ((-40 . -748) T) ((-226 . -528) 141585) ((-609 . -25) T) ((-490 . -153) 141569) ((-477 . -153) 141553) ((-187 . -1248) T) ((-948 . -816) T) ((-948 . -748) T) ((-793 . -815) T) ((-793 . -816) T) ((-520 . -1132) T) ((-516 . -1132) T) ((-793 . -748) T) ((-229 . -376) T) ((-1320 . -1082) 141537) ((-1319 . -1082) 141521) ((-1320 . -662) 141491) ((-1186 . -1132) 141469) ((-895 . -1253) T) ((-1319 . -662) 141439) ((-1119 . -874) T) ((-678 . -632) 141421) ((-895 . -571) T) ((-716 . -381) NIL) ((-44 . -1082) 141405) ((-1328 . -635) 141387) ((-1322 . -1132) T) ((-692 . -102) T) ((-372 . -1306) 141371) ((-367 . -1306) 141355) ((-44 . -662) 141339) ((-359 . -1306) 141323) ((-563 . -102) T) ((-1241 . -1248) T) ((-534 . -871) 141302) ((-733 . -1248) T) ((-987 . -874) 141281) ((-872 . -874) T) ((-501 . -239) T) ((-221 . -239) T) ((-1077 . -1132) T) ((-839 . -466) 141260) ((-154 . -1082) 141244) ((-1077 . -1102) 141173) ((-1058 . -1007) 141142) ((-841 . -1143) T) ((-1034 . -739) 141087) ((-154 . -662) 141071) ((-400 . -1143) T) ((-490 . -1007) 141040) ((-477 . -1007) 141009) ((-1215 . -874) T) ((-110 . -153) 140991) ((-73 . -632) 140973) ((-918 . -632) 140955) ((-1214 . -874) T) ((-1110 . -746) 140934) ((-1328 . -1080) T) ((-838 . -660) 140882) ((-305 . -1088) 140824) ((-171 . -1253) 140729) ((-229 . -1143) T) ((-336 . -23) T) ((-1199 . -1022) 140681) ((-1285 . -1087) 140586) ((-864 . -1132) T) ((-131 . -874) T) ((-1157 . -762) 140565) ((-1284 . -950) 140544) ((-1263 . -950) 140523) ((-893 . -748) T) ((-171 . -571) 140434) ((-594 . -670) 140421) ((-560 . -670) 140393) ((-421 . -1132) T) ((-270 . -1132) T) ((-216 . -632) 140375) ((-509 . -670) 140325) ((-229 . -23) T) ((-1263 . -842) 140278) ((-1320 . -102) T) ((-505 . -1248) T) ((-353 . -1317) 140255) ((-1319 . -102) T) ((-1285 . -111) 140147) ((-1144 . -921) 140014) ((-837 . -1082) 139915) ((-837 . -662) 139837) ((-146 . -632) 139819) ((-1024 . -133) T) ((-44 . -102) T) ((-246 . -871) 139770) ((-597 . -1248) T) ((-1267 . -1253) 139749) ((-103 . -503) 139733) ((-1322 . -739) 139703) ((-1118 . -47) 139664) ((-1093 . -1143) T) ((-975 . -1143) T) ((-129 . -34) T) ((-123 . -34) T) ((-1267 . -571) 139575) ((-803 . -47) 139552) ((-802 . -47) 139524) ((-1228 . -1248) T) ((-1202 . -133) T) ((-353 . -381) T) ((-495 . -1143) T) ((-1156 . -133) T) ((-895 . -376) T) ((-468 . -47) 139503) ((-878 . -133) T) ((-334 . -874) 139482) ((-154 . -102) T) ((-1093 . -23) T) ((-975 . -23) T) ((-585 . -571) T) ((-838 . -25) T) ((-838 . -21) T) 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137363) ((-1118 . -1248) T) ((-1066 . -300) 137338) ((-594 . -748) T) ((-560 . -816) T) ((-171 . -376) 137289) ((-560 . -813) T) ((-560 . -748) T) ((-509 . -748) T) ((-803 . -1248) T) ((-802 . -1248) T) ((-1177 . -503) 137273) ((-475 . -1248) T) ((-468 . -1248) T) ((-1320 . -1321) 137249) ((-1118 . -911) NIL) ((-895 . -1143) T) ((-119 . -939) NIL) ((-1319 . -1321) 137228) ((-671 . -1248) T) ((-803 . -911) NIL) ((-802 . -911) 137087) ((-1314 . -25) T) ((-1314 . -21) T) ((-1246 . -102) 137065) ((-1137 . -410) T) ((-642 . -670) 137052) ((-468 . -911) NIL) ((-697 . -102) 137002) ((-1118 . -1069) 136829) ((-895 . -23) T) ((-803 . -1069) 136688) ((-802 . -1069) 136545) ((-119 . -670) 136490) ((-468 . -1069) 136366) ((-286 . -1248) T) ((-326 . -635) 135930) ((-325 . -635) 135813) ((-50 . -1248) T) ((-404 . -668) 135782) ((-671 . -1069) 135766) ((-646 . -102) T) ((-595 . -1248) T) ((-532 . -1248) T) ((-226 . -503) 135750) ((-1298 . -34) T) ((-638 . -668) 135709) ((-301 . -1082) 135696) ((-137 . -635) 135680) ((-301 . -662) 135667) ((-652 . -739) 135651) ((-620 . -739) 135635) ((-692 . -38) 135595) ((-331 . -102) T) ((-1151 . -1087) 135582) ((-86 . -632) 135564) ((-50 . -1069) 135548) ((-1118 . -390) 135532) ((-803 . -390) 135516) ((-721 . -748) T) ((-721 . -816) T) ((-721 . -813) T) ((-60 . -57) 135478) ((-595 . -1069) 135465) ((-532 . -1069) 135442) ((-174 . -1248) T) ((-336 . -133) T) ((-326 . -1080) 135332) ((-325 . -1080) T) ((-171 . -1143) T) ((-802 . -390) 135316) ((-45 . -153) 135266) ((-1035 . -1022) 135248) ((-468 . -390) 135232) ((-421 . -175) T) ((-326 . -250) 135211) ((-325 . -250) T) ((-325 . -240) NIL) ((-305 . -1132) 134993) ((-229 . -133) T) ((-1151 . -111) 134978) ((-171 . -23) T) ((-820 . -149) 134957) ((-820 . -147) 134936) ((-260 . -660) 134842) ((-259 . -660) 134748) ((-331 . -296) 134714) ((-1186 . -528) 134647) ((-491 . -668) 134597) ((-657 . -866) T) ((-496 . -921) 134464) ((-1164 . -1132) T) ((-229 . -1091) T) ((-837 . -321) 134402) ((-1118 . -927) 134337) ((-803 . -927) 134280) ((-802 . -927) 134264) ((-1320 . -38) 134234) ((-1319 . -38) 134204) ((-1267 . -1143) T) ((-879 . -1143) T) ((-468 . -927) 134181) ((-882 . -1132) T) ((-1267 . -23) T) ((-1151 . -635) 134153) ((-1093 . -133) T) ((-879 . -23) T) ((-585 . -1143) T) ((-642 . -748) T) ((-525 . -874) T) ((-368 . -950) T) ((-366 . -950) T) ((-301 . -102) T) ((-358 . -950) T) ((-1001 . -1114) T) ((-975 . -133) T) ((-838 . -236) 134098) ((-119 . -816) NIL) ((-119 . -813) NIL) ((-119 . -748) T) ((-1077 . -528) 133999) ((-716 . -939) NIL) ((-585 . -23) T) ((-495 . -133) T) ((-419 . -239) 133950) ((-697 . -321) 133888) ((-227 . -1248) T) ((-657 . -1132) T) ((-652 . -783) T) ((-620 . -783) T) ((-1258 . -871) NIL) ((-1110 . -1082) 133798) ((-1034 . -302) T) ((-716 . -670) 133748) ((-260 . -25) T) ((-365 . -1132) T) ((-260 . -21) T) ((-259 . -25) T) ((-259 . -21) T) ((-154 . -38) 133732) ((-2 . -102) T) ((-935 . -950) T) ((-1110 . -662) 133600) ((-496 . -1306) 133570) ((-1151 . -1080) T) ((-733 . -319) T) ((-723 . -1088) T) ((-372 . -1082) 133522) ((-367 . -1082) 133474) ((-359 . -1082) 133426) ((-372 . -662) 133378) ((-227 . -1069) 133355) ((-367 . -662) 133307) ((-108 . -1082) 133257) ((-359 . -662) 133209) ((-305 . -739) 133151) ((-661 . -1248) T) ((-501 . -466) T) ((-421 . -528) 133063) ((-108 . -662) 133013) ((-221 . -466) T) ((-1151 . -240) T) ((-307 . -153) 132963) ((-1027 . -633) 132924) ((-1027 . -632) 132906) ((-1020 . -632) 132888) ((-118 . -1088) T) ((-678 . -1087) 132872) ((-229 . -507) T) ((-413 . -632) 132854) ((-413 . -633) 132831) ((-1085 . -1306) 132801) ((-678 . -111) 132780) ((-692 . -929) 132703) ((-1173 . -503) 132687) ((-1323 . -668) 132646) ((-395 . -668) 132615) ((-64 . -455) T) ((-64 . -410) T) ((-1191 . -102) T) ((-895 . -133) T) ((-498 . -102) 132565) ((-1146 . -1248) T) ((-1255 . -874) T) ((-1328 . -381) T) ((-1110 . -102) T) ((-1092 . -102) T) ((-365 . -739) 132510) ((-896 . -874) 132461) ((-753 . -149) 132440) ((-753 . -147) 132419) 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131166) ((-1190 . -102) T) ((-1267 . -133) T) ((-1263 . -874) 131065) ((-1202 . -25) T) ((-1202 . -21) T) ((-1191 . -321) 130860) ((-357 . -1248) T) ((-1156 . -25) T) ((-879 . -133) T) ((-407 . -1248) T) ((-1156 . -21) T) ((-878 . -25) T) ((-878 . -21) T) ((-803 . -319) 130839) ((-1186 . -503) 130823) ((-1182 . -153) 130773) ((-1177 . -632) 130735) ((-669 . -102) 130685) ((-651 . -102) T) ((-1177 . -633) 130646) ((-585 . -133) T) ((-638 . -870) 130625) ((-1055 . -813) T) ((-1055 . -816) T) ((-1055 . -748) T) ((-837 . -929) 130494) ((-734 . -1087) 130317) ((-616 . -874) 130296) ((-498 . -321) 130234) ((-467 . -432) 130204) ((-365 . -175) T) ((-301 . -38) 130191) ((-260 . -236) 130082) ((-259 . -236) 129973) ((-285 . -102) T) ((-284 . -102) T) ((-283 . -102) T) ((-282 . -102) T) ((-281 . -102) T) ((-280 . -102) T) ((-357 . -1069) 129950) ((-279 . -102) T) ((-215 . -102) T) ((-214 . -102) T) ((-212 . -102) T) ((-211 . -102) T) ((-210 . -102) T) ((-209 . -102) T) ((-206 . -102) T) ((-205 . 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-874) T) ((-1206 . -35) 128490) ((-1206 . -95) 128456) ((-1206 . -1237) 128422) ((-1206 . -1234) 128388) ((-1205 . -1234) 128354) ((-1205 . -1237) 128320) ((-1205 . -95) 128286) ((-1205 . -35) 128252) ((-1199 . -1234) 128218) ((-1199 . -1237) 128184) ((-1190 . -321) NIL) ((-89 . -411) T) ((-89 . -410) T) ((-1110 . -1183) 128163) ((-40 . -1248) T) ((-1199 . -95) 128129) ((-1065 . -23) T) ((-1199 . -35) 128095) ((-585 . -507) T) ((-1157 . -35) 128061) ((-1157 . -95) 128027) ((-1157 . -1237) 127993) ((-1157 . -1234) 127959) ((-374 . -1143) T) ((-372 . -1183) 127938) ((-367 . -1183) 127917) ((-359 . -1183) 127896) ((-1134 . -298) 127852) ((-983 . -1248) T) ((-948 . -1248) T) ((-108 . -1183) T) ((-854 . -1088) 127831) ((-793 . -1248) T) ((-669 . -321) 127769) ((-651 . -321) 127620) ((-694 . -1248) T) ((-734 . -1080) T) ((-1093 . -660) 127602) ((-1110 . -38) 127470) ((-975 . -660) 127418) ((-1035 . -149) T) ((-1035 . -147) NIL) ((-391 . -1143) T) ((-336 . -25) T) ((-334 . -23) T) ((-972 . 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. -1088) T) ((-1241 . -149) 63676) ((-334 . -1082) 63658) ((-1241 . -147) 63637) ((-1216 . -102) T) ((-1215 . -102) T) ((-1214 . -102) T) ((-1206 . -175) 63588) ((-334 . -662) 63570) ((-723 . -1248) T) ((-1205 . -175) 63501) ((-1199 . -175) 63432) ((-1184 . -635) 63413) ((-1157 . -175) 63364) ((-610 . -1088) T) ((-609 . -1088) T) ((-1035 . -1132) T) ((-1002 . -1132) T) ((-391 . -1082) 63329) ((-136 . -1248) T) ((-118 . -1248) T) ((-943 . -1132) T) ((-895 . -929) NIL) ((-391 . -662) 63294) ((-146 . -874) T) ((-820 . -818) 63278) ((-721 . -25) T) ((-721 . -21) T) ((-119 . -660) 63255) ((-723 . -911) 63237) ((-443 . -1132) T) ((-326 . -1253) 63216) ((-325 . -1253) T) ((-171 . -414) 63200) ((-856 . -1082) 63170) ((-488 . -1004) 63132) ((-72 . -632) 63114) ((-132 . -102) T) ((-131 . -102) T) ((-850 . -1082) 63098) ((-108 . -819) T) ((-108 . -814) T) ((-723 . -1069) 63080) ((-326 . -571) 63059) ((-325 . -571) T) ((-856 . -662) 63029) ((-850 . -662) 62999) ((-1328 . -23) T) ((-136 . -1069) 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. -921) 60880) ((-987 . -321) 60818) ((-856 . -102) T) ((-443 . -739) 60802) ((-229 . -843) T) ((-850 . -102) T) ((-847 . -102) T) ((-1320 . -670) 60776) ((-1284 . -1283) 60755) ((-493 . -153) 60705) ((-1284 . -1277) 60675) ((-1151 . -1253) T) ((-352 . -1069) 60642) ((-1284 . -1281) 60626) ((-1267 . -929) 60533) ((-1263 . -1262) 60512) ((-80 . -632) 60494) ((-931 . -632) 60476) ((-1263 . -1277) 60453) ((-1151 . -571) T) ((-948 . -871) T) ((-793 . -871) T) ((-694 . -871) T) ((-501 . -633) 60383) ((-501 . -632) 60324) ((-391 . -296) T) ((-1263 . -1260) 60308) ((-1285 . -1143) T) ((-221 . -633) 60238) ((-221 . -632) 60179) ((-1094 . -618) 60154) ((-840 . -635) 60138) ((-560 . -236) 60125) ((-530 . -153) 60109) ((-58 . -153) 60093) ((-510 . -153) 60077) ((-509 . -236) 60064) ((-372 . -1317) 60048) ((-367 . -1317) 60032) ((-359 . -1317) 60016) ((-326 . -376) 59995) ((-325 . -376) T) ((-496 . -1080) 59973) ((-716 . -660) 59955) ((-1319 . -670) 59929) ((-131 . -321) NIL) ((-1285 . -23) T) 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. -871) T) ((-1034 . -950) T) ((-1210 . -635) 56019) ((-154 . -748) T) ((-1144 . -381) 55998) ((-659 . -102) T) ((-1055 . -25) T) ((-1035 . -528) NIL) ((-260 . -426) 55967) ((-259 . -426) 55936) ((-1055 . -21) T) ((-896 . -1082) 55888) ((-610 . -739) 55861) ((-609 . -739) 55758) ((-820 . -298) 55716) ((-128 . -102) 55666) ((-854 . -1069) 55562) ((-171 . -843) 55541) ((-331 . -670) 55438) ((-837 . -34) T) ((-736 . -102) T) ((-1151 . -1143) T) ((-1057 . -1248) T) ((-896 . -662) 55390) ((-391 . -38) 55355) ((-353 . -25) T) ((-353 . -21) T) ((-186 . -102) T) ((-163 . -102) T) ((-257 . -102) T) ((-159 . -102) T) ((-368 . -1306) 55339) ((-366 . -1306) 55323) ((-358 . -1306) 55307) ((-171 . -363) 55286) ((-560 . -871) T) ((-1118 . -239) 55237) ((-1151 . -23) T) ((-88 . -632) 55219) ((-803 . -239) T) ((-723 . -319) T) ((-856 . -38) 55189) ((-850 . -38) 55159) ((-1311 . -635) 55101) ((-1285 . -133) T) ((-1182 . -300) 55080) ((-993 . -748) 54979) ((-993 . -815) 54932) ((-993 . -816) 54885) 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-1132) T) ((-31 . -102) T) ((-1267 . -668) 52265) ((-879 . -668) 52224) ((-838 . -739) 52073) ((-1302 . -1248) T) ((-591 . -885) T) ((-585 . -668) 52045) ((-119 . -871) NIL) ((-1202 . -426) 52029) ((-1156 . -426) 52013) ((-878 . -426) 51997) ((-897 . -102) 51948) ((-1284 . -102) T) ((-1263 . -102) T) ((-1258 . -528) 51717) ((-1235 . -321) 51655) ((-1206 . -298) 51620) ((-1205 . -298) 51578) ((-539 . -93) T) ((-1199 . -298) 51406) ((-323 . -632) 51388) ((-1128 . -1132) T) ((-1110 . -670) 51262) ((-733 . -466) T) ((-711 . -632) 51194) ((-301 . -748) T) ((-108 . -939) NIL) ((-711 . -633) 51155) ((-615 . -632) 51137) ((-591 . -632) 51119) ((-565 . -633) NIL) ((-565 . -632) 51101) ((-543 . -632) 51083) ((-526 . -523) 51062) ((-501 . -1087) 51012) ((-488 . -1082) 50847) ((-521 . -523) 50826) ((-488 . -662) 50667) ((-221 . -1087) 50617) ((-372 . -670) 50569) ((-367 . -670) 50521) ((-229 . -870) T) ((-359 . -670) 50473) ((-616 . -102) 50403) ((-501 . -111) 50337) ((-496 . -381) 50316) ((-108 . -670) 50266) ((-357 . -149) 50248) ((-246 . -503) 50232) ((-357 . -147) T) ((-353 . -236) 50219) ((-171 . -383) 50190) ((-972 . -1297) 50174) ((-105 . -1248) T) ((-221 . -111) 50108) ((-896 . -321) 50073) ((-972 . -1132) 50023) ((-820 . -633) 49984) ((-820 . -632) 49966) ((-740 . -102) T) ((-1323 . -1248) T) ((-395 . -1248) T) ((-343 . -1132) T) ((-217 . -635) 49943) ((-1151 . -133) T) ((-1314 . -739) 49913) ((-736 . -38) 49883) ((-326 . -507) 49862) ((-545 . -1248) T) ((-514 . -1248) T) ((-1284 . -296) 49828) ((-1263 . -296) 49794) ((-339 . -153) 49778) ((-453 . -1132) T) ((-1249 . -1248) T) ((-1094 . -300) 49753) ((-1256 . -874) T) ((-48 . -236) 49740) ((-1191 . -34) T) ((-1323 . -1069) 49717) ((-498 . -34) T) ((-482 . -632) 49699) ((-258 . -298) 49673) ((-395 . -1069) 49657) ((-1202 . -1088) T) ((-1156 . -1088) T) ((-878 . -1088) T) ((-1093 . -870) T) ((-501 . -635) 49607) ((-221 . -635) 49557) ((-838 . -175) 49468) ((-534 . -298) 49420) ((-1288 . -302) 49399) ((-1230 . -378) 49373) 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1744) ((-171 . -111) 1640) ((-854 . -133) 1592) ((-1298 . -321) 1530) ((-758 . -153) 1514) ((-993 . -874) 1413) ((-837 . -874) 1364) ((-501 . -319) T) ((-391 . -632) 1331) ((-534 . -1041) 1315) ((-391 . -633) 1229) ((-221 . -319) T) ((-143 . -153) 1211) ((-736 . -298) 1190) ((-501 . -1051) T) ((-594 . -38) 1177) ((-560 . -38) 1164) ((-509 . -38) 1129) ((-661 . -668) 1098) ((-221 . -1051) T) ((-895 . -1080) T) ((-856 . -632) 1080) ((-850 . -632) 1062) ((-847 . -632) 1044) ((-838 . -939) 1023) ((-1323 . -1143) T) ((-323 . -1248) T) ((-1267 . -1087) 846) ((-879 . -1087) 830) ((-895 . -250) T) ((-895 . -240) NIL) ((-711 . -1248) T) ((-1323 . -23) T) ((-838 . -670) 719) ((-565 . -1248) T) ((-419 . -351) 703) ((-585 . -1087) 690) ((-1267 . -111) 499) ((-723 . -660) 481) ((-879 . -111) 460) ((-395 . -23) T) ((-171 . -635) 238) ((-1220 . -528) 30) ((-900 . -1132) T) ((-703 . -1132) T) ((-698 . -1132) T) ((-674 . -1132) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 282cad28..55712c75 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3508696570) +(30 . 3508766235) (4512 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -488,676 +488,676 @@ |XPolynomialsCat| |XPolynomialRing| |XRecursivePolynomial| |YoungDiagram| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| - |Enumeration| |Mapping| |Record| |Union| |LyndonWordsList| |elRow2!| - |cosIfCan| |list| |anfactor| |e02adf| |lfintegrate| |medialSet| - |irCtor| |mindeg| |draw| |minrank| |algintegrate| |outputBinaryFile| - |aromberg| |cyclic| |simpson| |qualifier| |rowEchelonLocal| |bright| - |infLex?| |decrease| |numFunEvals3D| |startTable!| - |useEisensteinCriterion| |derivative| |clip| |setFieldInfo| |c06ecf| - |null| |OMputString| |randomLC| |outputMeasure| |back| |rightMult| - |insertTop!| |jvmUTF8ConstantTag| |interval| |f02abf| |not| - |acschIfCan| |prinpolINFO| |cache| |sort!| |showAll?| |lifting| - |numericIfCan| |f01rdf| |octon| |harmonic| |d01ajf| |and| |fractRadix| - |makeObject| |createMultiplicationMatrix| |minPoints3D| |push!| - |numFunEvals| |nthFactor| |acothIfCan| |setPoly| |closeComponent| |or| - |chainSubResultants| |primlimintfrac| |dimension| |rquo| |coef| - |factorSquareFree| |light| |supRittWu?| |in?| |curve?| |collect| |xor| - |one?| |lexGroebner| |symbol?| |overlap| |erf| |edf2df| - |diagonalMatrix| |rightRecip| |finite?| |binary| |case| |pade| - |fTable| |norm| |corrPoly| |rightNorm| |directSum| |iidprod| - |replaceKthElement| |arity| |Zero| |leftExtendedGcd| |connectTo| - |charthRoot| |purelyAlgebraic?| |left| |zerosOf| |rightPower| - |intPatternMatch| |limitPlus| |lyndon?| |One| |shift| |retractIfCan| - |lastSubResultantEuclidean| |ScanArabic| |asinhIfCan| |coerceP| - |complexLimit| |dilog| |right| |size| |ratDsolve| |reduceLODE| |ipow| - |setOrder| |laguerre| |monicRightFactorIfCan| |number?| |OMgetEndBind| - |s17ajf| |sin| |mapUnivariate| |setPrologue!| |linears| |intChoose| - |testDim| |fortran| |generic| |invertIfCan| |dec| |cRationalPower| - |jvmStringConstantTag| |cos| |ranges| |polyRDE| |e01bff| - |fortranTypeOf| |cubic| |f02aef| |numeric| |noValueMode| - |setScreenResolution3D| |presub| |tan| |depth| |bezoutDiscriminant| - |symmetricPower| |rootNormalize| |euclideanNormalForm| |perspective| - |directory| |Aleph| |radical| |s13acf| |rk4a| |constantOpIfCan| |cot| - |subscriptedVariables| |cyclotomic| |drawStyle| |outlineRender| - |lintgcd| |elt| |coshIfCan| |weight| |minPol| |basisOfMiddleNucleus| - EQ |sec| |mvar| |subCase?| |radix| |nonQsign| |approxNthRoot| - |logical?| |signature| |reducedQPowers| |e02zaf| - |semiResultantEuclideannaif| |sup| |csc| |printCode| |components| - |basisOfCenter| |nonLinearPart| |c06gqf| |numerators| - |jvmIntegerConstantTag| |radicalEigenvalues| |enterInCache| - |screenResolution3D| |asin| |powerSum| |complexSolve| - |leftAlternative?| |internalAugment| |surface| |monomials| |coleman| - |setCondition!| |tanSum| |fixedDivisor| |acos| |extendedint| |conjug| - |clearTheFTable| |irDef| |mesh| |rangeIsFinite| |attributeData| - |monicCompleteDecompose| |csch2sinh| |atan| |node| |computeCycleEntry| - |dark| |rischNormalize| |transpose| |extendedIntegrate| |df2st| - |curryLeft| |stFuncN| |setLength!| |csubst| |acot| - |jvmNameAndTypeConstantTag| |round| |gensym| |cAcsch| UP2UTS |create| - |lfextendedint| |bytes| |rightDivide| |selectFiniteRoutines| |asec| - |symbol| |algebraicSort| |shallowCopy| |adaptive3D?| |subspace| - |stiffnessAndStabilityFactor| SEGMENT |clipSurface| - |partialDenominators| |checkRur| |iiperm| |acsc| |expression| - |setProperty| |putColorInfo| |shanksDiscLogAlgorithm| |sh| |e02dcf| - |hypergeometric0F1| |scaleRoots| |unknown| |startTableGcd!| - |generalInfiniteProduct| |sinh| |integer| |infix| |content| - |particularSolution| |abs| |s18aff| |script| |rombergo| |alphabetic| - |factorSquareFreePolynomial| |sqfrFactor| |cosh| |getButtonValue| - |factorsOfDegree| |space| |explicitEntries?| |isOpen?| |resultantnaif| - |domainTemplate| |nextNormalPoly| |df2mf| |tanh| |An| |stopTableGcd!| - |makeMulti| |OMsetEncoding| |currentSubProgram| |eq?| |BasicMethod| - |nodes| |yCoordinates| |coth| |numberOfIrreduciblePoly| |cAcsc| F - |setPredicates| |usingTable?| |rightDiscriminant| |tex| - |numberOfOperations| |block| |showTheIFTable| |build| |sech| - |companionBlocks| |graphState| |basisOfCentroid| |verticalTab| - |denomLODE| |cond| |f07aef| |leaf?| |nil?| |readInt32!| |csch| - |presuper| |symbolTableOf| |separant| |outputFloating| |tValues| - |OMopenString| |expenseOfEvaluationIF| |setScreenResolution| - |linearDependenceOverZ| |fixedPointExquo| |algebraic?| |anticoord| - |uniform01| |e01saf| |tanh2trigh| |singleFactorBound| |zCoord| - |listConjugateBases| |edf2fi| |c06frf| |pastel| |tanIfCan| |roman| - |normalizedAssociate| |capacity| |iiacsc| |prime| LODO2FUN - |generalizedEigenvector| |OMconnInDevice| |isPower| |taylorIfCan| - |zeroOf| |characteristicSerie| |cyclotomicFactorization| |moduloP| - |setnext!| |exptMod| |equation| |representationType| |OMputEndAtp| - |iiasin| |symmetricProduct| |bubbleSort!| |createNormalPrimitivePoly| - |cSin| |cotIfCan| |realEigenvalues| |OMsupportsSymbol?| |outputFixed| - |rightExtendedGcd| |OMgetFloat| |orbit| |leftDivide| - |zeroSetSplitIntoTriangularSystems| |delete!| |interpolate| |headAst| - |linearPart| |generators| |orthonormalBasis| |qqq| |polygon| |e01bef| - |sizePascalTriangle| FG2F |constantKernel| |UnVectorise| |satisfy?| - |goodPoint| |iicot| F2FG |limitedIntegrate| |s17agf| |subMatrix| - |characteristicPolynomial| |complete| |s17aff| |supersub| |cCoth| - |univariatePolynomialsGcds| |lastSubResultantElseSplit| |c06fqf| - |super| |mathieu22| |atanIfCan| |lazyIntegrate| |laplace| |iicoth| - |listOfLists| |exprToGenUPS| |quasiComponent| |list?| |homogeneous?| - |bernoulli| |more?| |viewWriteAvailable| |mathieu11| |insert| - |underscore| |OMconnOutDevice| |someBasis| |intcompBasis| |f01maf| - |OMgetBind| |jvmPublic| |denominator| |d02raf| |badValues| |magnitude| - |matrixConcat3D| |eulerE| |putProperty| |linearAssociatedOrder| - |toseSquareFreePart| |jvmPrivate| |genus| |redPol| |failed?| - |RemainderList| |SturmHabicht| |initiallyReduce| |Gamma| |closed?| - |integralLastSubResultant| |OMclose| |pureLex| |figureUnits| - |contract| |submod| |associatedEquations| |stop| |style| |unmakeSUP| - |neglist| |optpair| |split| |palgLODE| |ode1| |normalDeriv| - |binaryTree| |dequeue| |empty?| |assert| |systemCommand| |legendreP| - |getZechTable| |jvmStrict| |getVariableOrder| |iCompose| - |expenseOfEvaluation| |nativeModuleExtension| |basisOfLeftNucleus| - |factors| |useEisensteinCriterion?| |componentUpperBound| |routines| - |setUnion| |morphism| |cycleRagits| |intensity| |normal| |ODESolve| - |open| |listBranches| |antisymmetricTensors| |arbitrary| |sinh2csch| - |quartic| |simplifyExp| |fortranLiteralLine| |lfinfieldint| - |characteristicSet| |arrayStack| |iicsc| |powern| |complexZeros| - |cos2sec| |setRow!| |sylvesterSequence| |solid?| |e04fdf| - |OMgetEndObject| |exportedOperators| |socf2socdf| |e04naf| - |mainCharacterization| |moebius| |viewThetaDefault| |palgintegrate| - |plotPolar| |subResultantGcdEuclidean| |genericRightTraceForm| - |lazyPseudoQuotient| |countRealRootsMultiple| |axes| - |nextPrimitiveNormalPoly| |merge!| |isImplies| |operations| - |beauzamyBound| |normalize| |randomR| |currentScope| |eq| |rotate| - |palgextint0| |writeLine!| |maxIndex| |log| |leftGcd| |c06fpf| - |mainVariable?| |iter| |commutativeEquality| |substring?| |hexDigit?| - |logpart| |totalDegree| |returns| |close| |gcdcofact| - |evaluateInverse| |associative?| |pmintegrate| |kovacic| - |torsionIfCan| |changeNameToObjf| |unrankImproperPartitions1| |pToDmp| - |predicate| |pow| |d01bbf| |rename| |ParCondList| |dot| - |printStatement| |calcRanges| |suffix?| |kmax| |jvmClassConstantTag| - |sequences| |lazyResidueClass| |fibonacci| |display| |critpOrder| - |resultantEuclideannaif| |tableForDiscreteLogarithm| - |selectSumOfSquaresRoutines| |innerint| |stronglyReduced?| - |weakBiRank| |numberOfVariables| |discreteLog| - |getSyntaxFormsFromFile| |iiexp| |maximumExponent| |front| - |commaSeparate| |leaves| |safeCeiling| |prefix?| |select!| - |areEquivalent?| |component| |clearTable!| |pdf2ef| - |getMultiplicationMatrix| |lhs| |dominantTerm| |isList| - |sturmSequence| |removeRedundantFactorsInPols| |unitNormalize| - |bitLength| |index?| |equality| |exp1| |explicitlyFinite?| |rhs| - |every?| |exQuo| |mapUp!| |decreasePrecision| |rootSimp| |rootKerSimp| - |Nul| |exp| |lowerPolynomial| |leftUnits| |pushdown| |boundOfCauchy| - |rootDirectory| |arg1| |expt| |sin?| |stosePrepareSubResAlgo| - |startStats!| |currentEnv| |lflimitedint| |evaluate| |width| |split!| - |diophantineSystem| |polygon?| |lepol| |newReduc| |arg2| - |genericRightDiscriminant| |s14aaf| |closed| |output| |seriesSolve| - |reopen!| |trailingCoefficient| |insertionSort!| |parent| |cCos| - |redmat| |superHeight| |atanhIfCan| |test| |hasSolution?| |comment| - |updatF| |dequeue!| |subPolSet?| |possiblyInfinite?| |var2Steps| - |toseInvertible?| |li| |getGoodPrime| |rightUnits| |conditions| - |parameters| |OMgetString| |complexForm| |extract!| |largest| - |isConnected?| |adaptive?| |linGenPos| |setrest!| |idealiserMatrix| - |match| |newSubProgram| |att2Result| |enterPointData| |exists?| - |scale| |tubeRadiusDefault| |equiv| |getOperator| |sylvesterMatrix| - |imagk| |nextsousResultant2| |bipolarCylindrical| |numerator| |tab1| - |OMencodingBinary| |setColumn!| |radPoly| |acoshIfCan| - |loadNativeModule| |diagonals| |factorSFBRlcUnit| |roughUnitIdeal?| - |conjunction| |totalfract| |abelianGroup| |message| - |lazyIrreducibleFactors| |doublyTransitive?| |makeEq| |optional| - |iidsum| |leadingSupport| |f04adf| |problemPoints| |orbits| - |commonDenominator| |f04mcf| |infix?| |bfKeys| |charClass| - |genericLeftNorm| |inf| |iiGamma| |mapCoef| |zeroVector| |cPower| - |makeYoungTableau| |remove| |prepareSubResAlgo| |mask| - |numberOfFactors| |sumOfKthPowerDivisors| |minimumDegree| - |tubePointsDefault| |flexible?| |result| |irVar| |Ci| |resize| - |ParCond| |lfunc| |legendre| |empty| |torsion?| |primes| - |sumOfDivisors| |mat| |inc| |f02ajf| |OMputInteger| |inconsistent?| - |last| |palglimint| |conjugate| |viewPhiDefault| |minset| - |viewWriteDefault| |eof?| |assoc| |schema| |integral?| |parametric?| - |cExp| |nextIrreduciblePoly| |upperBound| |leadingExponent| - |dimensions| |mirror| |any?| |primextendedint| |isNot| |aQuartic| - |map| |notelem| |integer?| |iiasech| |multisect| |realSolve| - |makeUnit| |iilog| |isOp| |getOperands| |expr| |ratpart| |makeTerm| - |f01bsf| |selectOrPolynomials| |e02ahf| |maxRowIndex| |leftRank| - |f02aff| |primaryDecomp| |associates?| |OMReadError?| |iicos| - |internalLastSubResultant| |KrullNumber| |label| |karatsubaOnce| - |collectUnder| |weierstrass| |jvmFloatConstantTag| |s17aef| - |direction| |showTheSymbolTable| |getPickedPoints| BY |fintegrate| - |condition| |youngDiagram| |integralRepresents| |hdmpToDmp| - |complexExpand| |generalizedInverse| |c06gcf| |prologue| - |OMputVariable| |rules| |f04qaf| |prefix| |qelt| |nilFactor| |mapmult| - |modifyPoint| |wronskianMatrix| |variable| |adaptive| |hasoln| - |nullary| |plot| |operation| |e02baf| |qsetelt| |linearlyDependent?| - |toScale| |noKaratsuba| |OMputSymbol| |iterators| |totolex| |critBonD| - |solveLinearlyOverQ| |integralCoordinates| |doubleFloatFormat| - |cosSinInfo| |xRange| |euclideanGroebner| |rightRankPolynomial| - |complexIntegrate| |pr2dmp| |f02fjf| |exprHasLogarithmicWeights| - |odd?| |getMeasure| |stoseInternalLastSubResultant| |jvmInterface| - |yRange| |reorder| |modulus| |lowerCase| |init| |leftFactor| |reseed| - |variable?| |resetVariableOrder| |writeUInt8!| |fixPredicate| - |quickSort| |cAcoth| |zRange| |deriv| |pushucoef| |part?| - |createThreeSpace| |next| |createPrimitiveNormalPoly| |readByte!| - |weights| |lazy?| |iteratedInitials| |option| |map!| LE - |changeWeightLevel| |trivialIdeal?| |rationalFunction| |s20adf| NOT - |ldf2vmf| |stoseInvertible?reg| |rotate!| |tableau| |univariate?| - |qsetelt!| |sizeMultiplication| |nthFlag| LT |midpoints| OR - |algebraicVariables| |e01sff| |zeroSetSplit| |nullary?| |d01akf| - |standardBasisOfCyclicSubmodule| |bothWays| |update| |cot2trig| - |transcendenceDegree| AND |viewSizeDefault| |normal?| - |fortranCompilerName| |generalTwoFactor| |viewDeltaYDefault| - |quasiMonic?| |d02gbf| |e02aef| |selectODEIVPRoutines| |viewpoint| - |nextSubsetGray| |wordInGenerators| |augment| |subResultantGcd| - |bigEndian| |mkcomm| |fixedPoints| |UP2ifCan| |inputOutputBinaryFile| - |red| |members| |zag| |duplicates?| |firstUncouplingMatrix| - |pushNewContour| |lookup| |extractSplittingLeaf| |complexEigenvectors| - |specialTrigs| |car| |nthRoot| |extend| |determinant| - |leftRankPolynomial| |s18adf| |rowEchelon| |wrregime| |sinhIfCan| - |indicialEquationAtInfinity| |acsch| |polCase| - |getMultiplicationTable| |quasiRegular| |rootSplit| |rem| |multMonom| - |s19acf| |exteriorDifferential| |differentialVariables| |iiasinh| - |functionIsFracPolynomial?| |semiResultantEuclidean1| |mantissa| - |viewport2D| |exactQuotient!| |quo| |rewriteSetWithReduction| |cCsc| - |errorInfo| |rightRemainder| |structuralConstants| |high| |lllip| - |OMgetType| |addiag| |bezoutResultant| |tan2trig| |OMconnectTCP| - |separate| |showTheFTable| |preprocess| |rdregime| |cap| |asimpson| - |positiveSolve| |extractBottom!| |div| |localIntegralBasis| - |reduceBasisAtInfinity| |fortranComplex| |iiacos| |f02xef| |positive?| - |cTanh| |f04arf| |selectPolynomials| |definingEquations| |getOrder| - |exquo| |genericLeftDiscriminant| |HermiteIntegrate| |double| - |categoryFrame| |mkPrim| |initials| |coefChoose| |coordinates| |imagJ| - |transcendentalDecompose| |mightHaveRoots| * ~= |primitive?| |open?| - |d03faf| |shuffle| |triangulate| |read!| |primlimitedint| |d03eef| - |rational?| |byteBuffer| |#| |getConstant| |order| |iiacsch| - |resultantEuclidean| |sorted?| |nthCoef| |integralMatrix| |stFunc2| - |squareFree| |reducedSystem| ~ |showIntensityFunctions| |OMputBVar| - |flagFactor| |setStatus!| |badNum| |readInt8!| |setDifference| |goto| - |rubiksGroup| |toroidal| = |allRootsOf| |findBinding| |fill!| - |simplify| |fracPart| |cn| |tryFunctionalDecomposition?| |function| - |pseudoQuotient| |parametersOf| |cyclicEqual?| |ocf2ocdf| |iFTable| - |acotIfCan| |ddFact| |printHeader| |finiteBound| - |squareFreeLexTriangular| |rur| |scripted?| |setEpilogue!| |/\\| < - |insertBottom!| |cdr| |OMputAttr| |setlast!| |makeSin| |ratPoly| - |matrixGcd| |composite| |\\/| > |zeroDim?| |leftMult| |declare!| - |algint| |radicalSimplify| |internalInfRittWu?| - |selectOptimizationRoutines| |getlo| |semiDiscriminantEuclidean| - |irreducibleFactor| <= |iicsch| |f2st| |vedf2vef| |laurentRep| |paren| - |dmp2rfi| |kroneckerDelta| |highCommonTerms| |univariatePolynomial| >= - |innerSolve| |OMopenFile| |elliptic| |bit?| |mainVariable| - |findConstructor| |formula| |OMsend| |argumentListOf| |clipWithRanges| - |normalDenom| |ricDsolve| |Is| |elColumn2!| |complex?| |increment| - |increase| |bipolar| |cons| |true| |useSingleFactorBound?| |inv| - |leftRegularRepresentation| |exponent| |radicalSolve| - |showArrayValues| |declare| |jvmNative| |compound?| |OMputEndBind| - |sparsityIF| + |ground?| |makeSUP| |derivationCoordinates| - |symmetric?| |gderiv| |rightExactQuotient| |ravel| |padecf| - |monomial?| |doubleResultant| |listOfMonoms| |jordanAlgebra?| - - |ground| |flatten| |divisor| |zeroDimPrime?| |bracket| |s13adf| - |nrows| |dflist| |setAdaptive| |reshape| / |quote| |leadingMonomial| - |segment| |computeCycleLength| |nthExponent| |iiacoth| |removeZeroes| - |rightQuotient| |cyclic?| |ncols| |e02ddf| |resultantReduit| - |leadingCoefficient| |reduceByQuasiMonic| |cAsec| |linSolve| |bfEntry| - |upperCase?| |dAndcExp| |readUInt32!| |maxColIndex| |lcm| |rdHack1| - |hex| |source| |primitiveMonomials| |getExplanations| |bezoutMatrix| - |irForm| |clipParametric| |polyRicDE| |constDsolve| - |selectMultiDimensionalRoutines| |removeRedundantFactors| |rank| - |setLegalFortranSourceExtensions| |setLabelValue| - |reducedDiscriminant| |reductum| |complementaryBasis| - |resultantReduitEuclidean| |float?| |element?| |headReduced?| |append| - |localAbs| |set| |f02bjf| |s14abf| |factorSquareFreeByRecursion| - |mathieu12| |printInfo| |baseRDE| |colorFunction| |s20acf| |biRank| - |overset?| |gcd| |vconcat| |target| |regime| |null?| |subHeight| - |unexpand| |linearlyDependentOverZ?| |antiAssociative?| - |algebraicDecompose| |expintegrate| |e04jaf| |false| |polyred| - |realZeros| |normal01| |zeroSquareMatrix| |squareFreePrim| - |backOldPos| |fprindINFO| |leftFactorIfCan| |writable?| |lagrange| - |balancedFactorisation| |bat1| |f04faf| |OMreadFile| |coerceImages| - |newLine| |integerIfCan| |gradient| |compiledFunction| |bits| |lllp| - |contains?| |table| |Ei| |outerProduct| |credPol| - |rewriteIdealWithRemainder| |subtractIfCan| |permutation| - |drawComplexVectorField| |approxSqrt| |gramschmidt| |cycles| |hermite| - |virtualDegree| |new| |lexTriangular| |position| |listRepresentation| - |removeSquaresIfCan| |localReal?| |prinshINFO| |contours| |infRittWu?| - |coerce| |groebnerIdeal| |lists| |iroot| |nand| |mergeDifference| - |romberg| |elRow1!| |errorKind| |physicalLength| |primintegrate| - |construct| |leftCharacteristicPolynomial| |c06gbf| |se2rfi| - |trapezoidalo| |getMatch| |writeByte!| |hspace| |loopPoints| - |universe| |groebner| |factorials| - |removeRoughlyRedundantFactorsInContents| |roughSubIdeal?| |ldf2lst| - |regularRepresentation| |string?| |stoseInvertibleSetreg| |void| - |normInvertible?| |nary?| |OMputAtp| |rewriteIdealWithHeadRemainder| - |dmpToP| |second| |multiple?| |s17ahf| |findCycle| |leastMonomial| - |autoReduced?| |algebraicOf| |symmetricRemainder| |indicialEquation| - |conjugates| |quatern| |third| |basis| |child| |coth2tanh| |unary?| - |quasiRegular?| |pleskenSplit| |drawComplex| |charpol| |row| - |extendedSubResultantGcd| |factorial| |zero| |dualSignature| - |quotient| |newTypeLists| |tanh2coth| |addPoint2| - |brillhartIrreducible?| |invmod| |semicolonSeparate| - |stoseLastSubResultant| |box| |chebyshevT| |binaryTournament| - |showRegion| |range| |cycleLength| |rightOne| |janko2| - |moreAlgebraic?| |radicalEigenvector| |listLoops| |leftReducedSystem| - |And| |e01daf| |createGenericMatrix| |setright!| - |conditionsForIdempotents| |simplifyPower| |elaborateFile| |rroot| - |inrootof| |operators| |mapGen| |Or| |rotatey| |rationalPoints| - |jvmDoubleConstantTag| |integral| |perfectNthRoot| - |inverseIntegralMatrixAtInfinity| |pop!| |alternating| |mapSolve| - |minus!| |Not| |isExpt| |mainForm| |cup| |numberOfComponents| |c05nbf| - |reduction| |permutationGroup| |rootRadius| |restorePrecision| - |s18def| |whileLoop| |rightTrace| |f07adf| |stronglyReduce| - |SturmHabichtCoefficients| |functorData| |distance| |laguerreL| - |mesh?| |over| |measure2Result| |exprToUPS| |listexp| |isTimes| - |sayLength| |entry| |bottom!| |changeBase| |basisOfRightNucleus| - |dual| |failed| |pushup| |stirling2| |match?| |eigenvalues| |d01amf| - |exprex| |irreducibleFactors| |simpsono| |hcrf| |sumSquares| - |modularFactor| |stripCommentsAndBlanks| |dihedral| |repeatUntilLoop| - |sort| |inputBinaryFile| |expandPower| |makeCrit| |completeHermite| - |elementary| |deepExpand| |palgint0| |keys| - |generalizedContinuumHypothesisAssumed?| |pdf2df| |perfectNthPower?| - |generalizedContinuumHypothesisAssumed| |readBytes!| |remove!| |imagi| - |oddlambert| |trace2PowMod| |partitions| |karatsubaDivide| |setelt| - |shallowExpand| |multiset| |LiePoly| |random| |commutative?| |ksec| - |before?| |logGamma| |makeFR| |error| |integralBasisAtInfinity| - |rationalPoint?| |character?| |repeating| |cTan| |hclf| - |positiveRemainder| |sizeLess?| |extractIndex| - |setAttributeButtonStep| |increasePrecision| |setelt!| |copy| |entry?| - |shiftLeft| |selectNonFiniteRoutines| |patternMatchTimes| - |multiplyExponents| |critMonD1| |s15adf| |divideIfCan!| - |principalAncestors| |isOr| |external?| |distFact| |sortConstraints| - |unit| |leftScalarTimes!| |freeOf?| |s14baf| - |jvmInterfaceMethodConstantTag| |callForm?| - |semiResultantReduitEuclidean| |autoCoerce| |imagI| |extendIfCan| - |recip| |redPo| |monicDecomposeIfCan| |genericLeftTrace| |maxPoints| - |rootOf| |plenaryPower| |denomRicDE| |setleaves!| |noLinearFactor?| - |oddintegers| |OMlistSymbols| |removeIrreducibleRedundantFactors| - |horizConcat| |asechIfCan| |forLoop| |top| |solveInField| - |nextColeman| |tubeRadius| |mappingAst| |cylindrical| - |validExponential| |bsolve| |central?| |mpsode| |multiplyCoefficients| - |continue| |rst| |pile| |d01gbf| |OMsupportsCD?| |idealSimplify| - |primextintfrac| |vectorise| |viewDeltaXDefault| |OMlistCDs| |trunc| - |parents| |lSpaceBasis| |exprHasAlgebraicWeight| |gethi| - |fortranDoubleComplex| |unparse| |t| |cyclicCopy| - |purelyTranscendental?| |showClipRegion| |backspace| |jvmFinal| - |firstNumer| |eval| |complexNumericIfCan| |froot| - |createMultiplicationTable| |completeHensel| |processTemplate| - |integralMatrixAtInfinity| |tRange| |c02agf| |inverseColeman| - |rootsOf| |setMinPoints| |optional?| |delay| |eisensteinIrreducible?| - |sum| |readInt16!| |addPoint| |degreePartition| |minColIndex| - |distribute| |npcoef| |droot| |coerceS| |s17akf| |datalist| |omError| - |UpTriBddDenomInv| |setRealSteps| |constantCoefficientRicDE| - |heapSort| |relativeApprox| |e02bdf| |f02axf| |d02bbf| |readable?| - |e02bef| |lyndon| |solve| |normalizedDivide| |f02aaf| - |lazyPseudoDivide| |relationsIdeal| |is?| |htrigs| |comp| - |macroExpand| |c06eaf| |rCoord| |singularitiesOf| - |clearFortranOutputStack| |cycleEntry| |outputGeneral| |s17acf| - |primintfldpoly| |d02bhf| |doubleRank| |leftDiscriminant| |interpret| - |curry| |s21baf| |factorByRecursion| |degreeSubResultantEuclidean| - |prepareDecompose| |measure| |setref| |exponential| - |removeSuperfluousQuasiComponents| |f02awf| |fortranLiteral| |powmod| - |numberOfCycles| |inverseLaplace| |expint| |mapdiv| |difference| - |reducedForm| |composites| |bat| |getProperty| |normalizeAtInfinity| - |makeGraphImage| |cSec| |e04gcf| |rightGcd| |indicialEquations| - |scalarMatrix| |trigs2explogs| |digits| |modularGcdPrimitive| - |nthFractionalTerm| |closedCurve?| |size?| |iflist2Result| - |patternMatch| |divide| |simplifyLog| |integralAtInfinity?| - |geometric| |palgextint| |oblateSpheroidal| |factorset| - |setVariableOrder| |fortranCharacter| |besselK| |identification| - |fortranCarriageReturn| |setStatus| |degreeSubResultant| - |numberOfImproperPartitions| |cycle| |divisorCascade| |nil| - |lookupFunction| |sturmVariationsOf| |infieldint| |smith| |categories| - |airyBi| |cAsech| |cyclicGroup| |squareFreePolynomial| - |removeRoughlyRedundantFactorsInPols| |environment| |mapMatrixIfCan| - |identityMatrix| |d01anf| |removeSinhSq| |vertConcat| |lowerBound| - |LazardQuotient2| |normalise| |initializeGroupForWordProblem| - |triangular?| |factor1| |elseBranch| |level| |trueEqual| - |symmetricTensors| |LagrangeInterpolation| |zero?| - |parabolicCylindrical| |setprevious!| |tanNa| |checkPrecision| - |primPartElseUnitCanonical| |fortranInteger| |approximate| |asinh| - |s13aaf| |hdmpToP| |leftTrace| |cyclicParents| |pointColorDefault| - |quoByVar| |partialQuotients| |reduced?| |eigenvector| |complex| - |acosh| |intermediateResultsIF| |addMatchRestricted| |branchPoint?| - |selectAndPolynomials| |redpps| |symbolIfCan| |jacobiIdentity?| - |singRicDE| |node?| |atanh| |dom| |OMcloseConn| |selectsecond| - |lieAlgebra?| |s17adf| |extractPoint| |nextSublist| |pointData| - |safetyMargin| |acoth| |obj| |resetNew| |hostPlatform| - |complexEigenvalues| |cyclicEntries| |opeval| |univcase| |normDeriv2| - |upperCase!| |asech| |typeForm| |makeResult| |pointSizeDefault| - |imagj| |rename!| |quotedOperators| |f01qef| - |permutationRepresentation| |colorDef| |binarySearchTree| |op| - |d01asf| |children| |halfExtendedSubResultantGcd1| |delta| - |functionIsContinuousAtEndPoints| |alphanumeric?| |normFactors| - |internalZeroSetSplit| |basisOfRightAnnihilator| |multiple| - |putProperties| |expandTrigProducts| |mathieu24| |normalizeIfCan| - |OMgetAtp| |adjoint| |lazyPremWithDefault| |applyQuote| |setImagSteps| - |iExquo| |e02daf| |getBadValues| |randnum| |karatsuba| - |matrixDimensions| |critT| |toseLastSubResultant| |consnewpol| - |indices| |psolve| |doubleDisc| |permutations| - |semiIndiceSubResultantEuclidean| |edf2efi| |s17dcf| |diff| |setTex!| - |subQuasiComponent?| |topFortranOutputStack| |factorPolynomial| - |reflect| UTS2UP |shufflein| |monicLeftDivide| |argscript| |ruleset| - |prindINFO| |prefixRagits| |simpleBounds?| - |genericRightMinimalPolynomial| |selectIntegrationRoutines| |tube| - |lifting1| |removeZero| |optimize| |writeBytes!| |oddInfiniteProduct| - |returnType!| |iipow| |zeroDimensional?| |zoom| |substitute| - |bringDown| |rk4qc| |sts2stst| |e01sbf| |leftRemainder| |lambda| - |phiCoord| |symmetricDifference| |hexDigit| |retract| |unitVector| - |groebnerFactorize| |const| |unitCanonical| |bindings| |suchThat| - |absolutelyIrreducible?| |pole?| |extractIfCan| |evenlambert| - |binaryFunction| |enqueue!| |argument| |possiblyNewVariety?| - |polygamma| |contractSolve| |divideIfCan| |revert| |horizontalTab| - |tracePowMod| |insert!| |taylorRep| |cAtanh| |wreath| |taylorQuoByVar| - |isAbsolutelyIrreducible?| |c05adf| |infinite?| |cardinality| - |aspFilename| |tanhIfCan| |LiePolyIfCan| |applyRules| |scopes| - |curryRight| |isAtom| |root?| |evenInfiniteProduct| |decomposeFunc| - |minGbasis| |implies| |dn| |removeCoshSq| |constantOperator| - |hitherPlane| |SturmHabichtSequence| |interReduce| |LyndonBasis| - |updateStatus!| |generalizedEigenvectors| |createPrimitiveElement| - |inspect| |explimitedint| |mainKernel| |unrankImproperPartitions0| - |nlde| |rightRank| |oneDimensionalArray| |continuedFraction| |f04asf| - |leftLcm| |llprop| |setfirst!| |pquo| |digamma| |clipBoolean| |digit?| - |flexibleArray| |minPoints| |df2ef| |OMreadStr| |e04ucf| |B1solve| - |unit?| |rewriteSetByReducingWithParticularGenerators| |curve| - |unravel| |upDateBranches| |newline| |critB| |alphanumeric| |makeop| - |hash| |elements| |truncate| |createLowComplexityTable| |printTypes| - |elem?| |mainSquareFreePart| |bombieriNorm| |repeating?| |count| - |OMgetEndBVar| |univariateSolve| |just| |internalSubQuasiComponent?| - |imagE| |category| |moebiusMu| |iicosh| |roughBasicSet| |changeName| - |maxdeg| |rightLcm| |lquo| |insertRoot!| |rightFactorIfCan| - |elliptic?| |domain| |rationalApproximation| |fillPascalTriangle| - |sechIfCan| |f02bbf| |inGroundField?| |iisec| |laplacian| |aQuadratic| - |completeEval| |generator| |rectangularMatrix| |package| |shiftRoots| - |monomialIntegrate| |latex| |unvectorise| |scan| |encodingDirectory| - |partialFraction| |asinIfCan| |generalSqFr| |e02def| |cSinh| - |var1Steps| |connect| |OMbindTCP| |besselY| |firstSubsetGray| |even?| - |rightTrim| |rischDE| |stoseSquareFreePart| |properties| |overlabel| - |addmod| |showScalarValues| |numberOfChildren| |topPredicate| - |gcdPolynomial| |summation| |leftTrim| |fmecg| |invertibleElseSplit?| - |birth| |modifyPointData| |translate| |char| |fixedPoint| - |stoseInvertible?| |collectQuasiMonic| |cfirst| |monicRightDivide| - |exactQuotient| |tower| |identitySquareMatrix| |whitePoint| |isMult| - |changeVar| |variationOfParameters| |setButtonValue| |leftTraceMatrix| - |swapColumns!| |stoseInvertibleSet| |useSingleFactorBound| - |externalList| |sumOfSquares| |mulmod| |compdegd| |s01eaf| |putGraph| - |binding| |groebner?| |semiDegreeSubResultantEuclidean| - |changeMeasure| |dihedralGroup| |totalGroebner| |rightTraceMatrix| - |check| |quadraticNorm| |maxrank| |ListOfTerms| |f01qdf| |innerSolve1| - |setIntersection| |numberOfMonomials| |getGraph| |SFunction| - |bumptab1| |meshPar1Var| |computePowers| |rootOfIrreduciblePoly| - |outputSpacing| |laurentIfCan| |palglimint0| - |semiSubResultantGcdEuclidean1| |c05pbf| |float| - |tryFunctionalDecomposition| |OMputApp| |coerceL| |yCoord| - |fortranDouble| |cSech| |pointColor| |FormatArabic| - |genericLeftTraceForm| |minimalPolynomial| |units| |matrix| - |OMputBind| |splitDenominator| |module| |removeDuplicates!| - |factorsOfCyclicGroupSize| |e02gaf| |logIfCan| |rationalPower| |xn| - |seriesToOutputForm| |removeDuplicates| |drawToScale| |complexNumeric| - |incr| |subResultantChain| |lighting| |antiCommutator| - |lastSubResultant| |e01bhf| |removeCosSq| |rangePascalTriangle| - |divideExponents| |localUnquote| |tubePoints| |polynomialZeros| - |iomode| |hi| |linearMatrix| |move| |solveid| |minRowIndex| - |fortranReal| |pol| |kernels| |traceMatrix| |sequence| |divisors| - |integralBasis| |normalElement| |rk4f| |jvmLongConstantTag| - |fractionPart| |approximants| |roughEqualIdeals?| |iisqrt2| |operator| - |LowTriBddDenomInv| |pointColorPalette| |nextItem| |complexElementary| - |elaborate| |extractProperty| |ip4Address| |primitivePart| |iisinh| - |readIfCan!| |code| |position!| |pmComplexintegrate| |univariate| - |rightScalarTimes!| |meatAxe| |exprHasWeightCosWXorSinWX| - |paraboloidal| |options| |tanQ| |low| |reverseLex| |setEmpty!| - |viewPosDefault| |center| |constructor| |ramified?| |prevPrime| - |lazyPquo| RF2UTS |hyperelliptic| |arguments| |addBadValue| |sdf2lst| - |lineColorDefault| |binomThmExpt| |outputAsScript| |isAnd| GE - |deleteProperty!| |times!| |useNagFunctions| |deepestTail| - |combineFeatureCompatibility| |tablePow| |string| |nsqfree| |parts| - |upperCase| |setvalue!| |subscript| GT |leftZero| |primeFactor| - |factor| |genericLeftMinimalPolynomial| |bumptab| |e02dff| |ceiling| - |antiCommutative?| |constantLeft| |jacobi| |chebyshevU| |ptFunc| - |sqrt| |untab| |host| |showTheRoutinesTable| |write!| |extension| - |testModulus| |mainDefiningPolynomial| |OMputEndError| |aLinear| - |normalForm| |recoverAfterFail| |real| |primeFrobenius| |gcdprim| - |rarrow| |sinhcosh| |iiacot| |f07fef| |singular?| |returnTypeOf| - |call| |bandedHessian| |precision| |imag| |c06ebf| |cothIfCan| - |mapBivariate| |linefeed| |linearForm| |delete| |setClosed| - |squareTop| |floor| |directProduct| |swapRows!| |eigenMatrix| - |graeffe| |rischDEsys| |fractRagits| |lift| |thetaCoord| - |reducedContinuedFraction| |rk4| |jacobian| |besselI| - |solveLinearPolynomialEquationByFractions| |countRealRoots| - |gcdcofactprim| |head| |internalSubPolSet?| |reduce| - |solveLinearPolynomialEquation| |tree| |getProperties| |whatInfinity| - |noncommutativeJordanAlgebra?| |unprotectedRemoveRedundantFactors| - |leftRecip| |f02adf| |brace| |pack!| |postfix| |minPoly| - |selectPDERoutines| |decimal| |status| |PDESolve| |BumInSepFFE| - |safeFloor| |solve1| |destruct| |f04axf| |numberOfComposites| - |deepestInitial| |isQuotient| |complexNormalize| |getIdentifier| - |sqfree| |rotatex| |nextsubResultant2| |wholeRadix| |stopTable!| - |rightRegularRepresentation| |stopTableInvSet!| |squareFreeFactors| - |nullSpace| |relerror| |e01sef| |purelyAlgebraicLeadingMonomial?| - |nextNormalPrimitivePoly| |wordInStrongGenerators| |lazyEvaluate| - |setMaxPoints3D| |setErrorBound| |createLowComplexityNormalBasis| - |merge| |setAdaptive3D| |baseRDEsys| |iisqrt3| |elaboration| - |setsubMatrix!| |myDegree| |s21bdf| |semiResultantEuclidean2| - |critMTonD1| |lazyPrem| |strongGenerators| |generate| |completeSmith| - |integers| |OMUnknownSymbol?| |antisymmetric?| |prolateSpheroidal| - |coercePreimagesImages| |rightZero| |monomial| |maxrow| |copies| - |assign| |OMgetVariable| |reify| |stoseIntegralLastSubResultant| - |rootPoly| |lowerCase!| |s17dgf| |getCurve| |subst| |f02agf| - |multivariate| |clearDenominator| |f07fdf| |generalLambert| |OMgetApp| - |incrementBy| |f04mbf| |height| |minordet| |swap!| |hessian| |subset?| - |csc2sin| |id| |OMgetEndError| |variables| |sample| |tubePlot| - |divergence| |stoseInvertibleSetsqfreg| |linkToFortran| |wholePart| - |packageCall| |expand| |secIfCan| |readLine!| |nothing| |lo| |rspace| - |squareMatrix| |jvmStatic| |defineProperty| |setTopPredicate| - |quadratic?| |compile| |lfextlimint| |makeprod| |filterWhile| - |supDimElseRittWu?| |mainMonomials| |aCubic| |step| |schwerpunkt| - |showAllElements| |getCode| |headRemainder| |RittWuCompare| |escape| - |filterUntil| |incrementKthElement| |OMputEndAttr| |padicallyExpand| - |expandLog| |invertible?| |any| |checkForZero| |objects| - |nextLatticePermutation| |ReduceOrder| |stack| |stFunc1| |square?| - |digit| |solid| |log10| |twoFactor| |select| |internal?| - |makingStats?| |symmetricGroup| |base| |solveRetract| |nextPartition| - |fortranLogical| |shape| |d02kef| |bitand| |chiSquare| |nodeOf?| - |infiniteProduct| |lazyVariations| |cot2tan| |factorOfDegree| |real?| - |taylor| |palgint| |permanent| |showSummary| |f01brf| |byte| |iiatan| - |bitior| |coerceListOfPairs| |mkIntegral| |algDsolve| |green| - |tan2cot| |laurent| |power| |cycleSplit!| |setClipValue| - |associatorDependence| |initiallyReduced?| - |dimensionOfIrreducibleRepresentation| |support| |separateDegrees| - |iitan| |puiseux| |rightUnit| |minIndex| |modularGcd| |showAttributes| - |leadingTerm| |outputAsTex| |gbasis| |blue| |limitedint| |uniform| - |represents| |withPredicates| |cosh2sech| |doubleComplex?| - |subNodeOf?| |hMonic| |refine| |iitanh| |e02bcf| |parseString| - |jordanAdmissible?| |makeRecord| |s17dhf| |palgRDE0| |OMgetEndAtp| - |zeroDimPrimary?| |basicSet| |hasTopPredicate?| |superscript| - |invertibleSet| |endOfFile?| |less?| |powerAssociative?| |e02bbf| - |leastPower| |cAcot| |realEigenvectors| |squareFreePart| |OMputFloat| - |iisech| |d01gaf| |curveColor| |fglmIfCan| |functionIsOscillatory| - |f04atf| |leftExactQuotient| |exponential1| |moduleSum| |int| - |explicitlyEmpty?| |f01rcf| |infieldIntegrate| |subNode?| - |knownInfBasis| |genericRightNorm| |diagonal?| |constant| - |coefficients| |crest| |FormatRoman| |cschIfCan| |fullDisplay| - |OMencodingXML| |tail| |lieAdmissible?| |eulerPhi| |typeLists| - |basisOfLeftAnnihilator| |genericRightTrace| |resetAttributeButtons| - |subresultantVector| |previous| |lazyPseudoRemainder| |bounds| - |cAcosh| |viewport3D| |isobaric?| |splitNodeOf!| |shiftRight| - |initial| |idealiser| |s18dcf| |hue| |constant?| |swap| - |leviCivitaSymbol| |rightMinimalPolynomial| |startPolynomial| - |sinIfCan| |cAsinh| |symmetricSquare| |makeSketch| |e02akf| - |splitLinear| |reindex| |OMwrite| |outputList| |leadingBasisTerm| - |resetBadValues| |frobenius| |partition| |iiatanh| |po| |musserTrials| - |apply| |double?| |retractable?| |mergeFactors| |viewZoomDefault| - |f2df| |genericPosition| |messagePrint| |shrinkable| Y - |curveColorPalette| |sn| |infinityNorm| |first| |cscIfCan| |varList| - GF2FG |zeroMatrix| |e04dgf| |diagonalProduct| |d01alf| |length| - |xCoord| |rest| |OMgetBVar| |mainValue| |mapExponents| - |mainCoefficients| |basisOfRightNucloid| |iprint| |tab| - |OMParseError?| |OMreceive| |scripts| |endSubProgram| |key| - |makeVariable| |epilogue| |totalDifferential| |createNormalElement| - |brillhartTrials| |tensorProduct| |middle| |constantIfCan| |addMatch| - |quoted?| |point| |fullPartialFraction| |compose| |GospersMethod| - |graphs| |rowEch| |argumentList!| |power!| |bandedJacobian| |filename| - |leftMinimalPolynomial| |saturate| |radicalOfLeftTraceForm| - |palgLODE0| |cyclotomicDecomposition| |hermiteH| |uncouplingMatrices| - |modTree| |d03edf| |basisOfNucleus| |imaginary| |chineseRemainder| - |mainMonomial| |solveLinear| |LazardQuotient| |createNormalPoly| - |commutator| |critM| |series| |parse| |clipPointsDefault| |heap| - |log2| |sec2cos| |numberOfComputedEntries| |hostByteOrder| - |showFortranOutputStack| |jvmSynchronized| |disjunction| - |collectUpper| |inverse| |twist| |insertMatch| |scalarTypeOf| - |discriminantEuclidean| |leftPower| |blankSeparate| - |mapUnivariateIfCan| |sech2cosh| |cartesian| |s21bbf| |formfeed| - |remainder| |transform| |factorList| |leadingIdeal| |c06gsf| |points| - |input| |pToHdmp| |factorAndSplit| |lambert| |systemSizeIF| |maxint| - |getDatabase| |imports| |bivariateSLPEBR| |integralDerivationMatrix| - |signAround| |basisOfLeftNucloid| |library| |min| |expIfCan| |ef2edf| - |plus| |f01ref| |euclideanSize| |rightAlternative?| |iiasec| - |voidMode| |coordinate| |c06fuf| |definingInequation| |HenselLift| - |polar| |halfExtendedResultant2| |numberOfNormalPoly| |makeViewport2D| - |monomialIntPoly| |semiLastSubResultantEuclidean| |stopMusserTrials| - |polarCoordinates| |branchIfCan| |value| |alternatingGroup| - |principalIdeal| |mappingMode| |compactFraction| |nthRootIfCan| - |copy!| |discriminant| |singularAtInfinity?| |groebgen| |deref| - |updatD| |inRadical?| |pair?| |slex| |unknownEndian| - |branchPointAtInfinity?| |Si| |OMencodingSGML| |OMserve| |times| - |primitivePart!| |name| |polyPart| |reset| |ideal| |mr| |rational| - |dimensionsOf| |sign| |pdct| |stirling1| |jvmMethodrefConstantTag| - |goodnessOfFit| |inHallBasis?| |body| |atoms| |ratDenom| - |unitsColorDefault| |leftNorm| |palgRDE| |prod| |minimize| |s19adf| - |negative?| |outputArgs| |cyclePartition| |numberOfPrimitivePoly| - |write| |comparison| |generalPosition| |f02akf| |createRandomElement| - |member?| |PollardSmallFactor| |jvmProtected| |acscIfCan| - |generateIrredPoly| |indiceSubResultant| - |stiffnessAndStabilityOfODEIF| |save| |df2fi| |copyInto!| - |extractClosed| |trigs| |OMgetSymbol| |Vectorise| |index| |s18acf| - |enumerate| |monom| |d02cjf| |f04jgf| |OMputEndBVar| |palginfieldint| - |d01aqf| |leftUnit| |hasHi| |nextPrime| |setleft!| |carriageReturn| - |createPrimitivePoly| |rewriteIdealWithQuasiMonicGenerators| - |var2StepsDefault| |child?| |mindegTerm| |OMgetObject| |coHeight| - |asecIfCan| |multiEuclideanTree| |pair| |screenResolution| - |minimumExponent| |leadingCoefficientRicDE| |mainVariables| ** - |indiceSubResultantEuclidean| |e04mbf| |lp| |closedCurve| - |factorGroebnerBasis| |vspace| |startTableInvSet!| - |linearAssociatedLog| |common| |halfExtendedSubResultantGcd2| - |makeSeries| |resultant| |deepCopy| |parabolic| |d01apf| - |hasPredicate?| |bumprow| |e02agf| |setPosition| |setMaxPoints| - |acosIfCan| |edf2ef| |sub| |hconcat| |cCot| |shade| |roughBase?| - |quasiAlgebraicSet| |ridHack1| |countable?| |partialNumerators| - |raisePolynomial| |sin2csc| |qPot| |port| |certainlySubVariety?| - |meshPar2Var| |s15aef| |queue| |initTable!| |OMunhandledSymbol| |show| - |kind| |reverse| |prinb| |s18aef| |OMUnknownCD?| |lowerCase?| |cLog| - |drawCurves| |mix| |var1StepsDefault| |ran| |OMencodingUnknown| - |basisOfCommutingElements| |say| |quotientByP| |mainContent| - |setchildren!| |monomRDE| |mapDown!| |euler| |interpretString| - |OMgetEndAttr| |controlPanel| |nthr| |trace| |categoryMode| - |monicModulo| |bag| |selectfirst| |lyndonIfCan| |distdfact| - |headReduce| |prem| |prime?| |inverseIntegralMatrix| |complexRoots| - |d02ejf| |setMinPoints3D| |printStats!| |meshFun2Var| |exponents| - |linearElement| |irreducible?| |currentCategoryFrame| |youngGroup| - |factorFraction| |addPointLast| |exprToXXP| |internalIntegrate| - |extendedResultant| |tanintegrate| |root| |extractTop!| - |physicalLength!| |computeInt| |s19abf| |symFunc| |totalLex| - |clearTheSymbolTable| |numberOfHues| |explogs2trigs| |mdeg| |iiacosh| - |nullity| |integerBound| |graphStates| |frst| |triangSolve| - |alphabetic?| |numericalIntegration| |iifact| |complement| |search| - |OMgetInteger| |ScanRoman| |monicDivide| |ord| |jvmTransient| - |fortranLinkerArgs| |isPlus| |bitCoef| |cCosh| |rootPower| |nor| - |cross| |rightCharacteristicPolynomial| |setValue!| - |removeSuperfluousCases| |clikeUniv| |convergents| |quadratic| - |s19aaf| |wholeRagits| |groebSolve| |graphCurves| |makeViewport3D| - |gcdPrimitive| |removeRoughlyRedundantFactorsInPol| |qfactor| - |createIrreduciblePoly| |associator| |completeEchelonBasis| - |symbolTable| |close!| |pointPlot| |chvar| |recolor| |constantRight| - |dfRange| |degree| |cCsch| |product| |reverse!| |rationalIfCan| - |intersect| |subresultantSequence| |univariatePolynomials| - |alternative?| |OMputError| |qinterval| |d01fcf| |weighted| - |pushFortranOutputStack| |jvmSuper| |writeInt8!| |unitNormal| |s17def| - |e01bgf| |iibinom| |triangularSystems| |leastAffineMultiple| |entries| - |realElementary| |popFortranOutputStack| |readUInt8!| |coord| - |accuracyIF| |trapezoidal| |debug3D| |perfectSqrt| |imagK| - |makeFloatFunction| |patternVariable| |numericalOptimization| - |pointLists| |lexico| |outputAsFortran| |find| |identity| - |extendedEuclidean| |rule| |associatedSystem| |monic?| |slash| - |region| |characteristic| |denominators| |bitTruth| |c02aff| - |littleEndian| |maxPoints3D| |conditionP| |top!| |realRoots| - |pascalTriangle| |mainPrimitivePart| |trim| |atom?| |rowEchLocal| - |stoseInvertible?sqfreg| |probablyZeroDim?| |sincos| |separateFactors| - |numberOfFractionalTerms| |linearPolynomials| |jvmAbstract| |Lazard| - |extensionDegree| |internalIntegrate0| |diagonal| |plusInfinity| - |toseInvertibleSet| |option?| |lazyGintegrate| |clearTheIFTable| - |interactiveEnv| |point?| |sPol| |LyndonCoordinates| - |wordsForStrongGenerators| |union| |multinomial| |appendPoint| - |minusInfinity| |subSet| |readLineIfCan!| |userOrdered?| - |pseudoRemainder| |solveLinearPolynomialEquationByRecursion| - |coth2trigh| |cycleElt| |limit| |f04maf| |subResultantsChain| - |axesColorDefault| |dictionary| |ScanFloatIgnoreSpacesIfCan| |max| - |definingPolynomial| |binomial| |expPot| |leftQuotient| |firstDenom| - |seed| |mapExpon| |rightFactorCandidate| |printingInfo?| - |mainExpression| |terms| |balancedBinaryTree| |plus!| |Lazard2| - |bivariatePolynomials| |pattern| |debug| |skewSFunction| |duplicates| - |jvmFieldrefConstantTag| |scanOneDimSubspaces| |cycleTail| - |OMgetError| |traverse| |ScanFloatIgnoreSpaces| |powers| D - |splitConstant| |chiSquare1| |computeBasis| |f02wef| - |semiSubResultantGcdEuclidean2| |ellipticCylindrical| |type| - |algebraicCoefficients?| |reciprocalPolynomial| |henselFact| - |nthExpon| |integrate| |halfExtendedResultant1| |signatureAst| - |crushedSet| |innerEigenvectors| |expextendedint| |vector| |pushdterm| - |transcendent?| |numberOfDivisors| |varselect| |Beta| - |nonSingularModel| |dim| |bivariate?| |differentiate| |setProperties| - |dioSolve| |fi2df| |readUInt16!| |choosemon| |e01baf| |diag| |concat| - |leftOne| |cAsin| |bernoulliB| |poisson| |setOfMinN| |optAttributes| - |repSq| |ode| |lprop| |multiEuclidean| |pushuconst| |predicates| - |invmultisect| |yellow| |finiteBasis| |overbar| |subTriSet?| - |createZechTable| |SturmHabichtMultiple| |qroot| |ode2| |clearCache| - |airyAi| |linearDependence| |iiabs| |OMputEndApp| - |linearAssociatedExp| |algSplitSimple| |perfectSquare?| |normalized?| - |vark| |cyclicSubmodule| |generic?| |s17dlf| |coefficient| - |create3Space| |ffactor| |eigenvectors| |exponentialOrder| |linear?| - |Frobenius| |OMputObject| |has?| |buildSyntax| |iisin| |cAtan| - |atrapezoidal| |primPartElseUnitCanonical!| |decompose| |iterationVar| - |print| |expintfldpoly| |isEquiv| |splitSquarefree| |concat!| |f01mcf| - |monomRDEsys| |makeCos| |resolve| |cAcos| |fractionFreeGauss!| - |pomopo!| |jvmVolatile| |Hausdorff| |lex| |viewDefaults| |sncndn| - |s21bcf| |convert| |c06ekf| |eyeDistance| |OMgetAttr| |dmpToHdmp| - |primitiveElement| |numer| |midpoint| |key?| |outputForm| |conical| - |quasiMonicPolynomials| |OMputEndObject| |printInfo!| |OMmakeConn| - |denom| |typeList| |ptree| |column| |rootProduct| |expressIdealMember| - |push| |leader| |thenBranch| |property| |nextPrimitivePoly| - |deleteRoutine!| |tanAn| |shellSort| |listYoungTableaus| |compBound| - |linear| |removeSinSq| |title| |inR?| |radicalRoots| |pi| |belong?| - |ignore?| |unaryFunction| |recur| |OMgetEndApp| |internalDecompose| - |mkAnswer| |infinity| |changeThreshhold| |replace| |LyndonWordsList1| - |e04ycf| |removeRedundantFactorsInContents| |setFormula!| |color| - |getStream| |padicFraction| |polynomial| |rotatez| |besselJ| - |ramifiedAtInfinity?| |rootBound| |leadingIndex| - |irreducibleRepresentation| |e| |radicalEigenvectors| |graphImage| - |removeConstantTerm| |OMread| |ref| |spherical| |d02gaf| - |constantToUnaryFunction| |f01qcf| |btwFact| |e02ajf| |jokerMode| - |kernel| |getRef| |principal?| |quadraticForm| |mathieu23| - |pseudoDivide| |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 + |Enumeration| |Mapping| |Record| |Union| |constantLeft| |mathieu22| + |list| |parametersOf| |setchildren!| |revert| |tubePointsDefault| + |swap| |whileLoop| |draw| |atanIfCan| |jacobi| |cyclicEqual?| + |monomRDE| |leviCivitaSymbol| |horizontalTab| |flexible?| |rightTrace| + |bright| |buildSyntax| |lazyIntegrate| |ocf2ocdf| |chebyshevU| + |mapDown!| |tracePowMod| |irVar| |rightMinimalPolynomial| |f07adf| + |iisin| |null| |laplace| |ptFunc| |iFTable| |euler| |Ci| |insert!| + |startPolynomial| |stronglyReduce| |cAtan| |not| |iicoth| |cache| + |acotIfCan| |untab| |interpretString| |taylorRep| |resize| |sinIfCan| + |SturmHabichtCoefficients| |atrapezoidal| |and| |makeObject| + |listOfLists| |host| |ddFact| |OMgetEndAttr| |cAtanh| |ParCond| + |functorData| |cAsinh| |or| |primPartElseUnitCanonical!| + |exprToGenUPS| |showTheRoutinesTable| |printHeader| |coef| + |controlPanel| |wreath| |lfunc| |symmetricSquare| |distance| |xor| + |decompose| |quasiComponent| |finiteBound| |write!| |nthr| + |taylorQuoByVar| |legendre| |makeSketch| |laguerreL| |iterationVar| + |case| |list?| |extension| |squareFreeLexTriangular| |categoryMode| + |isAbsolutelyIrreducible?| |outlineRender| |supRittWu?| |empty| + |e02akf| |mesh?| |expintfldpoly| |Zero| |homogeneous?| |testModulus| + |rur| |monicModulo| |left| |lintgcd| |in?| |c05adf| |torsion?| + |splitLinear| |over| |One| |isEquiv| |shift| |retractIfCan| + |bernoulli| |mainDefiningPolynomial| |scripted?| |bag| |infinite?| + |right| |coshIfCan| |size| |primes| |curve?| |reindex| + |measure2Result| |splitSquarefree| |more?| |OMputEndError| + |setEpilogue!| |selectfirst| |cardinality| |sumOfDivisors| |exprToUPS| + |OMwrite| |concat!| |viewWriteAvailable| |insertBottom!| |aLinear| + |lyndonIfCan| |mat| |aspFilename| |OMgetEndBind| |leadingBasisTerm| + |listexp| |f01mcf| |mathieu11| |normalForm| |cdr| |distdfact| |f02ajf| + |s17ajf| |tanhIfCan| |resetBadValues| |isTimes| |monomRDEsys| + |underscore| |OMputAttr| |recoverAfterFail| |headReduce| + |mapUnivariate| |OMputInteger| |LiePolyIfCan| |sayLength| |frobenius| + |makeCos| |elt| |OMconnOutDevice| |primeFrobenius| |setlast!| |prem| + EQ |applyRules| |inconsistent?| |bottom!| |partition| |cAcos| + |signature| |someBasis| |makeSin| |gcdprim| |prime?| |scopes| + |palglimint| |iiatanh| |changeBase| |fractionFreeGauss!| + |intcompBasis| |ratPoly| |rarrow| |inverseIntegralMatrix| |curryRight| + |conjugate| |basisOfRightNucleus| |po| |pomopo!| |f01maf| |matrixGcd| + |sinhcosh| |complexRoots| |isAtom| |viewPhiDefault| |musserTrials| + |dual| |jvmVolatile| |OMgetBind| |iiacot| |composite| |d02ejf| |node| + |minset| |root?| |double?| |pushup| |Hausdorff| |jvmPublic| |zeroDim?| + |f07fef| |setMinPoints3D| |evenInfiniteProduct| |viewWriteDefault| + |stirling2| |retractable?| |lex| |denominator| |singular?| |leftMult| + |printStats!| |symbol| |eof?| |parts| |decomposeFunc| |eigenvalues| + |mergeFactors| |viewDefaults| |d02raf| SEGMENT |algint| |returnTypeOf| + |meshFun2Var| |expression| |minGbasis| |schema| |d01amf| + |viewZoomDefault| |sncndn| |unknown| |badValues| |bandedHessian| + |radicalSimplify| |exponents| |integer| |integral?| |implies| |f2df| + |exprex| |s21bcf| |magnitude| |c06ebf| |internalInfRittWu?| + |linearElement| |dn| |parametric?| |genericPosition| + |irreducibleFactors| |c06ekf| |matrixConcat3D| |cothIfCan| + |selectOptimizationRoutines| |irreducible?| |cExp| |removeCoshSq| + |simpsono| |messagePrint| |eyeDistance| |eulerE| |getlo| + |mapBivariate| |currentCategoryFrame| |constantOperator| + |nextIrreduciblePoly| F |hcrf| |shrinkable| |OMgetAttr| |putProperty| + |linefeed| |semiDiscriminantEuclidean| |youngGroup| |upperBound| + |hitherPlane| |curveColorPalette| |sumSquares| |dmpToHdmp| |cond| + |linearAssociatedOrder| |irreducibleFactor| |linearForm| + |factorFraction| |leadingExponent| |SturmHabichtSequence| + |modularFactor| |infinityNorm| |primitiveElement| |toseSquareFreePart| + |iicsch| |setClosed| |addPointLast| |interReduce| |symbolTable| + |dimensions| |cscIfCan| |stripCommentsAndBlanks| |midpoint| + |jvmPrivate| |f2st| |squareTop| |exprToXXP| |LyndonBasis| |mirror| + |dihedral| GF2FG |key?| |genus| |vedf2vef| |floor| |internalIntegrate| + |pushFortranOutputStack| |any?| |updateStatus!| |repeatUntilLoop| + |zeroMatrix| |outputForm| |redPol| |swapRows!| |laurentRep| + |extendedResultant| |generalizedEigenvectors| |equation| + |popFortranOutputStack| |primextendedint| |inputBinaryFile| |e04dgf| + |conical| |failed?| |paren| |eigenMatrix| |tanintegrate| + |createPrimitiveElement| |isNot| |outputAsFortran| |diagonalProduct| + |expandPower| |quasiMonicPolynomials| |RemainderList| |graeffe| + |dmp2rfi| |root| |weight| |inspect| |aQuartic| |makeCrit| |d01alf| + |OMputEndObject| |SturmHabicht| |kroneckerDelta| |rischDEsys| + |extractTop!| |minPol| |explimitedint| |notelem| |xCoord| + |completeHermite| |printInfo!| |initiallyReduce| |highCommonTerms| + |fractRagits| |physicalLength!| |mainKernel| |integer?| |elementary| + |OMgetBVar| |OMmakeConn| |Gamma| |thetaCoord| |univariatePolynomial| + |computeInt| |testDim| |iiasech| |unrankImproperPartitions0| + |deepExpand| |mainValue| |typeList| |closed?| + |reducedContinuedFraction| |innerSolve| |s19abf| |insert| |nlde| + |multisect| |mapExponents| |palgint0| |column| + |integralLastSubResultant| |rk4| |OMopenFile| |symFunc| |rightRank| + |realSolve| |generalizedContinuumHypothesisAssumed?| + |mainCoefficients| |rootProduct| |elliptic| |jacobian| |totalLex| + |oneDimensionalArray| |makeUnit| |basisOfRightNucloid| |pdf2df| + |expressIdealMember| |algebraic?| |bit?| |besselI| |assert| + |clearTheSymbolTable| |iilog| |continuedFraction| |iprint| + |perfectNthPower?| |push| |stop| |anticoord| + |solveLinearPolynomialEquationByFractions| |mainVariable| + |numberOfHues| |f04asf| |isOp| |generalizedContinuumHypothesisAssumed| + |tab| |thenBranch| |uniform01| |findConstructor| |countRealRoots| + |explogs2trigs| |systemCommand| |readBytes!| |OMParseError?| + |property| |e01saf| |gcdcofactprim| |OMsend| |mdeg| |cCos| + |normalizeIfCan| |OMreceive| |remove!| |nextPrimitivePoly| + |tanh2trigh| |head| |argumentListOf| |iiacosh| |normal| |open| + |OMgetAtp| |redmat| |imagi| |endSubProgram| |iidprod| |deleteRoutine!| + |singleFactorBound| |clipWithRanges| |internalSubPolSet?| |nullity| + |adjoint| |superHeight| |makeVariable| |oddlambert| + |replaceKthElement| |tanAn| |zCoord| |integerBound| |generic| + |atanhIfCan| |lazyPremWithDefault| |trace2PowMod| |epilogue| + |shellSort| |arity| |listConjugateBases| |showTheFTable| |move| + |graphStates| |invertIfCan| |setImagSteps| |hasSolution?| + |totalDifferential| |partitions| |listYoungTableaus| |edf2fi| + |solveid| |preprocess| |frst| |operations| |cRationalPower| |updatF| + |iExquo| |createNormalElement| |karatsubaDivide| |eq| |compBound| + |c06frf| |rdregime| |minRowIndex| |log| |triangSolve| |e02daf| + |dequeue!| |iter| |f02aef| |removeSinSq| |pastel| |cap| |fortranReal| + |alphabetic?| |close| |getBadValues| |subPolSet?| |quatern| |refine| + |noValueMode| |inR?| |collect| |tanIfCan| |pol| |asimpson| + |numericalIntegration| |randnum| |possiblyInfinite?| |iitanh| |basis| + |setScreenResolution3D| |radicalRoots| |one?| |roman| |traceMatrix| + |positiveSolve| |iifact| |display| |var2Steps| |karatsuba| |e02bcf| + |child| |belong?| |normalizedAssociate| |lexGroebner| |extractBottom!| + |sequence| |matrixDimensions| |toseInvertible?| |parseString| + |coth2tanh| |ignore?| |capacity| |leader| |divisors| + |localIntegralBasis| |coHeight| |critT| |getGoodPrime| |lhs| |unary?| + |jordanAdmissible?| |unaryFunction| |leftExtendedGcd| |iiacsc| + |linear| |reduceBasisAtInfinity| |integralBasis| |asecIfCan| + |rightUnits| |toseLastSubResultant| |rhs| |s17dhf| |quasiRegular?| + |recur| |connectTo| |constantOpIfCan| |prime| |fortranComplex| + |normalElement| |multiEuclideanTree| |exp| |point| |consnewpol| + |OMgetString| |pleskenSplit| |palgRDE0| |subscriptedVariables| |arg1| + |polynomial| LODO2FUN |iiacos| |rk4f| |lambda| |screenResolution| + |drawComplex| |currentEnv| |indices| |width| |complexForm| + |OMgetEndAtp| |leaves| |intPatternMatch| |pushdterm| + |generalizedEigenvector| |arg2| |cyclotomic| |jvmLongConstantTag| + |f02xef| |minimumExponent| |output| |extract!| |psolve| + |zeroDimPrimary?| |charpol| |transcendent?| |OMconnInDevice| + |fractionPart| |positive?| |test| |leadingCoefficientRicDE| |series| + |true| |doubleDisc| |largest| |row| |basicSet| |numberOfDivisors| |li| + |isPower| |conditions| |approximants| |cTanh| |mainVariables| + |isConnected?| |permutations| |hasTopPredicate?| + |lastSubResultantEuclidean| |extendedSubResultantGcd| |varselect| + |match| |taylorIfCan| |f04arf| |roughEqualIdeals?| + |indiceSubResultantEuclidean| |factorial| |adaptive?| + |semiIndiceSubResultantEuclidean| |ScanArabic| |superscript| |Beta| + |zeroOf| |iisqrt2| |selectPolynomials| |e04mbf| |dualSignature| + |edf2efi| |linGenPos| |loadNativeModule| |asinhIfCan| |invertibleSet| + |nonSingularModel| |characteristicSerie| |definingEquations| + |LowTriBddDenomInv| |message| |closedCurve| |min| |s17dcf| |optional| + |setrest!| |quotient| |endOfFile?| |bivariate?| + |cyclotomicFactorization| |pointColorPalette| |getOrder| + |factorGroebnerBasis| |idealiserMatrix| |diff| |newTypeLists| |less?| + |setProperties| |genericLeftDiscriminant| |moduloP| |nextItem| + |remove| |vspace| |newSubProgram| |setTex!| |powerAssociative?| + |tanh2coth| |dioSolve| |result| |setnext!| |HermiteIntegrate| + |complexElementary| |startTableInvSet!| |att2Result| + |subQuasiComponent?| |e02bbf| |addPoint2| |fi2df| |elaborate| + |exptMod| |categoryFrame| |last| |linearAssociatedLog| + |topFortranOutputStack| |enterPointData| |brillhartIrreducible?| + |leastPower| |readUInt16!| |assoc| |representationType| |mkPrim| + |extractProperty| |halfExtendedSubResultantGcd2| |logical?| |exists?| + |factorPolynomial| |invmod| |cAcot| |choosemon| |OMputEndAtp| + |ip4Address| |initials| |makeSeries| |map| |reflect| |scale| + |realEigenvectors| |semicolonSeparate| |e01baf| |iiasin| |coefChoose| + |primitivePart| |resultant| |expr| |reducedQPowers| UTS2UP + |tubeRadiusDefault| |stoseLastSubResultant| |squareFreePart| |diag| + |symmetricProduct| |iisinh| |coordinates| |deepCopy| |e02zaf| + |shufflein| |equiv| |OMputFloat| |chebyshevT| |leftOne| |lift| |label| + |dec| |bubbleSort!| |imagJ| |readIfCan!| |parabolic| + |binaryTournament| |iisech| |semiResultantEuclideannaif| + |monicLeftDivide| |getOperator| |cAsin| BY |reduce| |condition| + |createNormalPrimitivePoly| |numeric| |lp| |position!| + |transcendentalDecompose| |d01apf| |sylvesterMatrix| |depth| |d01gaf| + |argscript| |rules| |showRegion| |bernoulliB| |prefix| |radical| + |cSin| |pmComplexintegrate| |mightHaveRoots| |hasPredicate?| + |variable| |prindINFO| |imagk| |range| |curveColor| |poisson| + |cotIfCan| |primitive?| |rightScalarTimes!| |bumprow| |iterators| + |nextsousResultant2| |prefixRagits| |fglmIfCan| |cycleLength| + |setOfMinN| |realEigenvalues| |meatAxe| |open?| |e02agf| + |bipolarCylindrical| |simpleBounds?| |functionIsOscillatory| + |rightOne| |optAttributes| |OMsupportsSymbol?| + |exprHasWeightCosWXorSinWX| |d03faf| |setPosition| + |genericRightMinimalPolynomial| |numerator| |f04atf| |janko2| |repSq| + |screenResolution3D| |outputFixed| |paraboloidal| |shuffle| + |setMaxPoints| |next| |selectIntegrationRoutines| |tab1| + |leftExactQuotient| |moreAlgebraic?| |ode| |option| |rightExtendedGcd| + |tanQ| |triangulate| |acosIfCan| NOT |sup| |OMencodingBinary| |tube| + |radicalEigenvector| |exponential1| |lprop| |read!| |OMgetFloat| + |center| |low| |edf2ef| OR |printCode| |setColumn!| |lifting1| + |moduleSum| |listLoops| |multiEuclidean| |primlimitedint| |orbit| + |update| |reverseLex| |sub| AND |components| |radPoly| |removeZero| + |leftReducedSystem| |explicitlyEmpty?| |pushuconst| |leftDivide| + |d03eef| |setEmpty!| |hconcat| |basisOfCenter| |writeBytes!| + |acoshIfCan| |e01daf| |f01rcf| |predicates| + |zeroSetSplitIntoTriangularSystems| |rational?| |viewPosDefault| + |cCot| |oddInfiniteProduct| |diagonals| |infieldIntegrate| + |createGenericMatrix| |invmultisect| |delete!| |byteBuffer| + |ramified?| |shade| |factorSFBRlcUnit| |returnType!| |setright!| + |subNode?| |yellow| |interpolate| |getConstant| |prevPrime| + |roughBase?| |rem| |iipow| |roughUnitIdeal?| |knownInfBasis| + |conditionsForIdempotents| |byte| |finiteBasis| |headAst| |mantissa| + |lazyPquo| |order| |quasiAlgebraicSet| |quo| |zeroDimensional?| + |conjunction| |simplifyPower| |genericRightNorm| |overbar| + |linearPart| |iiacsch| RF2UTS |ridHack1| |totalfract| |zoom| + |elaborateFile| |diagonal?| |subTriSet?| |generators| |hyperelliptic| + |resultantEuclidean| |countable?| |div| |substitute| |abelianGroup| + |rroot| |coefficients| |createZechTable| |orthonormalBasis| |sorted?| + |addBadValue| |partialNumerators| |exquo| |bringDown| + |lazyIrreducibleFactors| |inrootof| |crest| |SturmHabichtMultiple| + |qqq| |sdf2lst| |nthCoef| |raisePolynomial| * ~= |doublyTransitive?| + |rk4qc| |operators| |FormatRoman| |qroot| |polygon| |integralMatrix| + |lineColorDefault| |chainSubResultants| |sin2csc| |#| |makeEq| + |sts2stst| |mapGen| |cschIfCan| |ode2| |binomThmExpt| |e01bef| + |function| |stFunc2| |qPot| |primlimintfrac| ~ |iidsum| |e01sbf| + |rotatey| |fullDisplay| |airyAi| |int| |sizePascalTriangle| + |outputAsScript| |squareFree| |certainlySubVariety?| |dimension| = + |leadingSupport| |leftRemainder| |rationalPoints| |OMencodingXML| + |linearDependence| FG2F |reducedSystem| |isAnd| |meshPar2Var| |f04adf| + |phiCoord| |lieAdmissible?| |jvmDoubleConstantTag| |iiabs| + |constantKernel| |deleteProperty!| |showIntensityFunctions| |s15aef| + |/\\| < |problemPoints| |symmetricDifference| |eulerPhi| |integral| + |OMputEndApp| |times!| |OMputBVar| |laguerre| |queue| |\\/| > + |hexDigit| |orbits| |perfectNthRoot| |typeLists| |linearAssociatedExp| + |generalInfiniteProduct| |useNagFunctions| |super| |flagFactor| + |monicRightFactorIfCan| |initTable!| <= |unitVector| + |commonDenominator| |basisOfLeftAnnihilator| + |inverseIntegralMatrixAtInfinity| |algSplitSimple| |infix| |number?| + |deepestTail| |setStatus!| |OMunhandledSymbol| >= |groebnerFactorize| + |f04mcf| |genericRightTrace| |pop!| |perfectSquare?| |content| + |combineFeatureCompatibility| |badNum| |prinb| |resetAttributeButtons| + |alternating| |normalized?| |particularSolution| |tablePow| + |readInt8!| |s18aef| |weakBiRank| |cons| |inv| + |primPartElseUnitCanonical| |mapSolve| |subresultantVector| |vark| + |abs| |declare| |setDifference| |nsqfree| |OMUnknownCD?| |ground?| + + |fortranInteger| |numberOfVariables| |minus!| |lazyPseudoRemainder| + |cyclicSubmodule| |s18aff| |ravel| |goto| |upperCase| |lowerCase?| + |discreteLog| |ground| - |flatten| |s13aaf| |isExpt| |bounds| + |generic?| |rombergo| |lcm| |cLog| |reshape| / + |getSyntaxFormsFromFile| |hdmpToP| |leadingMonomial| |cAcosh| + |mainForm| |s17dlf| |alphabetic| |totalGroebner| |vector| |viewpoint| + |drawCurves| |iiexp| |leftTrace| |leadingCoefficient| |cup| + |viewport3D| |coefficient| |rightTraceMatrix| + |factorSquareFreePolynomial| |nextSubsetGray| |differentiate| |append| + |mix| |maximumExponent| |source| |primitiveMonomials| |cyclicParents| + |isobaric?| |numberOfComponents| |create3Space| |sqfrFactor| + |wordInGenerators| |check| |gcd| |var1StepsDefault| |front| + |pointColorDefault| |reductum| |ffactor| |getButtonValue| + |quadraticNorm| |augment| |false| |ran| |set| |commaSeparate| + |quoByVar| |checkForZero| |rewriteIdealWithRemainder| |eigenvectors| + |factorsOfDegree| |maxrank| |subResultantGcd| |OMencodingUnknown| + |target| |partialQuotients| |safeCeiling| |subtractIfCan| + |nextLatticePermutation| |exponentialOrder| |space| |bigEndian| + |ListOfTerms| |basisOfCommutingElements| |select!| |reduced?| + |permutation| |ReduceOrder| |linear?| |explicitEntries?| |mkcomm| + |f01qdf| |eigenvector| |areEquivalent?| |drawComplexVectorField| + |stFunc1| |Frobenius| |isOpen?| |innerSolve1| |fixedPoints| |ideal| + |intermediateResultsIF| |component| |table| |approxSqrt| + |outerProduct| |square?| |printInfo| |OMputObject| |UP2ifCan| + |resultantnaif| |setIntersection| |predicate| |rational| |new| + |addMatchRestricted| |position| |clearTable!| |digit| |gramschmidt| + |has?| |domainTemplate| |coerce| |inputOutputBinaryFile| + |numberOfMonomials| |dimensionsOf| |pdf2ef| |branchPoint?| |solid| + |cycles| |nextNormalPoly| |construct| |red| |getGraph| |sign| + |getMultiplicationMatrix| |selectAndPolynomials| |hermite| |twoFactor| + |multinomial| |df2mf| |SFunction| |members| |pdct| |virtualDegree| + |redpps| |dominantTerm| |internal?| |void| |appendPoint| |An| |zag| + |bumptab1| |second| |stirling1| |symbolIfCan| |isList| |lexTriangular| + |makingStats?| |subSet| |duplicates?| |stopTableGcd!| |meshPar1Var| + |third| |jvmMethodrefConstantTag| |jacobiIdentity?| |sturmSequence| + |listRepresentation| |symmetricGroup| |readLineIfCan!| |makeMulti| + |computePowers| |firstUncouplingMatrix| |goodnessOfFit| |zero| + |singRicDE| |removeRedundantFactorsInPols| |removeSquaresIfCan| + |solveRetract| |userOrdered?| |OMsetEncoding| |rootOfIrreduciblePoly| + |pushNewContour| |inHallBasis?| |unitNormalize| |node?| |localReal?| + |nextPartition| |pseudoRemainder| |currentSubProgram| |outputSpacing| + |lookup| |atoms| |And| |comment| |bitLength| |OMcloseConn| + |fortranLogical| |prinshINFO| + |solveLinearPolynomialEquationByRecursion| |presub| |eq?| |parameters| + |extractSplittingLeaf| |laurentIfCan| |ratDenom| |Or| |index?| + |selectsecond| |contours| |shape| |coth2trigh| |bezoutDiscriminant| + |BasicMethod| |palglimint0| |complexEigenvectors| |unitsColorDefault| + |Not| |equality| |lieAlgebra?| |d02kef| |infRittWu?| |cycleElt| + |symmetricPower| |nodes| |specialTrigs| + |semiSubResultantGcdEuclidean1| |leftNorm| |exp1| |s17adf| + |groebnerIdeal| |chiSquare| |limit| |yCoordinates| |c05pbf| |car| + |palgRDE| |erf| |explicitlyFinite?| |extractPoint| |iroot| |nodeOf?| + |f04maf| |entry| |numberOfIrreduciblePoly| + |tryFunctionalDecomposition| |nthRoot| |prod| |failed| |match?| + |every?| |nextSublist| |nand| |infiniteProduct| |subResultantsChain| + |cAcsc| |OMputApp| |extend| |limitPlus| |minimize| |exQuo| |pointData| + |mergeDifference| |lazyVariations| |axesColorDefault| |directory| + |inc| |lyndon?| |setPredicates| |coerceL| |determinant| |s19adf| + |dilog| |mapUp!| |safetyMargin| |romberg| |cot2tan| |dictionary| + |usingTable?| |setelt| |leftRankPolynomial| |yCoord| |negative?| |sin| + |decreasePrecision| |resetNew| |factorOfDegree| |elRow1!| + |ScanFloatIgnoreSpacesIfCan| |nonLinearPart| |error| + |rightDiscriminant| |fortranDouble| |s18adf| |outputArgs| |cos| + |rootSimp| |coerceP| |hostPlatform| |errorKind| |real?| |max| |c06gqf| + |numberOfOperations| |copy| |cSech| |rowEchelon| |cyclePartition| + |tan| |rootKerSimp| |physicalLength| |complexEigenvalues| |palgint| + |complexLimit| |definingPolynomial| |numerators| |block| |pointColor| + |wrregime| |numberOfPrimitivePoly| |cot| |Nul| |primintegrate| + |cyclicEntries| |ratDsolve| |permanent| |binomial| |showTheIFTable| + |autoCoerce| |FormatArabic| |sinhIfCan| |comparison| |sec| + |lowerPolynomial| |opeval| |leftCharacteristicPolynomial| |f01brf| + |expPot| |build| |genericLeftTraceForm| |indicialEquationAtInfinity| + |generalPosition| |csc| |leftUnits| |univcase| |iiatan| |c06gbf| + |leftQuotient| |top| |companionBlocks| |minimalPolynomial| |polCase| + |f02akf| |asin| |normDeriv2| |pushdown| |coerceListOfPairs| |se2rfi| + |firstDenom| |continue| |graphState| |getMultiplicationTable| + |OMputBind| |createRandomElement| |acos| |boundOfCauchy| |upperCase!| + |mkIntegral| |trapezoidalo| |seed| |basisOfCentroid| + |splitDenominator| |quasiRegular| |t| |member?| |atan| + |jvmStringConstantTag| |makeResult| |rootDirectory| |algDsolve| + |getMatch| |mapExpon| |eval| |verticalTab| |rootSplit| |module| + |PollardSmallFactor| |acot| |ranges| |expt| |pointSizeDefault| + |writeByte!| |green| |rightFactorCandidate| |multMonom| |denomLODE| + |removeDuplicates!| |init| |jvmProtected| |asec| |polyRDE| |sin?| + |imagj| |hspace| |tan2cot| |printingInfo?| |f07aef| + |factorsOfCyclicGroupSize| |s19acf| |acscIfCan| |acsc| |rename!| + |stosePrepareSubResAlgo| |power| |loopPoints| |mainExpression| |leaf?| + |exteriorDifferential| |e02gaf| |generateIrredPoly| |sinh| + |quotedOperators| |startStats!| |universe| |cycleSplit!| |terms| + |nil?| |differentialVariables| |logIfCan| |indiceSubResultant| |comp| + |cosh| |lflimitedint| |f01qef| |setClipValue| |groebner| + |balancedBinaryTree| |readInt32!| |iiasinh| |rationalPower| + |stiffnessAndStabilityOfODEIF| |factorials| |evaluate| + |permutationRepresentation| |associatorDependence| |interpret| |plus!| + |presuper| |functionIsFracPolynomial?| |xn| |df2fi| |push!| |split!| + |colorDef| |removeRoughlyRedundantFactorsInContents| + |initiallyReduced?| |Lazard2| |symbolTableOf| |seriesToOutputForm| + |semiResultantEuclidean1| |copyInto!| |numFunEvals| |binarySearchTree| + |diophantineSystem| |dimensionOfIrreducibleRepresentation| + |roughSubIdeal?| |bivariatePolynomials| |separant| |removeDuplicates| + |viewport2D| |extractClosed| |nthFactor| |macroExpand| |d01asf| + |polygon?| |ldf2lst| |support| |skewSFunction| |outputFloating| + |drawToScale| |exactQuotient!| |trigs| |lepol| |children| + |separateDegrees| |regularRepresentation| |duplicates| |tValues| + |subResultantChain| |rewriteSetWithReduction| |OMgetSymbol| |nil| + |iitan| |e01bff| |newReduc| |halfExtendedSubResultantGcd1| + |categories| |string?| |jvmFieldrefConstantTag| |OMopenString| |cCsc| + |lighting| |Vectorise| |fortranTypeOf| + |functionIsContinuousAtEndPoints| |genericRightDiscriminant| + |rightUnit| |stoseInvertibleSetreg| |scanOneDimSubspaces| + |expenseOfEvaluationIF| |antiCommutator| |errorInfo| |s18acf| + |alphanumeric?| |level| |minIndex| |s14aaf| |lifting| + |normInvertible?| |cycleTail| |setScreenResolution| |rightRemainder| + |lastSubResultant| |enumerate| |approximate| |nary?| |subst| |closed| + |normFactors| |modularGcd| |numericIfCan| |OMgetError| + |linearDependenceOverZ| |e01bhf| |structuralConstants| |d02cjf| + |complex| |seriesSolve| |leadingTerm| |internalZeroSetSplit| |f01rdf| + |OMputAtp| |traverse| |fixedPointExquo| |high| |removeCosSq| |f04jgf| + |dom| |basisOfRightAnnihilator| |reopen!| + |rewriteIdealWithHeadRemainder| |outputAsTex| |ScanFloatIgnoreSpaces| + |rangePascalTriangle| |lllip| |OMputEndBVar| |obj| |putProperties| + |trailingCoefficient| |gbasis| |dmpToP| |powers| |acsch| |drawStyle| + |OMgetType| |divideExponents| |palginfieldint| |objects| + |insertionSort!| |expandTrigProducts| |multiple?| |blue| + |splitConstant| |localUnquote| |cn| |addiag| |d01aqf| |op| |base| + |mathieu24| |parent| |limitedint| |s17ahf| |chiSquare1| + |bezoutResultant| |tubePoints| |leftUnit| |uniform| |findCycle| + |computeBasis| |polynomialZeros| |tan2trig| |hasHi| + |indicialEquations| |mainCharacterization| |powerSum| |represents| + |leastMonomial| |f02wef| |iomode| |OMconnectTCP| |nextPrime| |moebius| + |scalarMatrix| |complexSolve| |withPredicates| |autoReduced?| + |semiSubResultantGcdEuclidean2| |linearMatrix| |separate| |setleft!| + |trigs2explogs| |viewThetaDefault| |algebraicOf| |cosh2sech| + |ellipticCylindrical| |carriageReturn| |palgintegrate| |digits| + |doubleComplex?| |symmetricRemainder| |algebraicCoefficients?| + |monomialIntegrate| |f02fjf| |createPrimitivePoly| |optimize| + |modularGcdPrimitive| |plotPolar| |indicialEquation| |subNodeOf?| + |reciprocalPolynomial| |exprHasLogarithmicWeights| |latex| + |rewriteIdealWithQuasiMonicGenerators| |nthFractionalTerm| + |subResultantGcdEuclidean| |hMonic| |conjugates| |henselFact| + |retract| |odd?| |unvectorise| |var2StepsDefault| |bindings| + |genericRightTraceForm| |closedCurve?| |nthExpon| |getMeasure| |scan| + |child?| |size?| |lazyPseudoQuotient| |prolateSpheroidal| |polyRicDE| + |integrate| |encodingDirectory| |stoseInternalLastSubResultant| + |mindegTerm| |iflist2Result| |countRealRootsMultiple| |constDsolve| + |coercePreimagesImages| |halfExtendedResultant1| |LyndonWordsList| + |jvmInterface| |partialFraction| |OMgetObject| |previous| + |patternMatch| |axes| |rightZero| |selectMultiDimensionalRoutines| + |signatureAst| |elRow2!| |reorder| |asinIfCan| |sn| + |nextPrimitiveNormalPoly| |divide| |removeRedundantFactors| |maxrow| + |crushedSet| |cosIfCan| |modulus| |generalSqFr| |factorList| + |asechIfCan| |merge!| |simplifyLog| |copies| + |setLegalFortranSourceExtensions| |prinpolINFO| |innerEigenvectors| + |anfactor| |e02def| |lowerCase| |forLoop| |leadingIdeal| + |integralAtInfinity?| |isImplies| |setLabelValue| |assign| |sort!| + |expextendedint| |e02adf| |cSinh| |leftFactor| |c06gsf| |solveInField| + |beauzamyBound| |geometric| |OMgetVariable| |reducedDiscriminant| + |showAll?| |lfintegrate| |var1Steps| |reseed| |nextColeman| |points| + |palgextint| |normalize| |norm| |hash| |reify| |complementaryBasis| + |leastAffineMultiple| |basisOfMiddleNucleus| |medialSet| |variable?| + |connect| |tubeRadius| |pToHdmp| |oblateSpheroidal| |count| |corrPoly| + |randomR| |resultantReduitEuclidean| |stoseIntegralLastSubResultant| + |entries| |category| |irCtor| |OMbindTCP| |resetVariableOrder| + |factorAndSplit| |mappingAst| |rightNorm| |factorset| |currentScope| + |rootPoly| |float?| |realElementary| |cylindrical| |domain| |mindeg| + |writeUInt8!| |besselY| |mvar| |lambert| |element?| |setVariableOrder| + |rotate| |generator| |lowerCase!| |readUInt8!| |package| |minrank| + |firstSubsetGray| |fixPredicate| |systemSizeIF| |validExponential| + |charthRoot| |fortranCharacter| |palgextint0| |s17dgf| |headReduced?| + |coord| |char| |algintegrate| |quickSort| |even?| |maxint| |bsolve| + |prefix?| |besselK| |rightTrim| |writeLine!| |localAbs| |getCurve| + |properties| |accuracyIF| |outputBinaryFile| |cAcoth| |rischDE| + |central?| |getDatabase| |purelyAlgebraic?| |maxIndex| + |identification| |leftTrim| |f02agf| |f02bjf| |trapezoidal| + |translate| |imports| |aromberg| |stoseSquareFreePart| |deriv| + |subCase?| |mpsode| |zerosOf| |tower| |fortranCarriageReturn| + |leftGcd| |s14abf| |clearDenominator| |debug3D| |acothIfCan| |cyclic| + |pushucoef| |overlabel| |bivariateSLPEBR| |multiplyCoefficients| + |rightPower| |c06fpf| |setStatus| |f07fdf| + |factorSquareFreeByRecursion| |perfectSqrt| |setPoly| + |integralDerivationMatrix| |simpson| |addmod| |part?| |rst| |float| + |degreeSubResultant| |mainVariable?| |mathieu12| |generalLambert| + |imagK| |closeComponent| |qualifier| |showScalarValues| + |createThreeSpace| |signAround| |pile| |commutativeEquality| + |numberOfImproperPartitions| |OMgetApp| |baseRDE| |makeFloatFunction| + |rowEchelonLocal| |createPrimitiveNormalPoly| |numberOfChildren| + |basisOfLeftNucloid| |d01gbf| |infix?| |directSum| |hexDigit?| |cycle| + |colorFunction| |f04mbf| |patternVariable| |infLex?| |readByte!| + |topPredicate| |OMsupportsCD?| |expIfCan| |mask| |units| |matrix| + |divisorCascade| |logpart| |s20acf| |minordet| |numericalOptimization| + |decrease| |weights| |ef2edf| |gcdPolynomial| |idealSimplify| |radix| + |biRank| |lookupFunction| |complexNumeric| |totalDegree| |swap!| + |incr| |pointLists| |numFunEvals3D| |summation| |lazy?| + |primextintfrac| |f01ref| |returns| |hessian| |sturmVariationsOf| |hi| + |overset?| |lexico| |startTable!| |iteratedInitials| |fmecg| + |euclideanSize| |vectorise| |kernels| |gcdcofact| |infieldint| + |vconcat| |subset?| |find| |useEisensteinCriterion| + |invertibleElseSplit?| |changeWeightLevel| |rightAlternative?| + |viewDeltaXDefault| |evaluateInverse| |sort| |smith| |operator| + |regime| |csc2sin| |identity| |derivative| |iiasec| |keys| + |trivialIdeal?| |birth| |OMlistCDs| GE |code| |associative?| + |univariate| |airyBi| |OMgetEndError| |null?| |extendedEuclidean| + |options| |clip| |voidMode| |rationalFunction| |modifyPointData| + |trunc| GT |constructor| |random| |pmintegrate| |cAsech| |subHeight| + |sample| |associatedSystem| |lSpaceBasis| |setFieldInfo| |fixedPoint| + |s20adf| |coordinate| LE |kovacic| |cyclicGroup| |tubePlot| |unexpand| + |monic?| |string| |exprHasAlgebraicWeight| |c06ecf| |ldf2vmf| + |stoseInvertible?| |c06fuf| LT |squareFreePolynomial| |torsionIfCan| + |factor| |divergence| |linearlyDependentOverZ?| |slash| + |rootNormalize| |qelt| |OMputString| |stoseInvertible?reg| + |collectQuasiMonic| |gethi| |definingInequation| |changeNameToObjf| + |removeRoughlyRedundantFactorsInPols| |sqrt| |antiAssociative?| + |stoseInvertibleSetsqfreg| |operation| |region| |qsetelt| + |euclideanNormalForm| |randomLC| |rotate!| |cfirst| + |fortranDoubleComplex| |HenselLift| |environment| + |unrankImproperPartitions1| |real| |linkToFortran| + |algebraicDecompose| |characteristic| |xRange| |perspective| |polar| + |outputMeasure| |monicRightDivide| |tableau| |unparse| |nonQsign| + |mapMatrixIfCan| |pToDmp| |imag| |expintegrate| |wholePart| + |denominators| |approxNthRoot| |yRange| |delete| |back| |univariate?| + |exactQuotient| |halfExtendedResultant2| |cyclicCopy| |directProduct| + |identityMatrix| |pow| |packageCall| |e04jaf| |bitTruth| |zRange| + |rightMult| |identitySquareMatrix| |sizeMultiplication| + |numberOfNormalPoly| |purelyTranscendental?| |cubic| |d01anf| |d01bbf| + |polyred| |secIfCan| |c02aff| |map!| |insertTop!| |tree| |nthFlag| + |whitePoint| |makeViewport2D| |showClipRegion| |rename| |brace| + |removeSinhSq| |realZeros| |readLine!| |littleEndian| |qsetelt!| + |jvmUTF8ConstantTag| |isMult| |midpoints| |backspace| + |monomialIntPoly| |vertConcat| |ParCondList| |destruct| |rspace| + |normal01| |maxPoints3D| |isQuotient| |changeVar| |algebraicVariables| + |jvmFinal| |semiLastSubResultantEuclidean| |sum| |lowerBound| |dot| + |zeroSquareMatrix| |squareMatrix| |conditionP| |jvmIntegerConstantTag| + |e01sff| |symbol?| |variationOfParameters| |stopMusserTrials| + |firstNumer| |printStatement| |LazardQuotient2| |jvmStatic| + |squareFreePrim| |top!| |setButtonValue| |leftAlternative?| |overlap| + |zeroSetSplit| |polarCoordinates| |complexNumericIfCan| |call| + |calcRanges| |normalise| |backOldPos| |defineProperty| |realRoots| + |nullary?| |edf2df| |internalAugment| |setPrologue!| |leftTraceMatrix| + |generate| |froot| |branchIfCan| |kmax| + |initializeGroupForWordProblem| |monomial| |fprindINFO| + |setTopPredicate| |pascalTriangle| |linears| |surface| |swapColumns!| + |d01akf| |createMultiplicationTable| |alternatingGroup| |quadratic?| + |jvmClassConstantTag| |triangular?| |multivariate| |leftFactorIfCan| + |rquo| |mainPrimitivePart| |incrementBy| |intChoose| |height| + |monomials| |standardBasisOfCyclicSubmodule| |stoseInvertibleSet| + |completeHensel| |principalIdeal| |writable?| |factor1| |id| + |sequences| |variables| |lfextlimint| |factorSquareFree| |trim| + |useSingleFactorBound| |bothWays| |expand| |processTemplate| + |mappingMode| |nothing| |elseBranch| |lo| |light| |lazyResidueClass| + |makeprod| |lagrange| |atom?| |integralMatrixAtInfinity| |interval| + |filterWhile| |externalList| |cot2trig| |compile| |compactFraction| + |step| |trueEqual| |fibonacci| |balancedFactorisation| + |supDimElseRittWu?| |rowEchLocal| |sumOfSquares| |f02abf| + |diagonalMatrix| |filterUntil| |transcendenceDegree| |tRange| + |nthRootIfCan| |tanh| |critpOrder| |mainMonomials| |double| + |symmetricTensors| |stack| |bat1| |stoseInvertible?sqfreg| |log10| + |mulmod| |rightRecip| |acschIfCan| |select| |viewSizeDefault| |copy!| + |c02agf| |coth| |fractRadix| |LagrangeInterpolation| + |resultantEuclideannaif| |f04faf| |aCubic| |probablyZeroDim?| + |normal?| |compdegd| |finite?| |bitand| |inverseColeman| + |discriminant| |sech| |createMultiplicationMatrix| + |tableForDiscreteLogarithm| |zero?| |taylor| |schwerpunkt| + |OMreadFile| |showSummary| |sincos| |s01eaf| |fortranCompilerName| + |bitior| |rootsOf| |singularAtInfinity?| |csch| |parabolicCylindrical| + |minPoints3D| |selectSumOfSquaresRoutines| |laurent| |coerceImages| + |showAllElements| |separateFactors| |generalTwoFactor| |putGraph| + |groebgen| |setMinPoints| |asinh| |innerint| |setprevious!| |puiseux| + |newLine| |getCode| |showAttributes| |numberOfFractionalTerms| + |binding| |viewDeltaYDefault| |optional?| |deref| |acosh| |tanNa| + |stronglyReduced?| |integerIfCan| |headRemainder| |linearPolynomials| + |groebner?| |quasiMonic?| |updatD| |delay| |atanh| |gradient| + |RittWuCompare| |jvmAbstract| |makeRecord| |d02gbf| + |semiDegreeSubResultantEuclidean| |eisensteinIrreducible?| + |inRadical?| |Aleph| |acoth| |OMclose| |omError| |declare!| |escape| + |compiledFunction| |Lazard| |e02aef| |changeMeasure| |readInt16!| + |pair?| |s13acf| |asech| |pureLex| |UpTriBddDenomInv| |typeForm| + |bits| |incrementKthElement| |extensionDegree| |dihedralGroup| + |selectODEIVPRoutines| |addPoint| |slex| |setRealSteps| |figureUnits| + |rk4a| |OMputEndAttr| |delta| |lllp| |internalIntegrate0| |coleman| + |formula| |unknownEndian| |degreePartition| |multiple| |contract| + |constantCoefficientRicDE| |contains?| |padicallyExpand| |diagonal| + |constant| |setCondition!| |leftLcm| |getOperands| + |branchPointAtInfinity?| |minColIndex| |applyQuote| |heapSort| + |submod| |tail| |Ei| |expandLog| |toseInvertibleSet| |tanSum| + |ratpart| |llprop| |distribute| |Si| |associatedEquations| + |relativeApprox| |credPol| |invertible?| |option?| |fixedDivisor| + |makeTerm| |setfirst!| |initial| |npcoef| |OMencodingSGML| |style| + |e02bdf| |lazyGintegrate| |droot| |extendedint| |f01bsf| |pquo| + |normalDenom| |nrows| |OMserve| |substring?| |f02axf| |ruleset| + |unmakeSUP| |fortran| |solveLinearPolynomialEquation| |segment| + |clearTheIFTable| |conjug| |selectOrPolynomials| |digamma| |ncols| + |coerceS| |primitivePart!| |neglist| |d02bbf| |getProperties| + |ricDsolve| |interactiveEnv| |clearTheFTable| |apply| |clipBoolean| + |e02ahf| |polyPart| |s17akf| |suffix?| |readable?| |whatInfinity| + |optpair| |Is| Y |digit?| |irDef| |point?| |first| |rank| + |maxRowIndex| |varList| |noncommutativeJordanAlgebra?| |suchThat| + |e02bef| |split| |elColumn2!| |reduceLODE| |sPol| |mesh| |rest| + |leftRank| |flexibleArray| |brillhartTrials| |shallowExpand| |ipow| + |palgLODE| |lyndon| |complex?| |unprotectedRemoveRedundantFactors| + |LyndonCoordinates| |rangeIsFinite| |key| |f02aff| |minPoints| + |multiset| |tensorProduct| |increment| |solve| |ode1| |leftRecip| + |setOrder| |wordsForStrongGenerators| |attributeData| |df2ef| + |primaryDecomp| |LiePoly| |middle| |normalDeriv| |normalizedDivide| + |increase| |f02adf| |filename| |monicCompleteDecompose| |associates?| + |OMreadStr| |commutative?| |constantIfCan| |binaryTree| |f02aaf| + |bipolar| |pack!| |complement| |binary| |csch2sinh| |e04ucf| + |OMReadError?| |ksec| |addMatch| |dequeue| |lazyPseudoDivide| + |useSingleFactorBound?| |postfix| |OMgetInteger| |before?| + |computeCycleEntry| |parse| |iicos| |B1solve| |quoted?| |pade| + |relationsIdeal| |empty?| |minPoly| |leftRegularRepresentation| + |ScanRoman| |logGamma| |unit?| |dark| |lists| + |internalLastSubResultant| |fullPartialFraction| |fTable| |legendreP| + |is?| |exponent| |selectPDERoutines| |monicDivide| |rischNormalize| + |rewriteSetByReducingWithParticularGenerators| |KrullNumber| |makeFR| + |compose| |OMgetEndApp| |getZechTable| |htrigs| |decimal| + |radicalSolve| |ord| |input| |transpose| |curve| |karatsubaOnce| + |integralBasisAtInfinity| |GospersMethod| |internalDecompose| + |jvmStrict| |c06eaf| |script| |showArrayValues| |status| + |jvmTransient| |library| |unravel| |extendedIntegrate| |plus| + |collectUnder| |rationalPoint?| |graphs| |mkAnswer| |rCoord| + |getVariableOrder| |jvmNative| |PDESolve| |fortranLinkerArgs| |df2st| + |upDateBranches| |weierstrass| |character?| |rowEch| + |changeThreshhold| |singularitiesOf| |iCompose| |value| |compound?| + |BumInSepFFE| |isPlus| |curryLeft| |newline| |jvmFloatConstantTag| + |repeating| |argumentList!| |replace| |expenseOfEvaluation| + |clearFortranOutputStack| |tex| |safeFloor| |OMputEndBind| |bitCoef| + |critB| |cTan| |s17aef| |stFuncN| |box| |times| |power!| |name| + |LyndonWordsList1| |reset| |mr| |nativeModuleExtension| |cycleEntry| + |sparsityIF| |solve1| |cCosh| |setLength!| |alphanumeric| |hclf| + |direction| |bandedJacobian| |body| |e04ycf| |basisOfLeftNucleus| + |outputGeneral| |f04axf| |makeSUP| |rootPower| |csubst| |makeop| + |showTheSymbolTable| |leftMinimalPolynomial| |positiveRemainder| + |write| |removeRedundantFactorsInContents| |factors| |s17acf| + |derivationCoordinates| |numberOfComposites| |nor| + |jvmNameAndTypeConstantTag| |elements| |getPickedPoints| |sizeLess?| + |saturate| |save| |setFormula!| |useEisensteinCriterion?| + |primintfldpoly| |symmetric?| |deepestInitial| |cross| |kind| |index| + |round| |fintegrate| |truncate| |monom| |radicalOfLeftTraceForm| + |extractIndex| |color| |d02bhf| |componentUpperBound| |gderiv| + |complexNormalize| |rightCharacteristicPolynomial| |gensym| + |createLowComplexityTable| |youngDiagram| |setAttributeButtonStep| + |palgLODE0| |getStream| |doubleRank| |routines| |getIdentifier| + |rightExactQuotient| |setValue!| |cyclotomicDecomposition| |cAcsch| + |pair| |integralRepresents| |printTypes| |increasePrecision| ** + |padicFraction| |leftDiscriminant| |setUnion| |padecf| |sqfree| + |removeSuperfluousCases| |common| UP2UTS |elem?| |hdmpToDmp| |setelt!| + |hermiteH| |rotatez| |morphism| |curry| |rotatex| |monomial?| + |clikeUniv| |create| |complexExpand| |mainSquareFreePart| + |uncouplingMatrices| |entry?| |besselJ| |s21baf| |cycleRagits| + |doubleResultant| |nextsubResultant2| |convergents| |modTree| + |lfextendedint| |bombieriNorm| |generalizedInverse| |shiftLeft| |port| + |ramifiedAtInfinity?| |factorByRecursion| |intensity| |listOfMonoms| + |wholeRadix| |quadratic| |show| |reverse| |bytes| |c06gcf| + |repeating?| |d03edf| |selectNonFiniteRoutines| |rootBound| |ODESolve| + |degreeSubResultantEuclidean| |jordanAlgebra?| |stopTable!| |s19aaf| + |basisOfNucleus| |rightDivide| |OMgetEndBVar| |prologue| |say| + |patternMatchTimes| |leadingIndex| |listBranches| |prepareDecompose| + |divisor| |rightRegularRepresentation| |wholeRagits| |trace| + |selectFiniteRoutines| |OMputVariable| |univariateSolve| |imaginary| + |multiplyExponents| |irreducibleRepresentation| |measure| + |antisymmetricTensors| |zeroDimPrime?| |stopTableInvSet!| |groebSolve| + |algebraicSort| |just| |f04qaf| |critMonD1| |chineseRemainder| + |radicalEigenvectors| |arbitrary| |setref| |bracket| + |squareFreeFactors| |graphCurves| |arguments| |shallowCopy| + |nilFactor| |internalSubQuasiComponent?| |s15adf| |mainMonomial| + |graphImage| |exponential| |sinh2csch| |s13adf| |nullSpace| + |makeViewport3D| |adaptive3D?| |imagE| |mapmult| |divideIfCan!| + |solveLinear| |removeConstantTerm| |removeSuperfluousQuasiComponents| + |quartic| |dflist| |relerror| |gcdPrimitive| |subspace| |moebiusMu| + |modifyPoint| |principalAncestors| |LazardQuotient| |OMread| |parents| + |search| |f02awf| |simplifyExp| |e01sef| |setAdaptive| + |removeRoughlyRedundantFactorsInPol| |radicalEigenvalues| + |stiffnessAndStabilityFactor| |iicosh| |wronskianMatrix| + |createNormalPoly| |isOr| |ref| |fortranLiteral| |fortranLiteralLine| + |quote| |purelyAlgebraicLeadingMonomial?| |qfactor| |enterInCache| + |union| |clipSurface| |adaptive| |roughBasicSet| |external?| + |commutator| |spherical| |powmod| |lfinfieldint| |precision| + |computeCycleLength| |nextNormalPrimitivePoly| |createIrreduciblePoly| + |partialDenominators| |changeName| |hasoln| |critM| |distFact| + |d02gaf| |numberOfCycles| |characteristicSet| |nthExponent| + |wordInStrongGenerators| |associator| |checkRur| |nullary| |maxdeg| + |sortConstraints| |clipPointsDefault| |constantToUnaryFunction| + |arrayStack| |datalist| |inverseLaplace| |iiacoth| |lazyEvaluate| + |completeEchelonBasis| |iiperm| |rightLcm| |plot| |unit| |heap| + |f01qcf| |iicsc| |expint| |setMaxPoints3D| |removeZeroes| |close!| + |setProperty| |e02baf| |lquo| |log2| |leftScalarTimes!| |btwFact| + |powern| |mapdiv| |setErrorBound| |rightQuotient| |pointPlot| + |putColorInfo| |insertRoot!| |linearlyDependent?| |freeOf?| |sec2cos| + |e02ajf| |rule| |complexZeros| |difference| + |createLowComplexityNormalBasis| |cyclic?| |chvar| + |shanksDiscLogAlgorithm| |toScale| |rightFactorIfCan| + |numberOfComputedEntries| |s14baf| |jokerMode| |reducedForm| |cos2sec| + |e02ddf| |merge| |recolor| |sh| |elliptic?| |noKaratsuba| + |jvmInterfaceMethodConstantTag| |hostByteOrder| |getRef| |setRow!| + |composites| |setAdaptive3D| |resultantReduit| |constantRight| + |rationalApproximation| |e02dcf| |plusInfinity| |OMputSymbol| + |callForm?| |showFortranOutputStack| |principal?| |sylvesterSequence| + |bat| |baseRDEsys| |reduceByQuasiMonic| |dfRange| |hypergeometric0F1| + |fillPascalTriangle| |totolex| |minusInfinity| |jvmSynchronized| + |semiResultantReduitEuclidean| |quadraticForm| |solid?| |getProperty| + |octon| |iisqrt3| |cAsec| |degree| |scaleRoots| |critBonD| |sechIfCan| + |disjunction| |imagI| |mathieu23| |normalizeAtInfinity| |harmonic| + |e04fdf| |elaboration| |linSolve| |cCsch| |startTableGcd!| |f02bbf| + |solveLinearlyOverQ| |collectUpper| |extendIfCan| |pseudoDivide| + |makeGraphImage| |d01ajf| |OMgetEndObject| |bfEntry| |setsubMatrix!| + |product| |integralCoordinates| |inGroundField?| |recip| |inverse| + |pattern| |debug| |exportedOperators| |cSec| |upperCase?| |myDegree| + |reverse!| |iisec| |checkPrecision| |doubleFloatFormat| |redPo| + |twist| D |any| |socf2socdf| |e04gcf| |dAndcExp| |s21bdf| + |rationalIfCan| |type| |laplacian| |cosSinInfo| |insertMatch| + |monicDecomposeIfCan| |e04naf| |rightGcd| |readUInt32!| + |semiResultantEuclidean2| |intersect| |euclideanGroebner| |aQuadratic| + |scalarTypeOf| |genericLeftTrace| |critMTonD1| |maxColIndex| + |subresultantSequence| |completeEval| |rightRankPolynomial| |dim| + |maxPoints| |discriminantEuclidean| |UnVectorise| |rdHack1| |lazyPrem| + |univariatePolynomials| |concat| |complexIntegrate| + |rectangularMatrix| |leftPower| |rootOf| |satisfy?| |hex| + |strongGenerators| |alternative?| |shiftRoots| |pr2dmp| |plenaryPower| + |blankSeparate| |goodPoint| |getExplanations| |completeSmith| + |OMputError| |mapUnivariateIfCan| |denomRicDE| |clearCache| |iicot| + |bezoutMatrix| |integers| |qinterval| |bfKeys| |const| |setleaves!| + |sech2cosh| F2FG |irForm| |OMUnknownSymbol?| |d01fcf| |charClass| + |unitCanonical| |noLinearFactor?| |cartesian| |limitedIntegrate| + |clipParametric| |antisymmetric?| |weighted| |absolutelyIrreducible?| + |genericLeftNorm| |s21bbf| |oddintegers| |print| |s17agf| |jvmSuper| + |inf| |pole?| |formfeed| |OMlistSymbols| |resolve| |subMatrix| + |rubiksGroup| |setvalue!| |writeInt8!| |iiGamma| |extractIfCan| + |remainder| |removeIrreducibleRedundantFactors| |convert| |toroidal| + |characteristicPolynomial| |numer| |subscript| |unitNormal| |mapCoef| + |evenlambert| |transform| |horizConcat| |leftZero| |complete| |denom| + |allRootsOf| |s17def| |ptree| |zeroVector| |binaryFunction| |s17aff| + |primeFactor| |findBinding| |e01bgf| |cPower| |enqueue!| |c05nbf| + |splitNodeOf!| |genericLeftMinimalPolynomial| |supersub| |title| + |fill!| |pi| |iibinom| |argument| |outputList| |makeYoungTableau| + |reduction| |shiftRight| |cCoth| |infinity| |bumptab| |simplify| + |triangularSystems| |possiblyNewVariety?| |prepareSubResAlgo| + |idealiser| |permutationGroup| |univariatePolynomialsGcds| |fracPart| + |e02dff| |numberOfFactors| |polygamma| |rootRadius| |s18dcf| |e| + |tryFunctionalDecomposition?| |lastSubResultantElseSplit| |ceiling| + |length| |quotientByP| |sumOfKthPowerDivisors| |contractSolve| + |restorePrecision| |hue| |antiCommutative?| |kernel| |c06fqf| + |pseudoQuotient| |scripts| |mainContent| |minimumDegree| |divideIfCan| + |s18def| |constant?| |nil| |infinite| |arbitraryExponent| + |approximate| |complex| |shallowMutable| |canonical| |noetherian| + |central| |partiallyOrderedSet| |arbitraryPrecision| + |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| + |additiveValuation| |unitsKnown| |canonicalUnitNormal| + |multiplicativeValuation| |finiteAggregate| |shallowlyMutable| + |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2216 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1234)) ((-95) |has| |#1| (-1234)) ((-102) . T) ((-111 #0# #0#) -2216 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2216 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2216 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1202 |#1|)) . 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T) ((-921 $ #3=(-1208)) -2216 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-929 #3#) -2216 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-911 (-391)) |has| |#1| (-911 (-391))) ((-911 (-560)) |has| |#1| (-911 (-560))) ((-909 |#1|) . T) ((-939) -12 (|has| |#1| (-319)) (|has| |#1| (-939))) ((-950) -2216 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1234))) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1082 #0#) -2216 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2216 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) |has| |#1| (-363)) ((-1234) |has| |#1| (-1234)) ((-1237) |has| |#1| (-1234)) ((-1248) . 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-421 (-560))) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-38 |#1|) . T) ((-38 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-35) |has| |#1| (-1234)) ((-95) |has| |#1| (-1234)) ((-102) . T) ((-111 #0# #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-133) . T) ((-147) -2191 (|has| |#1| (-363)) (|has| |#1| (-147))) ((-149) |has| |#1| (-149)) ((-635 #0#) -2191 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-363)) (|has| |#1| (-376))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-632 (-887)) . T) ((-175) . T) ((-633 (-171 (-229))) |has| |#1| (-1051)) ((-633 (-171 (-391))) |has| |#1| (-1051)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-633 #1=(-1202 |#1|)) . 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T) ((-466) -2191 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-507) |has| |#1| (-1234)) ((-528 (-1208) |#1|) |has| |#1| (-528 (-1208) |#1|)) ((-528 |#1| |#1|) |has| |#1| (-321 |#1|)) ((-571) -2191 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-668 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-670 #2=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-662 |#1|) . T) ((-662 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-660 #2#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-739 |#1|) . T) ((-739 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-746 |#1| #1#) . T) ((-748) . T) ((-921 $ #3=(-1208)) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-929 #3#) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-911 (-391)) |has| |#1| (-911 (-391))) ((-911 (-560)) |has| |#1| (-911 (-560))) ((-909 |#1|) . T) ((-939) -12 (|has| |#1| (-319)) (|has| |#1| (-939))) ((-950) -2191 (|has| |#1| (-363)) (|has| |#1| (-376)) (|has| |#1| (-319))) ((-1033) -12 (|has| |#1| (-1033)) (|has| |#1| (-1234))) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1082 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1082 |#1|) . T) ((-1082 $) . T) ((-1087 #0#) -2191 (|has| |#1| (-363)) (|has| |#1| (-376))) ((-1087 |#1|) . T) ((-1087 $) . T) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) |has| |#1| (-363)) ((-1234) |has| |#1| (-1234)) ((-1237) |has| |#1| (-1234)) ((-1248) . 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|explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3249 (((-1190) $) NIL T ELT)) (-3208 (((-1151) $) NIL T ELT)) (-2587 (((-887) $) NIL T ELT)) (-2762 (((-114) $ $) NIL T ELT)) (-2362 (((-114) $ $) NIL T ELT))) +((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 66 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 44 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) 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(-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) (((-198) (-809)) (T -198)) NIL (-809) -((-2329 (((-114) $ $) NIL T ELT)) (-4141 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 63 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-2917 (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 36 T ELT) (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 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(-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) (((-199) (-809)) (T -199)) NIL (-809) -((-2329 (((-114) $ $) NIL T ELT)) (-4141 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 76 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-2917 (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 40 T ELT) (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 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(((-1151) $) NIL T ELT)) (-2587 (((-887) $) NIL T ELT)) (-2762 (((-114) $ $) NIL T ELT)) (-2362 (((-114) $ $) NIL T ELT))) +((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 93 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 49 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) $ $) NIL T ELT))) (((-201) (-809)) (T -201)) NIL (-809) -((-2329 (((-114) $ $) NIL T ELT)) (-4141 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 90 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-2917 (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -2917 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3249 (((-1190) $) NIL T ELT)) (-3208 (((-1151) $) NIL T ELT)) (-2587 (((-887) $) NIL T ELT)) (-2762 (((-114) $ $) NIL T ELT)) (-2362 (((-114) $ $) NIL T ELT))) +((-2294 (((-114) $ $) NIL T ELT)) (-1864 (((-1066) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) 90 T ELT) (((-1066) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229))) (-1066)) NIL T ELT)) (-4102 (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) 51 T ELT) (((-2 (|:| -4102 (-391)) (|:| |explanations| (-1190)) (|:| |extra| (-1066))) (-1094) (-2 (|:| |fn| (-326 (-229))) (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) NIL T ELT)) (-3049 (((-1190) $) NIL T ELT)) (-3139 (((-1151) $) NIL T ELT)) (-2539 (((-887) $) NIL T ELT)) (-3860 (((-114) $ $) NIL T ELT)) (-2329 (((-114) 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T) ((-102) -2216 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2216 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2216 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-635 (-560)) -2216 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2216 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-887))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1298 |#2|)) . T) ((-236 $) -2216 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2216 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . 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T) ((-102) -2191 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-102)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-111 |#2| |#2|) -2191 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-133) -2191 (|has| |#2| (-1080)) (|has| |#2| (-815)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-21))) ((-635 #0=(-421 (-560))) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-635 (-560)) -2191 (|has| |#2| (-1080)) (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132)))) ((-635 |#2|) |has| |#2| (-1132)) ((-632 (-887)) -2191 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-632 (-887))) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-632 (-1298 |#2|)) . T) ((-236 $) -2191 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-234 |#2|) |has| |#2| (-1080)) ((-240) -12 (|has| |#2| (-240)) (|has| |#2| (-1080))) ((-239) -2191 (-12 (|has| |#2| (-239)) (|has| |#2| (-1080))) (-12 (|has| |#2| (-240)) (|has| |#2| (-1080)))) ((-274 |#2|) |has| |#2| (-1080)) ((-298 #1=(-560) |#2|) . T) ((-300 #1# |#2|) . T) ((-321 |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-381) |has| |#2| (-381)) ((-390 |#2|) |has| |#2| (-1080)) ((-426 |#2|) |has| |#2| (-1132)) ((-503 |#2|) . T) ((-618 #1# |#2|) . T) ((-528 |#2| |#2|) -12 (|has| |#2| (-321 |#2|)) (|has| |#2| (-1132))) ((-668 (-560)) -2191 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-21))) ((-668 |#2|) -2191 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-668 $) |has| |#2| (-1080)) ((-670 #2=(-560)) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-670 |#2|) -2191 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-670 $) |has| |#2| (-1080)) ((-662 |#2|) -2191 (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-660 #2#) -12 (|has| |#2| (-660 (-560))) (|has| |#2| (-1080))) ((-660 |#2|) |has| |#2| (-1080)) ((-739 |#2|) -2191 (|has| |#2| (-376)) (|has| |#2| (-175))) ((-748) |has| |#2| (-1080)) ((-814) |has| |#2| (-815)) ((-815) |has| |#2| (-815)) ((-816) |has| |#2| (-815)) ((-819) |has| |#2| (-815)) ((-871) -2191 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-874) -2191 (|has| |#2| (-871)) (|has| |#2| (-815))) ((-921 $ #3=(-1208)) -2191 (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080)))) ((-927 (-1208)) -12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080))) ((-929 #3#) -2191 (-12 (|has| |#2| (-929 (-1208))) (|has| |#2| (-1080))) (-12 (|has| |#2| (-927 (-1208))) (|has| |#2| (-1080)))) ((-1069 #0#) -12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ((-1069 (-560)) -12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ((-1069 |#2|) |has| |#2| (-1132)) ((-1082 |#2|) -2191 (|has| |#2| (-1080)) (|has| |#2| (-748)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1087 |#2|) -2191 (|has| |#2| (-1080)) (|has| |#2| (-376)) (|has| |#2| (-175))) ((-1080) |has| |#2| (-1080)) ((-1088) |has| |#2| (-1080)) ((-1143) |has| |#2| (-1080)) ((-1132) -2191 (|has| |#2| (-1132)) (|has| |#2| (-1080)) (|has| |#2| (-871)) (|has| |#2| (-815)) (|has| |#2| (-748)) (|has| |#2| (-381)) (|has| |#2| (-376)) (|has| |#2| (-175)) (|has| |#2| (-133)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1248) . T) ((-1306 |#2|) |has| |#2| (-376))) +((-2294 (((-114) $ $) NIL (|has| |#2| (-102)) ELT)) (-3626 (((-114) $) NIL (|has| |#2| (-23)) ELT)) (-2373 (($ (-948)) 62 (|has| |#2| (-1080)) ELT)) (-3303 (((-1304) $ (-560) (-560)) NIL (|has| $ (-6 -4510)) ELT)) (-2180 (($ $ $) 68 (|has| |#2| (-815)) ELT)) (-2494 (((-3 $ "failed") $ $) 53 (|has| |#2| (-133)) ELT)) (-3067 (((-114) $ (-793)) NIL T ELT)) (-1450 (((-793)) NIL (|has| |#2| (-381)) ELT)) (-2696 ((|#2| $ (-560) |#2|) NIL (|has| $ (-6 -4510)) ELT)) (-3366 (($) NIL T CONST)) (-1442 (((-3 (-560) "failed") $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-3 (-421 (-560)) "failed") $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) (((-3 |#2| "failed") $) 30 (|has| |#2| (-1132)) ELT)) (-3056 (((-560) $) NIL (-12 (|has| |#2| (-1069 (-560))) (|has| |#2| (-1132))) ELT) (((-421 (-560)) $) NIL (-12 (|has| |#2| (-1069 (-421 (-560)))) (|has| |#2| (-1132))) ELT) ((|#2| $) 28 (|has| |#2| (-1132)) ELT)) 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T) ((-571) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1208)) -2216 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-921 $ |#3|) . T) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-927 |#3|) . T) ((-929 #2#) -2216 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T) ((-1253) |has| |#1| (-939))) -((-2329 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-4234 ((|#1| $) 61 T ELT)) (-2818 ((|#1| $) 51 T ELT)) (-2945 (((-114) $ (-793)) 8 T ELT)) (-3599 (($) 7 T CONST)) (-2208 (($ $) 67 T ELT)) (-4184 (($ $) 55 T ELT)) (-1389 ((|#1| |#1| $) 53 T ELT)) (-2685 ((|#1| $) 52 T ELT)) (-3437 (((-663 |#1|) $) 33 (|has| $ (-6 -4509)) ELT)) (-1749 (((-114) $ (-793)) 9 T ELT)) (-2248 (((-663 |#1|) $) 32 (|has| $ (-6 -4509)) ELT)) (-3987 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4509))) ELT)) (-2199 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4510)) ELT)) (-2091 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-3722 (((-114) $ (-793)) 10 T ELT)) (-3816 (((-793) $) 68 T ELT)) (-3249 (((-1190) $) 25 (|has| |#1| (-1132)) ELT)) (-3177 ((|#1| $) 46 T ELT)) (-1368 ((|#1| |#1| $) 59 T ELT)) (-2386 ((|#1| |#1| $) 58 T ELT)) (-3146 (($ |#1| $) 47 T ELT)) (-3590 (((-793) $) 62 T ELT)) (-3208 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-1911 ((|#1| $) 69 T ELT)) (-4124 ((|#1| $) 57 T ELT)) (-2303 ((|#1| $) 56 T ELT)) (-1991 ((|#1| $) 48 T ELT)) (-1934 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-2853 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-1626 (((-114) $ $) 14 T ELT)) (-3137 ((|#1| |#1| $) 65 T ELT)) (-1796 (((-114) $) 11 T ELT)) (-2061 (($) 12 T ELT)) (-1979 ((|#1| $) 66 T ELT)) (-1795 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-1483 (((-793) $) 50 T ELT)) (-3217 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4509)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4509))) ELT)) (-2778 (($ $) 13 T ELT)) (-2587 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-2716 ((|#1| $) 60 T ELT)) (-2762 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-4099 (($ (-663 |#1|)) 49 T ELT)) (-1366 ((|#1| $) 70 T ELT)) (-2087 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4509)) ELT)) (-2362 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2340 (((-793) $) 6 (|has| $ (-6 -4509)) ELT))) +((-1804 (*1 *2 *3) (-12 (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *4 *3 *5 *6)))) (-2844 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 *4)))) (-2252 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2252 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-4283 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3294 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-1687 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-793)))) (-3294 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-663 (-793))))) (-1687 (*1 *2 *1 *3) (-12 (-4 *1 (-262 *4 *3 *5 *6)) (-4 *4 (-1080)) (-4 *3 (-871)) (-4 *5 (-277 *3)) (-4 *6 (-815)) (-5 *2 (-793)))) (-2464 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-114)))) (-1892 (*1 *2 *1) (-12 (-4 *1 (-262 *3 *4 *2 *5)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-815)) (-4 *2 (-277 *4)))) (-3747 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-2884 (*1 *1 *1) (-12 (-4 *1 (-262 *2 *3 *4 *5)) (-4 *2 (-1080)) (-4 *3 (-871)) (-4 *4 (-277 *3)) (-4 *5 (-815)))) (-1804 (*1 *2 *1) (-12 (-4 *3 (-240)) (-4 *3 (-1080)) (-4 *4 (-871)) (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-1 *1 (-793))) (-4 *1 (-262 *3 *4 *5 *6))))) +(-13 (-979 |t#1| |t#4| |t#3|) (-234 |t#1|) (-1069 |t#2|) (-10 -8 (-15 -1804 ((-1 $ (-793)) |t#2|)) (-15 -2844 ((-663 |t#2|) $)) (-15 -2252 ((-793) $ |t#2|)) (-15 -2252 ((-793) $)) (-15 -4283 ((-793) $ |t#2|)) (-15 -3294 ((-663 (-793)) $)) (-15 -1687 ((-793) $)) (-15 -3294 ((-663 (-793)) $ |t#2|)) (-15 -1687 ((-793) $ |t#2|)) (-15 -2464 ((-114) $)) (-15 -1892 (|t#3| $)) (-15 -3747 ($ $)) (-15 -2884 ($ $)) (IF (|has| |t#1| (-240)) (PROGN (-6 (-528 |t#2| |t#1|)) (-6 (-528 |t#2| $)) (-6 (-321 $)) (-15 -1804 ((-1 $ (-793)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2191 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) . T) ((-635 |#2|) . T) ((-635 |#3|) . T) ((-635 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-632 (-887)) . T) ((-175) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| |#1| (-633 (-549))) (|has| |#3| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-633 (-915 (-391)))) (|has| |#3| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-633 (-915 (-560)))) (|has| |#3| (-633 (-915 (-560))))) ((-236 $) -2191 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-234 |#1|) . T) ((-240) |has| |#1| (-240)) ((-239) -2191 (|has| |#1| (-239)) (|has| |#1| (-240))) ((-274 |#1|) . T) ((-302) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-321 $) . T) ((-338 |#1| |#4|) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2191 (|has| |#1| (-939)) (|has| |#1| (-466))) ((-528 |#2| |#1|) |has| |#1| (-240)) ((-528 |#2| $) |has| |#1| (-240)) ((-528 |#3| |#1|) . T) ((-528 |#3| $) . T) ((-528 $ $) . T) ((-571) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-668 #0#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #0#) |has| |#1| (-38 (-421 (-560)))) ((-670 #1=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #0#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-660 #1#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #0#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466))) ((-748) . T) ((-921 $ #2=(-1208)) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-921 $ |#3|) . T) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-927 |#3|) . T) ((-929 #2#) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-929 |#3|) . T) ((-911 (-391)) -12 (|has| |#1| (-911 (-391))) (|has| |#3| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-911 (-560))) (|has| |#3| (-911 (-560)))) ((-979 |#1| |#4| |#3|) . T) ((-939) |has| |#1| (-939)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 |#1|) . T) ((-1069 |#2|) . T) ((-1069 |#3|) . T) ((-1082 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1087 #0#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1248) . T) ((-1253) |has| |#1| (-939))) +((-2294 (((-114) $ $) 22 (|has| |#1| (-102)) ELT)) (-3505 ((|#1| $) 61 T ELT)) (-2765 ((|#1| $) 51 T ELT)) (-3067 (((-114) $ (-793)) 8 T ELT)) (-3366 (($) 7 T CONST)) (-3409 (($ $) 67 T ELT)) (-4318 (($ $) 55 T ELT)) (-2868 ((|#1| |#1| $) 53 T ELT)) (-2387 ((|#1| $) 52 T ELT)) (-1559 (((-663 |#1|) $) 33 (|has| $ (-6 -4509)) ELT)) (-1456 (((-114) $ (-793)) 9 T ELT)) (-2559 (((-663 |#1|) $) 32 (|has| $ (-6 -4509)) ELT)) (-2791 (((-114) |#1| $) 30 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4509))) ELT)) (-3459 (($ (-1 |#1| |#1|) $) 37 (|has| $ (-6 -4510)) ELT)) (-2067 (($ (-1 |#1| |#1|) $) 38 T ELT)) (-2020 (((-114) $ (-793)) 10 T ELT)) (-4474 (((-793) $) 68 T ELT)) (-3049 (((-1190) $) 25 (|has| |#1| (-1132)) ELT)) (-1688 ((|#1| $) 46 T ELT)) (-3460 ((|#1| |#1| $) 59 T ELT)) (-1466 ((|#1| |#1| $) 58 T ELT)) (-1368 (($ |#1| $) 47 T ELT)) (-3547 (((-793) $) 62 T ELT)) (-3139 (((-1151) $) 24 (|has| |#1| (-1132)) ELT)) (-2472 ((|#1| $) 69 T ELT)) (-1696 ((|#1| $) 57 T ELT)) (-1884 ((|#1| $) 56 T ELT)) (-1950 ((|#1| $) 48 T ELT)) (-2667 (((-114) (-1 (-114) |#1|) $) 35 (|has| $ (-6 -4509)) ELT)) (-2799 (($ $ (-663 (-305 |#1|))) 29 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-305 |#1|)) 28 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ |#1| |#1|) 27 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT) (($ $ (-663 |#1|) (-663 |#1|)) 26 (-12 (|has| |#1| (-321 |#1|)) (|has| |#1| (-1132))) ELT)) (-2618 (((-114) $ $) 14 T ELT)) (-4440 ((|#1| |#1| $) 65 T ELT)) (-3868 (((-114) $) 11 T ELT)) (-1423 (($) 12 T ELT)) (-1845 ((|#1| $) 66 T ELT)) (-3855 (($) 64 T ELT) (($ (-663 |#1|)) 63 T ELT)) (-2117 (((-793) $) 50 T ELT)) (-3150 (((-793) (-1 (-114) |#1|) $) 34 (|has| $ (-6 -4509)) ELT) (((-793) |#1| $) 31 (-12 (|has| |#1| (-1132)) (|has| $ (-6 -4509))) ELT)) (-2721 (($ $) 13 T ELT)) (-2539 (((-887) $) 20 (|has| |#1| (-632 (-887))) ELT)) (-1503 ((|#1| $) 60 T ELT)) (-3860 (((-114) $ $) 23 (|has| |#1| (-102)) ELT)) (-1446 (($ (-663 |#1|)) 49 T ELT)) (-3436 ((|#1| $) 70 T ELT)) (-1657 (((-114) (-1 (-114) |#1|) $) 36 (|has| $ (-6 -4509)) ELT)) (-2329 (((-114) $ $) 21 (|has| |#1| (-102)) ELT)) (-2305 (((-793) $) 6 (|has| $ (-6 -4509)) ELT))) (((-263 |#1|) (-142) (-1248)) (T -263)) -((-1795 (*1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-1795 (*1 *1 *2) (-12 (-5 *2 (-663 *3)) (-4 *3 (-1248)) (-4 *1 (-263 *3)))) (-3590 (*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1248)) (-5 *2 (-793)))) (-4234 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-2716 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-1368 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-2386 (*1 *2 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-4124 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-2303 (*1 *2 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248)))) (-4184 (*1 *1 *1) (-12 (-4 *1 (-263 *2)) (-4 *2 (-1248))))) -(-13 (-1152 |t#1|) (-1026 |t#1|) (-10 -8 (-15 -1795 ($)) (-15 -1795 ($ (-663 |t#1|))) (-15 -3590 ((-793) $)) (-15 -4234 (|t#1| $)) (-15 -2716 (|t#1| $)) (-15 -1368 (|t#1| |t#1| $)) (-15 -2386 (|t#1| |t#1| $)) (-15 -4124 (|t#1| $)) (-15 -2303 (|t#1| $)) (-15 -4184 ($ $)))) -(((-34) . 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T) ((-111 #0# #0#) |has| |#1| (-571)) ((-111 |#1| |#1|) |has| |#1| (-175)) ((-111 $ $) |has| |#1| (-571)) ((-133) -2216 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147)) (|has| |#1| (-21))) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #0#) -2216 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-571))) ((-635 #1=(-421 (-975 |#1|))) |has| |#1| (-571)) ((-635 (-560)) -2216 (|has| |#1| (-1080)) (|has| |#1| (-1069 (-560))) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-635 #2=(-630 $)) . T) ((-635 #3=(-975 |#1|)) |has| |#1| (-1080)) ((-635 #4=(-1208)) . T) ((-635 |#1|) . T) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) |has| |#1| (-571)) ((-633 (-549)) |has| |#1| (-633 (-549))) ((-633 (-915 (-391))) |has| |#1| (-633 (-915 (-391)))) ((-633 (-915 (-560))) |has| |#1| (-633 (-915 (-560)))) ((-250) |has| |#1| (-571)) ((-302) |has| |#1| (-571)) ((-319) |has| |#1| (-571)) ((-321 $) . T) ((-310) . T) ((-376) |has| |#1| (-571)) ((-390 |#1|) |has| |#1| (-1080)) ((-414 |#1|) . T) ((-426 |#1|) . T) ((-466) |has| |#1| (-571)) ((-487) |has| |#1| (-487)) ((-528 (-630 $) $) . T) ((-528 $ $) . 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T) ((-950) |has| |#1| (-571)) ((-1069 (-421 (-560))) -2216 (|has| |#1| (-1069 (-421 (-560)))) (-12 (|has| |#1| (-571)) (|has| |#1| (-1069 (-560))))) ((-1069 #1#) |has| |#1| (-571)) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 #3#) |has| |#1| (-1080)) ((-1069 #4#) . T) ((-1069 |#1|) . T) ((-1082 #0#) |has| |#1| (-571)) ((-1082 |#1|) |has| |#1| (-175)) ((-1082 $) |has| |#1| (-571)) ((-1087 #0#) |has| |#1| (-571)) ((-1087 |#1|) |has| |#1| (-175)) ((-1087 $) |has| |#1| (-571)) ((-1080) -2216 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1088) -2216 (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1143) -2216 (|has| |#1| (-1143)) (|has| |#1| (-1080)) (|has| |#1| (-571)) (|has| |#1| (-487)) (|has| |#1| (-175)) (|has| |#1| (-149)) (|has| |#1| (-147))) ((-1132) . T) ((-1248) . 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T) ((-23) . T) ((-47 |#1| #0=(-560)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 |#2|) |has| |#1| (-376)) ((-38 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-376)) ((-111 $ $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-147))) (|has| |#1| (-147))) ((-149) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-149))) (|has| |#1| (-149))) ((-635 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1208)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1208)))) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-229)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-633 (-549)) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-633 (-915 (-560))))) ((-236 $) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-234 |#2|) |has| |#1| (-376)) ((-240) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-239) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-239))) (-12 (|has| |#1| (-376)) (|has| |#2| (-240))) (|has| |#1| (-15 * (|#1| (-560) |#1|)))) ((-274 |#2|) |has| |#1| (-376)) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1208) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1208) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-813) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-814) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-816) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-819) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-842) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-870) -12 (|has| |#1| (-376)) (|has| |#2| (-842))) ((-871) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-874) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-871))) (-12 (|has| |#1| (-376)) (|has| |#2| (-842)))) ((-921 $ #4=(-1208)) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-927 (-1208)) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-929 #4#) -2216 (-12 (|has| |#1| (-376)) (|has| |#2| (-929 (-1208)))) (-12 (|has| |#1| (-376)) (|has| |#2| (-927 (-1208)))) (-12 (|has| |#1| (-15 * (|#1| (-560) |#1|))) (|has| |#1| (-927 (-1208))))) ((-911 (-391)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-391)))) ((-911 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-911 (-560)))) ((-909 |#2|) |has| |#1| (-376)) ((-939) -12 (|has| |#1| (-376)) (|has| |#2| (-939))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1208)))) ((-1069 |#2|) . T) ((-1082 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1253) |has| |#1| (-376)) ((-1260 |#1|) . T) ((-1277 |#1| #0#) . 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T) ((-298 |#2| $) -12 (|has| |#1| (-376)) (|has| |#2| (-298 |#2| |#2|))) ((-298 $ $) |has| (-560) (-1143)) ((-302) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-376) |has| |#1| (-376)) ((-351 |#2|) |has| |#1| (-376)) ((-390 |#2|) |has| |#1| (-376)) ((-414 |#2|) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-528 (-1208) |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-528 (-1208) |#2|))) ((-528 |#2| |#2|) -12 (|has| |#1| (-376)) (|has| |#2| (-321 |#2|))) ((-571) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 |#2|) |has| |#1| (-376)) ((-668 $) . T) ((-670 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 #3=(-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-670 |#1|) . T) ((-670 |#2|) |has| |#1| (-376)) ((-670 $) . T) ((-662 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 |#2|) |has| |#1| (-376)) ((-662 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-660 #3#) -12 (|has| |#1| (-376)) (|has| |#2| (-660 (-560)))) ((-660 |#2|) |has| |#1| (-376)) ((-739 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 |#2|) |has| |#1| (-376)) ((-739 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . 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T) ((-950) |has| |#1| (-376)) ((-1022 |#2|) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1051) -12 (|has| |#1| (-376)) (|has| |#2| (-1051))) ((-1069 (-421 (-560))) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 (-560)) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-560)))) ((-1069 #2#) -12 (|has| |#1| (-376)) (|has| |#2| (-1069 (-1208)))) ((-1069 |#2|) . T) ((-1082 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 |#2|) |has| |#1| (-376)) ((-1082 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 |#2|) |has| |#1| (-376)) ((-1087 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) -12 (|has| |#1| (-376)) (|has| |#2| (-1183))) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1253) |has| |#1| (-376)) ((-1260 |#1|) . T) ((-1277 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2216 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2216 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2216 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1208)) -2216 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-927 #2#) . T) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-929 #2#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2191 (|has| |#1| (-1069 (-421 (-560)))) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 #2=(-1113)) . T) ((-635 |#1|) . T) ((-635 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-633 (-549)) -12 (|has| (-1113) (-633 (-549))) (|has| |#1| (-633 (-549)))) ((-633 (-915 (-391))) -12 (|has| (-1113) (-633 (-915 (-391)))) (|has| |#1| (-633 (-915 (-391))))) ((-633 (-915 (-560))) -12 (|has| (-1113) (-633 (-915 (-560)))) (|has| |#1| (-633 (-915 (-560))))) ((-236 $) . T) ((-234 |#1|) . T) ((-240) . T) ((-239) . T) ((-274 |#1|) . T) ((-298 (-421 $) (-421 $)) |has| |#1| (-571)) ((-298 |#1| |#1|) . T) ((-298 $ $) . T) ((-302) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-321 $) . T) ((-338 |#1| #0#) . T) ((-390 |#1|) . T) ((-426 |#1|) . T) ((-466) -2191 (|has| |#1| (-939)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-528 #2# |#1|) . T) ((-528 #2# $) . T) ((-528 $ $) . T) ((-571) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-668 #1#) |has| |#1| (-38 (-421 (-560)))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) |has| |#1| (-38 (-421 (-560)))) ((-670 #3=(-560)) |has| |#1| (-660 (-560))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) |has| |#1| (-38 (-421 (-560)))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-660 #3#) |has| |#1| (-660 (-560))) ((-660 |#1|) . T) ((-739 #1#) |has| |#1| (-38 (-421 (-560)))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2#) . T) ((-921 $ #4=(-1208)) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-927 #2#) . T) ((-927 (-1208)) |has| |#1| (-927 (-1208))) ((-929 #2#) . T) ((-929 #4#) -2191 (|has| |#1| (-929 (-1208))) (|has| |#1| (-927 (-1208)))) ((-911 (-391)) -12 (|has| (-1113) (-911 (-391))) (|has| |#1| (-911 (-391)))) ((-911 (-560)) -12 (|has| (-1113) (-911 (-560))) (|has| |#1| (-911 (-560)))) ((-979 |#1| #0# #2#) . T) ((-939) |has| |#1| (-939)) ((-950) |has| |#1| (-376)) ((-1069 (-421 (-560))) |has| |#1| (-1069 (-421 (-560)))) ((-1069 (-560)) |has| |#1| (-1069 (-560))) ((-1069 #2#) . T) ((-1069 |#1|) . T) ((-1082 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1082 |#1|) . T) ((-1082 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2191 (|has| |#1| (-939)) (|has| |#1| (-571)) (|has| |#1| (-466)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1183) |has| |#1| (-1183)) ((-1248) . 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T) ((-662 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1082 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2191 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2191 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . 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T) ((-23) . T) ((-47 |#1| #0=(-421 (-560))) . T) ((-25) . T) ((-38 #1=(-421 (-560))) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 |#2|) . T) ((-635 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-632 (-887)) . T) ((-175) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) ((-250) |has| |#1| (-376)) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . T) ((-298 $ $) |has| (-421 (-560)) (-1143)) ((-302) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-319) |has| |#1| (-376)) ((-376) |has| |#1| (-376)) ((-466) |has| |#1| (-376)) ((-507) |has| |#1| (-38 (-421 (-560)))) ((-571) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-668 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-668 (-560)) . T) ((-668 |#1|) . T) ((-668 $) . T) ((-670 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-670 |#1|) . T) ((-670 $) . T) ((-662 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-662 |#1|) |has| |#1| (-175)) ((-662 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-739 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-739 |#1|) |has| |#1| (-175)) ((-739 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376))) ((-748) . T) ((-921 $ #2=(-1208)) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-927 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-929 #2#) -12 (|has| |#1| (-15 * (|#1| (-421 (-560)) |#1|))) (|has| |#1| (-927 (-1208)))) ((-1004 |#1| #0# (-1113)) . T) ((-950) |has| |#1| (-376)) ((-1033) |has| |#1| (-38 (-421 (-560)))) ((-1069 |#2|) . T) ((-1082 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1082 |#1|) . T) ((-1082 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1087 #1#) -2216 (|has| |#1| (-376)) (|has| |#1| (-38 (-421 (-560))))) ((-1087 |#1|) . T) ((-1087 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-376)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1253) |has| |#1| (-376)) ((-1277 |#1| #0#) . T) ((-1281 |#1|) . 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T) ((-1082 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1087 #1#) |has| |#1| (-38 (-421 (-560)))) ((-1087 |#1|) . T) ((-1087 $) -2216 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-1080) . T) ((-1088) . T) ((-1143) . T) ((-1132) . T) ((-1234) |has| |#1| (-38 (-421 (-560)))) ((-1237) |has| |#1| (-38 (-421 (-560)))) ((-1248) . T) ((-1277 |#1| #0#) . 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T) ((-23) . T) ((-47 |#1| #0=(-793)) . T) ((-25) . T) ((-38 #1=(-421 (-560))) |has| |#1| (-38 (-421 (-560)))) ((-38 |#1|) |has| |#1| (-175)) ((-38 $) |has| |#1| (-571)) ((-35) |has| |#1| (-38 (-421 (-560)))) ((-95) |has| |#1| (-38 (-421 (-560)))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-421 (-560)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-133) . T) ((-147) |has| |#1| (-147)) ((-149) |has| |#1| (-149)) ((-635 #1#) |has| |#1| (-38 (-421 (-560)))) ((-635 (-560)) . T) ((-635 |#1|) |has| |#1| (-175)) ((-635 $) |has| |#1| (-571)) ((-632 (-887)) . T) ((-175) -2191 (|has| |#1| (-571)) (|has| |#1| (-175))) ((-236 $) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-240) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-239) |has| |#1| (-15 * (|#1| (-793) |#1|))) ((-296) |has| |#1| (-38 (-421 (-560)))) ((-298 #0# |#1|) . 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NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3472693 3472698 3472703 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3472678 3472683 3472688 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3472663 3472668 3472673 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1328 3471656 3472538 3472615 "ZMOD" 3472620 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1327 3470692 3470874 3471097 "ZLINDEP" 3471488 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1326 3459854 3461760 3463732 "ZDSOLVE" 3468822 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1325 3459088 3459241 3459430 "YSTREAM" 3459700 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1324 3458448 3458757 3458872 "YDIAGRAM" 3458995 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1323 3455896 3457749 3457953 "XRPOLY" 3458291 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1322 3452163 3453767 3454342 "XPR" 3455368 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1321 3449494 3451170 3451225 "XPOLYC" 3451513 NIL XPOLYC (NIL T T) -9 NIL 3451626 NIL) (-1320 3446889 3448825 3449029 "XPOLY" 3449325 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1319 3442835 3445406 3445794 "XPBWPOLY" 3446547 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1318 3437727 3439306 3439361 "XFALG" 3441533 NIL XFALG (NIL T T) -9 NIL 3442322 NIL) (-1317 3432996 3435703 3435745 "XF" 3436366 NIL XF (NIL T) -9 NIL 3436766 NIL) (-1316 3432593 3432705 3432874 "XF-" 3432879 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1315 3431708 3431830 3432035 "XEXPPKG" 3432485 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1314 3429449 3431558 3431654 "XDPOLY" 3431659 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1313 3428104 3428842 3428885 "XALG" 3428890 NIL XALG (NIL T) -9 NIL 3429001 NIL) (-1312 3421014 3426081 3426575 "WUTSET" 3427696 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1311 3419116 3420066 3420389 "WP" 3420825 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1310 3418664 3418938 3419008 "WHILEAST" 3419068 T WHILEAST (NIL) -8 NIL NIL NIL) (-1309 3418076 3418381 3418475 "WHEREAST" 3418592 T WHEREAST (NIL) -8 NIL NIL NIL) (-1308 3416950 3417160 3417455 "WFFINTBS" 3417873 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1307 3414818 3415281 3415743 "WEIER" 3416522 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1306 3413742 3414300 3414342 "VSPACE" 3414478 NIL VSPACE (NIL T) -9 NIL 3414552 NIL) (-1305 3413574 3413607 3413698 "VSPACE-" 3413703 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1304 3413371 3413425 3413493 "VOID" 3413528 T VOID (NIL) -8 NIL NIL NIL) (-1303 3409639 3410434 3411171 "VIEWDEF" 3412656 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1302 3398583 3401187 3403360 "VIEW3D" 3407488 T VIEW3D (NIL) -8 NIL NIL NIL) (-1301 3390600 3392494 3394073 "VIEW2D" 3397026 T VIEW2D (NIL) -8 NIL NIL NIL) (-1300 3388700 3389095 3389501 "VIEW" 3390216 T VIEW (NIL) -7 NIL NIL NIL) (-1299 3387253 3387536 3387854 "VECTOR2" 3388430 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1298 3382159 3387023 3387115 "VECTOR" 3387196 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3375104 3379863 3379906 "VECTCAT" 3380901 NIL VECTCAT (NIL T) -9 NIL 3381488 NIL) (-1296 3374046 3374372 3374762 "VECTCAT-" 3374767 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1295 3373452 3373697 3373817 "VARIABLE" 3373961 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1294 3373385 3373390 3373420 "UTYPE" 3373425 T UTYPE (NIL) -9 NIL NIL NIL) (-1293 3372193 3372369 3372631 "UTSODETL" 3373211 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1292 3369585 3370093 3370617 "UTSODE" 3371734 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1291 3359588 3365518 3365561 "UTSCAT" 3366673 NIL UTSCAT (NIL T) -9 NIL 3367431 NIL) (-1290 3356714 3357658 3358647 "UTSCAT-" 3358652 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1289 3356335 3356384 3356517 "UTS2" 3356665 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1288 3347645 3354096 3354576 "UTS" 3355913 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1287 3341512 3344455 3344498 "URAGG" 3346568 NIL URAGG (NIL T) -9 NIL 3347291 NIL) (-1286 3338235 3339314 3340437 "URAGG-" 3340442 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1285 3333604 3336870 3337335 "UPXSSING" 3337899 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1284 3326026 3333508 3333580 "UPXSCONS" 3333585 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1283 3314777 3322228 3322290 "UPXSCCA" 3322864 NIL UPXSCCA (NIL T T) -9 NIL 3323097 NIL) (-1282 3314397 3314500 3314674 "UPXSCCA-" 3314679 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1281 3303048 3310224 3310267 "UPXSCAT" 3310915 NIL UPXSCAT (NIL T) -9 NIL 3311524 NIL) (-1280 3302472 3302557 3302736 "UPXS2" 3302963 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1279 3293957 3301854 3302118 "UPXS" 3302266 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1278 3292593 3292864 3293215 "UPSQFREE" 3293700 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1277 3285417 3288859 3288914 "UPSCAT" 3289994 NIL UPSCAT (NIL T T) -9 NIL 3290760 NIL) (-1276 3284573 3284828 3285155 "UPSCAT-" 3285160 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1275 3284194 3284243 3284376 "UPOLYC2" 3284524 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3268335 3277321 3277364 "UPOLYC" 3279465 NIL UPOLYC (NIL T) -9 NIL 3280686 NIL) (-1273 3259204 3262103 3265243 "UPOLYC-" 3265248 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3258525 3258650 3258814 "UPMP" 3259093 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1271 3258072 3258159 3258298 "UPDIVP" 3258438 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1270 3256610 3256889 3257205 "UPDECOMP" 3257821 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1269 3255823 3255953 3256139 "UPCDEN" 3256494 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1268 3255336 3255411 3255560 "UP2" 3255748 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1267 3245925 3255019 3255148 "UP" 3255255 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1266 3245130 3245267 3245472 "UNISEG2" 3245768 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1265 3243483 3244334 3244611 "UNISEG" 3244888 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3242525 3242723 3242949 "UNIFACT" 3243299 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1263 3229249 3242429 3242501 "ULSCONS" 3242506 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1262 3209059 3222329 3222391 "ULSCCAT" 3223029 NIL ULSCCAT (NIL T T) -9 NIL 3223318 NIL) (-1261 3208055 3208354 3208742 "ULSCCAT-" 3208747 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1260 3196503 3203601 3203644 "ULSCAT" 3204507 NIL ULSCAT (NIL T) -9 NIL 3205238 NIL) (-1259 3195927 3196012 3196191 "ULS2" 3196418 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1258 3177751 3195239 3195481 "ULS" 3195743 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1257 3176670 3177370 3177484 "UINT8" 3177595 T UINT8 (NIL) -8 NIL NIL 3177687) (-1256 3175588 3176288 3176402 "UINT64" 3176513 T UINT64 (NIL) -8 NIL NIL 3176605) (-1255 3174506 3175206 3175320 "UINT32" 3175431 T UINT32 (NIL) -8 NIL NIL 3175523) (-1254 3173424 3174124 3174238 "UINT16" 3174349 T UINT16 (NIL) -8 NIL NIL 3174441) (-1253 3171503 3172670 3172700 "UFD" 3172912 T UFD (NIL) -9 NIL 3173026 NIL) (-1252 3171285 3171343 3171438 "UFD-" 3171443 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1251 3170343 3170550 3170766 "UDVO" 3171091 T UDVO (NIL) -7 NIL NIL NIL) (-1250 3168109 3168568 3169039 "UDPO" 3169907 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1249 3167821 3168064 3168095 "TYPEAST" 3168100 T TYPEAST (NIL) -8 NIL NIL NIL) (-1248 3167754 3167759 3167789 "TYPE" 3167794 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3166707 3166927 3167167 "TWOFACT" 3167548 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1246 3165682 3166116 3166351 "TUPLE" 3166507 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1245 3163319 3163892 3164431 "TUBETOOL" 3165165 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1244 3162125 3162366 3162608 "TUBE" 3163112 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1243 3150260 3154882 3154979 "TSETCAT" 3160248 NIL TSETCAT (NIL T T T T) -9 NIL 3161780 NIL) (-1242 3144728 3146592 3148483 "TSETCAT-" 3148488 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1241 3138907 3143700 3143983 "TS" 3144480 NIL TS (NIL T) -8 NIL NIL NIL) (-1240 3133380 3134393 3135322 "TRMANIP" 3138043 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1239 3132809 3132884 3133047 "TRIMAT" 3133312 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1238 3130621 3130912 3131269 "TRIGMNIP" 3132558 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1237 3130105 3130254 3130284 "TRIGCAT" 3130497 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1236 3129750 3129853 3129994 "TRIGCAT-" 3129999 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1235 3126364 3128608 3128889 "TREE" 3129504 NIL TREE (NIL T) -8 NIL NIL NIL) (-1234 3125470 3126166 3126196 "TRANFUN" 3126231 T TRANFUN (NIL) -9 NIL 3126297 NIL) (-1233 3124689 3124940 3125220 "TRANFUN-" 3125225 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1232 3124487 3124525 3124586 "TOPSP" 3124650 T TOPSP (NIL) -7 NIL NIL NIL) (-1231 3123817 3123950 3124104 "TOOLSIGN" 3124368 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1230 3122331 3122994 3123233 "TEXTFILE" 3123600 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1229 3122106 3122143 3122215 "TEX1" 3122294 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1228 3119910 3120559 3120988 "TEX" 3121699 T TEX (NIL) -8 NIL NIL NIL) (-1227 3119546 3119621 3119711 "TEMUTL" 3119842 T TEMUTL (NIL) -7 NIL NIL NIL) (-1226 3117640 3117980 3118305 "TBCMPPK" 3119269 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1225 3108960 3115726 3115782 "TBAGG" 3116182 NIL TBAGG (NIL T T) -9 NIL 3116393 NIL) (-1224 3103844 3105518 3107272 "TBAGG-" 3107277 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1223 3103210 3103335 3103480 "TANEXP" 3103733 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1222 3102661 3102985 3103075 "TALGOP" 3103155 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1221 3102055 3102172 3102310 "TABLEAU" 3102558 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1220 3095069 3101912 3102005 "TABLE" 3102010 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3089599 3090897 3092145 "TABLBUMP" 3093855 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1218 3088809 3088968 3089149 "SYSTEM" 3089440 T SYSTEM (NIL) -8 NIL NIL NIL) (-1217 3085214 3085967 3086750 "SYSSOLP" 3088060 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1216 3084976 3085169 3085200 "SYSPTR" 3085205 T SYSPTR (NIL) -8 NIL NIL NIL) (-1215 3083815 3084507 3084633 "SYSNNI" 3084819 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084911) (-1214 3083022 3083577 3083656 "SYSINT" 3083716 NIL SYSINT (NIL NIL) -8 NIL NIL 3083761) (-1213 3079120 3080300 3081010 "SYNTAX" 3082334 T SYNTAX (NIL) -8 NIL NIL NIL) (-1212 3076200 3076880 3077512 "SYMTAB" 3078510 T SYMTAB (NIL) -8 NIL NIL NIL) (-1211 3071299 3072351 3073334 "SYMS" 3075239 T SYMS (NIL) -8 NIL NIL NIL) (-1210 3068198 3070750 3070983 "SYMPOLY" 3071101 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1209 3067703 3067790 3067913 "SYMFUNC" 3068110 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1208 3063501 3065015 3065828 "SYMBOL" 3066912 T SYMBOL (NIL) -8 NIL NIL NIL) (-1207 3056974 3058729 3060449 "SWITCH" 3061803 T SWITCH (NIL) -8 NIL NIL NIL) (-1206 3049728 3055930 3056224 "SUTS" 3056738 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3041213 3049110 3049374 "SUPXS" 3049522 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3040360 3040499 3040716 "SUPFRACF" 3041081 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1203 3039975 3040040 3040153 "SUP2" 3040295 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1202 3030512 3039593 3039719 "SUP" 3039884 NIL SUP (NIL T) -8 NIL NIL NIL) (-1201 3028936 3029234 3029590 "SUMRF" 3030211 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1200 3028259 3028337 3028529 "SUMFS" 3028857 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1199 3010118 3027571 3027813 "SULS" 3028075 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 3009666 3009940 3010010 "SUCHTAST" 3010070 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1197 3008907 3009191 3009331 "SUCH" 3009574 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1196 3002546 3003813 3004772 "SUBSPACE" 3007995 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1195 3001966 3002066 3002230 "SUBRESP" 3002434 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1194 2995977 2997259 2998406 "STTFNC" 3000866 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1193 2989171 2990642 2991953 "STTF" 2994713 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2980288 2982353 2984147 "STTAYLOR" 2987412 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1191 2973042 2980152 2980235 "STRTBL" 2980240 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1190 2967439 2972751 2972850 "STRING" 2972965 T STRING (NIL) -8 NIL NIL NIL) (-1189 2966943 2967026 2967170 "STREAM3" 2967356 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1188 2965907 2966108 2966343 "STREAM2" 2966756 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1187 2965589 2965647 2965740 "STREAM1" 2965849 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1186 2957703 2963208 2963819 "STREAM" 2965013 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1185 2956695 2956900 2957131 "STINPROD" 2957519 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1184 2955810 2956184 2956332 "STEPAST" 2956569 T STEPAST (NIL) -8 NIL NIL NIL) (-1183 2955306 2955551 2955581 "STEP" 2955675 T STEP (NIL) -9 NIL 2955746 NIL) (-1182 2948362 2955205 2955282 "STBL" 2955287 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1181 2942912 2947525 2947568 "STAGG" 2947721 NIL STAGG (NIL T) -9 NIL 2947810 NIL) (-1180 2940464 2941216 2942088 "STAGG-" 2942093 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1179 2938436 2940234 2940326 "STACK" 2940407 NIL STACK (NIL T) -8 NIL NIL NIL) (-1178 2937753 2938266 2938296 "SRING" 2938301 T SRING (NIL) -9 NIL 2938321 NIL) (-1177 2929760 2935894 2936350 "SREGSET" 2937383 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2922107 2923554 2925067 "SRDCMPK" 2928366 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2914407 2919466 2919496 "SRAGG" 2920799 T SRAGG (NIL) -9 NIL 2921407 NIL) (-1174 2913358 2913679 2914058 "SRAGG-" 2914063 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2906942 2912305 2912726 "SQMATRIX" 2912984 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2900354 2903660 2904387 "SPLTREE" 2906287 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2896179 2897010 2897656 "SPLNODE" 2899780 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2895154 2895459 2895489 "SPFCAT" 2895933 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2893849 2894101 2894365 "SPECOUT" 2894912 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2884495 2886813 2886843 "SPADXPT" 2891521 T SPADXPT (NIL) -9 NIL 2893687 NIL) (-1167 2884250 2884296 2884365 "SPADPRSR" 2884448 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2881853 2884205 2884236 "SPADAST" 2884241 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2873454 2875557 2875600 "SPACEC" 2879973 NIL SPACEC (NIL T) -9 NIL 2881789 NIL) (-1164 2871254 2873386 2873435 "SPACE3" 2873440 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2869986 2870177 2870468 "SORTPAK" 2871059 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2868048 2868381 2868793 "SOLVETRA" 2869650 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2867086 2867320 2867581 "SOLVESER" 2867821 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2862318 2863278 2864273 "SOLVERAD" 2866138 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2858043 2858742 2859471 "SOLVEFOR" 2861685 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2851647 2857391 2857488 "SNTSCAT" 2857493 NIL SNTSCAT (NIL T T T T) -9 NIL 2857563 NIL) (-1157 2845191 2849970 2850361 "SMTS" 2851337 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2838906 2845079 2845156 "SMP" 2845161 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2837035 2837366 2837764 "SMITH" 2838603 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2828560 2833614 2833717 "SMATCAT" 2835068 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835618 NIL) (-1153 2825332 2826323 2827501 "SMATCAT-" 2827506 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2822801 2824540 2824583 "SKAGG" 2824844 NIL SKAGG (NIL T) -9 NIL 2824979 NIL) (-1151 2818319 2822284 2822461 "SINT" 2822613 T SINT (NIL) -8 NIL NIL 2822768) (-1150 2818085 2818129 2818195 "SIMPAN" 2818275 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2816905 2817144 2817419 "SIGNRF" 2817844 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2815720 2815889 2816173 "SIGNEF" 2816734 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2814960 2815303 2815427 "SIGAST" 2815618 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2814185 2814495 2814635 "SIG" 2814842 T SIG (NIL) -8 NIL NIL NIL) (-1145 2811837 2812329 2812835 "SHP" 2813726 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2805210 2811738 2811814 "SHDP" 2811819 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2804721 2804961 2804991 "SGROUP" 2805084 T SGROUP (NIL) -9 NIL 2805146 NIL) (-1142 2804573 2804605 2804678 "SGROUP-" 2804683 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2801292 2802062 2802785 "SGCF" 2803872 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2794994 2800738 2800835 "SFRTCAT" 2800840 NIL SFRTCAT (NIL T T T T) -9 NIL 2800879 NIL) (-1139 2788313 2789433 2790569 "SFRGCD" 2793977 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2781331 2782512 2783698 "SFQCMPK" 2787246 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2780933 2781040 2781151 "SFORT" 2781272 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2779859 2780773 2780894 "SEXOF" 2780899 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2775448 2776355 2776450 "SEXCAT" 2779072 NIL SEXCAT (NIL T T T T T) -9 NIL 2779632 NIL) (-1134 2774363 2775329 2775397 "SEX" 2775402 T SEX (NIL) -8 NIL NIL NIL) (-1133 2772485 2773076 2773381 "SETMN" 2774104 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2772015 2772203 2772233 "SETCAT" 2772350 T SETCAT (NIL) -9 NIL 2772435 NIL) (-1131 2771783 2771847 2771946 "SETCAT-" 2771951 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2767886 2770244 2770287 "SETAGG" 2771157 NIL SETAGG (NIL T) -9 NIL 2771497 NIL) (-1129 2767308 2767460 2767697 "SETAGG-" 2767702 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2764117 2767242 2767290 "SET" 2767295 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2763500 2763813 2763914 "SEQAST" 2764038 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2762627 2762993 2763054 "SEGXCAT" 2763340 NIL SEGXCAT (NIL T T) -9 NIL 2763460 NIL) (-1125 2761552 2761820 2761863 "SEGCAT" 2762385 NIL SEGCAT (NIL T) -9 NIL 2762606 NIL) (-1124 2761167 2761232 2761345 "SEGBIND2" 2761487 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2760057 2760530 2760738 "SEGBIND" 2760994 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759576 2759858 2759935 "SEGAST" 2760002 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2758785 2758921 2759125 "SEG2" 2759420 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2757701 2758451 2758633 "SEG" 2758638 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2756934 2757636 2757683 "SDVAR" 2757688 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2748285 2756704 2756834 "SDPOL" 2756839 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2746854 2747144 2747463 "SCPKG" 2748000 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2745976 2746190 2746382 "SCOPE" 2746684 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2745172 2745330 2745509 "SCACHE" 2745831 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2744756 2744990 2745020 "SASTCAT" 2745025 T SASTCAT (NIL) -9 NIL 2745038 NIL) (-1113 2744159 2744591 2744667 "SAOS" 2744702 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2743718 2743759 2743932 "SAERFFC" 2744118 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2743305 2743346 2743505 "SAEFACT" 2743677 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2736346 2743202 2743282 "SAE" 2743287 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2734649 2734981 2735382 "RURPK" 2736012 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2733226 2733592 2733897 "RULESET" 2734483 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2732796 2733020 2733103 "RULECOLD" 2733178 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2729911 2730549 2731007 "RULE" 2732477 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2729695 2729729 2729800 "RTVALUE" 2729862 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2729106 2729412 2729506 "RSTRCAST" 2729623 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2723876 2724749 2725669 "RSETGCD" 2728305 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2712440 2718184 2718281 "RSETCAT" 2722400 NIL RSETCAT (NIL T T T T) -9 NIL 2723497 NIL) (-1101 2710259 2710906 2711730 "RSETCAT-" 2711735 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2702567 2704021 2705541 "RSDCMPK" 2708858 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2700436 2700999 2701073 "RRCC" 2702159 NIL RRCC (NIL T T) -9 NIL 2702503 NIL) (-1098 2699757 2699961 2700240 "RRCC-" 2700245 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2699140 2699453 2699554 "RPTAST" 2699678 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2671519 2682252 2682319 "RPOLCAT" 2692985 NIL RPOLCAT (NIL T T T) -9 NIL 2696145 NIL) (-1095 2662489 2665357 2668479 "RPOLCAT-" 2668484 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2652942 2660700 2661182 "ROUTINE" 2662029 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2649005 2652568 2652708 "ROMAN" 2652824 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2647117 2647865 2648125 "ROIRC" 2648810 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2642837 2645606 2645636 "RNS" 2645940 T RNS (NIL) -9 NIL 2646214 NIL) (-1090 2641244 2641729 2642263 "RNS-" 2642338 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2640205 2640609 2640811 "RNGBIND" 2641095 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2639498 2640002 2640032 "RNG" 2640037 T RNG (NIL) -9 NIL 2640058 NIL) (-1087 2638793 2639271 2639314 "RMODULE" 2639319 NIL RMODULE (NIL T) -9 NIL 2639346 NIL) (-1086 2637617 2637723 2638059 "RMCAT2" 2638694 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2634119 2636963 2637260 "RMATRIX" 2637379 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2626618 2629206 2629321 "RMATCAT" 2632680 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633662 NIL) (-1083 2625957 2626140 2626447 "RMATCAT-" 2626452 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2625530 2625744 2625787 "RLINSET" 2625849 NIL RLINSET (NIL T) -9 NIL 2625893 NIL) (-1081 2625091 2625172 2625300 "RINTERP" 2625449 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2624015 2624689 2624719 "RING" 2624775 T RING (NIL) -9 NIL 2624867 NIL) (-1079 2623795 2623851 2623948 "RING-" 2623953 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2622606 2622873 2623131 "RIDIST" 2623559 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2613231 2622074 2622280 "RGCHAIN" 2622454 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2612489 2612973 2613014 "RGBCSPC" 2613072 NIL RGBCSPC (NIL T) -9 NIL 2613124 NIL) (-1075 2611555 2612014 2612055 "RGBCMDL" 2612287 NIL RGBCMDL (NIL T) -9 NIL 2612401 NIL) (-1074 2611195 2611264 2611367 "RFFACTOR" 2611486 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2610914 2610955 2611052 "RFFACT" 2611154 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2608965 2609395 2609777 "RFDIST" 2610554 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2605905 2606573 2607243 "RF" 2608329 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2605352 2605450 2605613 "RETSOL" 2605807 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2604970 2605068 2605111 "RETRACT" 2605244 NIL RETRACT (NIL T) -9 NIL 2605331 NIL) (-1068 2604813 2604844 2604931 "RETRACT-" 2604936 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2604361 2604635 2604705 "RETAST" 2604765 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2596711 2604014 2604141 "RESULT" 2604256 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2595146 2595980 2596179 "RESRING" 2596614 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2594770 2594831 2594929 "RESLATC" 2595083 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2594469 2594510 2594617 "REPSQ" 2594729 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2594160 2594201 2594312 "REPDB" 2594428 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2587992 2589449 2590672 "REP2" 2592972 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2584295 2585050 2585858 "REP1" 2587219 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2581675 2582297 2582899 "REP" 2583715 T REP (NIL) -7 NIL NIL NIL) (-1058 2573683 2579816 2580272 "REGSET" 2581305 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2572392 2572831 2573081 "REF" 2573468 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2571757 2571872 2572039 "REDORDER" 2572276 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2567128 2570970 2571197 "RECLOS" 2571585 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2566162 2566361 2566576 "REALSOLV" 2566935 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2562609 2563447 2564331 "REAL0Q" 2565327 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2558162 2559198 2560259 "REAL0" 2561590 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2557996 2558049 2558079 "REAL" 2558084 T REAL (NIL) -9 NIL 2558119 NIL) (-1050 2557407 2557713 2557807 "RDUCEAST" 2557924 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2556806 2556884 2557091 "RDIV" 2557329 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2555856 2556048 2556261 "RDIST" 2556628 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2554441 2554740 2555112 "RDETRS" 2555564 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2552235 2552707 2553245 "RDETR" 2553983 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2550854 2551138 2551535 "RDEEFS" 2551951 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2549357 2549669 2550094 "RDEEF" 2550542 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2542836 2546311 2546341 "RCFIELD" 2547636 T RCFIELD (NIL) -9 NIL 2548367 NIL) (-1042 2540792 2541404 2542100 "RCFIELD-" 2542175 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2536844 2538865 2538908 "RCAGG" 2539992 NIL RCAGG (NIL T) -9 NIL 2540457 NIL) (-1040 2536454 2536566 2536729 "RCAGG-" 2536734 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2535771 2535901 2536066 "RATRET" 2536338 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2535312 2535391 2535512 "RATFACT" 2535699 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2534590 2534740 2534892 "RANDSRC" 2535182 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2534318 2534368 2534441 "RADUTIL" 2534539 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2526456 2533149 2533460 "RADIX" 2534041 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2516064 2526298 2526428 "RADFF" 2526433 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2515693 2515786 2515816 "RADCAT" 2515976 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2515463 2515523 2515623 "RADCAT-" 2515628 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2513374 2515233 2515325 "QUEUE" 2515406 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2512999 2513048 2513179 "QUATCT2" 2513325 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2505370 2509422 2509464 "QUATCAT" 2510255 NIL QUATCAT (NIL T) -9 NIL 2511021 NIL) (-1028 2501251 2502546 2503936 "QUATCAT-" 2504032 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2497090 2501184 2501232 "QUAT" 2501237 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2494346 2496138 2496181 "QUAGG" 2496562 NIL QUAGG (NIL T) -9 NIL 2496737 NIL) (-1025 2493894 2494168 2494238 "QQUTAST" 2494298 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2492805 2493407 2493572 "QFORM" 2493775 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2492430 2492479 2492610 "QFCAT2" 2492756 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2482120 2488277 2488319 "QFCAT" 2488987 NIL QFCAT (NIL T) -9 NIL 2489988 NIL) (-1021 2477454 2478902 2480489 "QFCAT-" 2480585 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2476885 2477019 2477151 "QEQUAT" 2477344 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2469903 2471084 2472270 "QCMPACK" 2475818 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2469132 2469314 2469550 "QALGSET2" 2469721 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2466582 2467118 2467548 "QALGSET" 2468787 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2465249 2465491 2465810 "PWFFINTB" 2466355 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2463394 2463592 2463948 "PUSHVAR" 2465063 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2459121 2460337 2460380 "PTRANFN" 2462291 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2457458 2457803 2458127 "PTPACK" 2458832 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2457081 2457144 2457255 "PTFUNC2" 2457395 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2450997 2455870 2455913 "PTCAT" 2456213 NIL PTCAT (NIL T) -9 NIL 2456366 NIL) (-1010 2450646 2450687 2450813 "PSQFR" 2450956 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2449218 2449534 2449870 "PSEUDLIN" 2450344 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2435738 2438313 2440639 "PSETPK" 2446978 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2428446 2431474 2431572 "PSETCAT" 2434613 NIL PSETCAT (NIL T T T T) -9 NIL 2435427 NIL) (-1006 2426171 2426913 2427737 "PSETCAT-" 2427742 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2425484 2425679 2425709 "PSCURVE" 2425981 T PSCURVE (NIL) -9 NIL 2426148 NIL) (-1004 2421200 2422974 2423041 "PSCAT" 2423893 NIL PSCAT (NIL T T T) -9 NIL 2424133 NIL) (-1003 2420194 2420476 2420879 "PSCAT-" 2420884 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2418393 2419253 2419518 "PRTITION" 2419951 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2417804 2418110 2418204 "PRTDAST" 2418321 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2406648 2409070 2411260 "PRS" 2415666 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2404268 2405970 2406010 "PRQAGG" 2406193 NIL PRQAGG (NIL T) -9 NIL 2406295 NIL) (-998 2403447 2403896 2403924 "PROPLOG" 2404063 T PROPLOG (NIL) -9 NIL 2404178 NIL) (-997 2403045 2403108 2403231 "PROPFUN2" 2403370 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2402342 2402481 2402653 "PROPFUN1" 2402906 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2400323 2401089 2401386 "PROPFRML" 2402078 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2399768 2399899 2400027 "PROPERTY" 2400215 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2393656 2397934 2398754 "PRODUCT" 2398994 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2393446 2393484 2393543 "PRINT" 2393617 T PRINT (NIL) -7 NIL NIL NIL) (-991 2392762 2392903 2393055 "PRIMES" 2393326 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2390809 2391228 2391694 "PRIMELT" 2392341 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2390526 2390587 2390615 "PRIMCAT" 2390739 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2389515 2389711 2389939 "PRIMARR2" 2390344 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2385237 2389453 2389498 "PRIMARR" 2389503 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2384874 2384936 2385047 "PREASSOC" 2385175 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2381832 2384332 2384566 "PR" 2384685 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2381283 2381440 2381468 "PPCURVE" 2381673 T PPCURVE (NIL) -9 NIL 2381809 NIL) (-983 2380830 2381078 2381161 "PORTNUM" 2381220 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2378167 2378588 2379180 "POLYROOT" 2380411 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2377544 2377608 2377842 "POLYLIFT" 2378103 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2373765 2374268 2374897 "POLYCATQ" 2377089 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2359406 2365512 2365577 "POLYCAT" 2369091 NIL POLYCAT 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"PMPREDFS" 2332485 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2331308 2331430 2331586 "PMPRED" 2331842 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2329962 2330180 2330558 "PMPLCAT" 2331070 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329488 2329573 2329725 "PMLSAGG" 2329877 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2328955 2329037 2329219 "PMKERNEL" 2329406 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328566 2328647 2328760 "PMINS" 2328874 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2328002 2328077 2328286 "PMFS" 2328491 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2327218 2327348 2327553 "PMDOWN" 2327879 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326467 2326601 2326764 "PMASSFS" 2327105 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2325610 2325792 2325973 "PMASS" 2326306 T PMASS (NIL) -7 NIL NIL NIL) (-957 2325259 2325333 2325427 "PLOTTOOL" 2325536 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320911 2322105 2323027 "PLOT3D" 2324357 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2319799 2320000 2320235 "PLOT1" 2320715 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2314220 2315610 2316758 "PLOT" 2318671 T PLOT (NIL) -8 NIL NIL NIL) (-953 2289395 2294286 2299137 "PLEQN" 2309486 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2289082 2289135 2289238 "PINTERPA" 2289342 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2288388 2288522 2288702 "PINTERP" 2288947 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2286472 2287638 2287666 "PID" 2287863 T PID (NIL) -9 NIL 2287990 NIL) (-949 2286217 2286260 2286335 "PICOERCE" 2286429 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2285313 2285981 2286068 "PI" 2286108 T PI (NIL) -8 NIL NIL 2286175) (-947 2284621 2284772 2284948 "PGROEB" 2285169 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2280060 2281019 2281925 "PGE" 2283735 T PGE (NIL) -7 NIL NIL NIL) (-945 2278141 2278430 2278796 "PGCD" 2279777 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277467 2277582 2277743 "PFRPAC" 2278025 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2273725 2276015 2276368 "PFR" 2277146 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2272078 2272358 2272683 "PFOTOOLS" 2273472 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270593 2270850 2271201 "PFOQ" 2271835 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2269076 2269306 2269662 "PFO" 2270377 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2266154 2267667 2267695 "PFECAT" 2268280 T PFECAT (NIL) -9 NIL 2268664 NIL) (-938 2265581 2265753 2265967 "PFECAT-" 2265972 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2264154 2264436 2264737 "PFBRU" 2265330 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2261983 2262372 2262804 "PFBR" 2263805 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2257922 2261872 2261941 "PF" 2261946 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2252976 2254129 2254999 "PERMGRP" 2257085 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2250888 2252000 2252041 "PERMCAT" 2252441 NIL PERMCAT (NIL T) -9 NIL 2252739 NIL) (-932 2250535 2250582 2250706 "PERMAN" 2250841 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2246337 2248044 2248692 "PERM" 2249920 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2243578 2246002 2246124 "PENDTREE" 2246248 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242459 2242722 2242763 "PDSPC" 2243296 NIL PDSPC (NIL T) -9 NIL 2243541 NIL) (-928 2241514 2241780 2242142 "PDSPC-" 2242147 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2240228 2241164 2241205 "PDRING" 2241210 NIL PDRING (NIL T) -9 NIL 2241238 NIL) (-926 2238971 2239733 2239787 "PDMOD" 2239792 NIL PDMOD (NIL T T) -9 NIL 2239896 NIL) (-925 2236138 2236964 2237632 "PDEPROB" 2238323 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2233647 2234187 2234742 "PDEPACK" 2235603 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232535 2232749 2233000 "PDECOMP" 2233446 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2230052 2230943 2230971 "PDECAT" 2231758 T PDECAT (NIL) -9 NIL 2232471 NIL) (-921 2229669 2229736 2229790 "PDDOM" 2229955 NIL PDDOM (NIL T T) -9 NIL 2230035 NIL) (-920 2229482 2229518 2229625 "PDDOM-" 2229630 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2229227 2229266 2229356 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2029641 2029736 2029959 "ODECONST" 2030203 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2027704 2028413 2028441 "ODECAT" 2029046 T ODECAT (NIL) -9 NIL 2029577 NIL) (-821 2027336 2027385 2027512 "OCTCT2" 2027655 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2023829 2027041 2027163 "OCT" 2027246 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2023052 2023622 2023650 "OCAMON" 2023655 T OCAMON (NIL) -9 NIL 2023676 NIL) (-818 2017316 2020095 2020135 "OC" 2021232 NIL OC (NIL T) -9 NIL 2022090 NIL) (-817 2014351 2015291 2016281 "OC-" 2016375 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2013771 2014196 2014224 "OASGP" 2014229 T OASGP (NIL) -9 NIL 2014249 NIL) (-815 2012897 2013494 2013522 "OAMONS" 2013562 T OAMONS (NIL) -9 NIL 2013605 NIL) (-814 2012188 2012717 2012745 "OAMON" 2012750 T OAMON (NIL) -9 NIL 2012770 NIL) (-813 2011299 2011937 2011965 "OAGROUP" 2011970 T OAGROUP (NIL) -9 NIL 2011990 NIL) (-812 2010981 2011037 2011126 "NUMTUBE" 2011243 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004500 2006072 2007608 "NUMQUAD" 2009465 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 2000180 2001214 2002249 "NUMODE" 2003485 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997461 1998401 1998429 "NUMINT" 1999352 T NUMINT (NIL) -9 NIL 2000116 NIL) (-808 1996373 1996606 1996824 "NUMFMT" 1997263 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982556 1985677 1988209 "NUMERIC" 1993880 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1976260 1982004 1982099 "NTSCAT" 1982104 NIL NTSCAT (NIL T T T T) -9 NIL 1982143 NIL) (-805 1975440 1975619 1975812 "NTPOLFN" 1976099 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1975066 1975129 1975238 "NSUP2" 1975377 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961841 1971891 1972703 "NSUP" 1974287 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950677 1961615 1961748 "NSMP" 1961753 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1949085 1949410 1949767 "NREP" 1950365 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947664 1947928 1948286 "NPCOEF" 1948828 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946712 1946845 1947061 "NORMRETR" 1947545 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944723 1945043 1945452 "NORMPK" 1946420 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944402 1944436 1944560 "NORMMA" 1944689 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1944185 1944220 1944289 "NONE1" 1944366 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1943949 1944142 1944171 "NONE" 1944176 T NONE (NIL) -8 NIL NIL NIL) (-794 1943440 1943508 1943687 "NODE1" 1943881 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941532 1942563 1942818 "NNI" 1943165 T NNI (NIL) -8 NIL NIL 1943400) (-792 1939928 1940265 1940629 "NLINSOL" 1941200 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1936109 1937164 1938063 "NIPROB" 1939049 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934848 1935100 1935402 "NFINTBAS" 1935871 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1933932 1934498 1934539 "NETCLT" 1934711 NIL NETCLT (NIL T) -9 NIL 1934793 NIL) (-788 1932604 1932871 1933152 "NCODIV" 1933700 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1932360 1932403 1932478 "NCNTFRAC" 1932561 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930516 1930904 1931324 "NCEP" 1931985 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1929179 1930126 1930154 "NASRING" 1930264 T NASRING (NIL) -9 NIL 1930344 NIL) (-784 1928962 1929018 1929112 "NASRING-" 1929117 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1927929 1928580 1928608 "NARNG" 1928725 T NARNG (NIL) -9 NIL 1928816 NIL) (-782 1927603 1927688 1927822 "NARNG-" 1927827 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926440 1926689 1926924 "NAGSP" 1927388 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917484 1919396 1921069 "NAGS" 1924787 T NAGS (NIL) -7 NIL NIL NIL) (-779 1916008 1916340 1916671 "NAGF07" 1917173 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910480 1911837 1913144 "NAGF04" 1914721 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1903352 1905062 1906695 "NAGF02" 1908867 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898516 1899676 1900793 "NAGF01" 1902255 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1892096 1893710 1895295 "NAGE04" 1896951 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1883157 1885386 1887516 "NAGE02" 1889986 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1879050 1880057 1881021 "NAGE01" 1882213 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876827 1877379 1877937 "NAGD03" 1878512 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868523 1870505 1872459 "NAGD02" 1874893 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1862262 1863759 1865199 "NAGD01" 1867103 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858399 1859293 1860130 "NAGC06" 1861445 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856846 1857196 1857552 "NAGC05" 1858063 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1856210 1856341 1856485 "NAGC02" 1856722 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1855011 1855738 1855778 "NAALG" 1855857 NIL NAALG (NIL T) -9 NIL 1855918 NIL) (-765 1854840 1854875 1854965 "NAALG-" 1854970 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848712 1849898 1851085 "MULTSQFR" 1853736 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1848019 1848106 1848290 "MULTFACT" 1848624 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1840157 1844602 1844655 "MTSCAT" 1845725 NIL MTSCAT (NIL T T) -9 NIL 1846241 NIL) (-761 1839863 1839923 1840015 "MTHING" 1840097 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839649 1839688 1839748 "MSYSCMD" 1839823 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836394 1839210 1839251 "MSETAGG" 1839256 NIL MSETAGG (NIL T) -9 NIL 1839290 NIL) (-758 1832108 1835149 1835469 "MSET" 1836107 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827700 1829487 1830232 "MRING" 1831408 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1827260 1827333 1827464 "MRF2" 1827627 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826872 1826913 1827057 "MRATFAC" 1827219 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824442 1824779 1825210 "MPRFF" 1826577 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817769 1824296 1824393 "MPOLY" 1824398 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1817253 1817294 1817502 "MPCPF" 1817728 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816761 1816810 1816994 "MPC3" 1817204 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1815944 1816037 1816258 "MPC2" 1816676 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1814221 1814582 1814972 "MONOTOOL" 1815604 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813366 1813749 1813777 "MONOID" 1813996 T MONOID (NIL) -9 NIL 1814143 NIL) (-747 1812882 1813031 1813212 "MONOID-" 1813217 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801848 1808702 1808761 "MONOGEN" 1809435 NIL MONOGEN (NIL T T) -9 NIL 1809891 NIL) (-745 1798898 1799801 1800801 "MONOGEN-" 1800920 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797615 1798163 1798191 "MONADWU" 1798583 T MONADWU (NIL) -9 NIL 1798821 NIL) (-743 1796945 1797146 1797394 "MONADWU-" 1797399 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1796230 1796534 1796562 "MONAD" 1796769 T MONAD (NIL) -9 NIL 1796881 NIL) (-741 1795897 1795993 1796125 "MONAD-" 1796130 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1794036 1794810 1795089 "MOEBIUS" 1795650 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1793204 1793704 1793744 "MODULE" 1793749 NIL MODULE (NIL T) -9 NIL 1793788 NIL) (-738 1792742 1792868 1793058 "MODULE-" 1793063 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1790272 1791106 1791433 "MODRING" 1792566 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1786994 1788377 1788898 "MODOP" 1789801 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785480 1786061 1786338 "MODMONOM" 1786857 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1774234 1783771 1784185 "MODMON" 1785117 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1771067 1773078 1773354 "MODFIELD" 1774109 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1769978 1770348 1770538 "MMLFORM" 1770897 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769498 1769547 1769726 "MMAP" 1769929 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767391 1768330 1768371 "MLO" 1768794 NIL MLO (NIL T) -9 NIL 1769036 NIL) (-729 1764739 1765273 1765875 "MLIFT" 1766872 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1764118 1764214 1764368 "MKUCFUNC" 1764650 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763711 1763787 1763910 "MKRECORD" 1764041 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762734 1762920 1763148 "MKFUNC" 1763522 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1762110 1762226 1762382 "MKFLCFN" 1762617 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761375 1761489 1761674 "MKBCFUNC" 1762003 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757372 1760929 1761065 "MINT" 1761259 T MINT (NIL) -8 NIL NIL NIL) (-722 1756154 1756427 1756704 "MHROWRED" 1757127 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1750905 1754689 1755094 "MFLOAT" 1755769 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1750250 1750338 1750509 "MFINFACT" 1750817 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746529 1747413 1748297 "MESH" 1749386 T MESH (NIL) -7 NIL NIL NIL) (-718 1744883 1745231 1745584 "MDDFACT" 1746216 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741419 1744014 1744055 "MDAGG" 1744310 NIL MDAGG (NIL T) -9 NIL 1744453 NIL) (-716 1729135 1740712 1740919 "MCMPLX" 1741232 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1728254 1728418 1728619 "MCDEN" 1728984 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1726102 1726414 1726794 "MCALCFN" 1727984 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1724979 1725267 1725500 "MAYBE" 1725908 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722537 1723114 1723676 "MATSTOR" 1724450 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1717959 1721909 1722157 "MATRIX" 1722322 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713659 1714432 1715168 "MATLIN" 1717316 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1712235 1712406 1712739 "MATCAT2" 1713494 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701574 1705292 1705369 "MATCAT" 1710401 NIL MATCAT (NIL T T T) -9 NIL 1711873 NIL) (-707 1697527 1698837 1700250 "MATCAT-" 1700255 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695603 1695963 1696347 "MAPPKG3" 1697202 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694560 1694757 1694979 "MAPPKG2" 1695427 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1693017 1693343 1693670 "MAPPKG1" 1694266 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1692018 1692423 1692600 "MAPPAST" 1692860 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691623 1691687 1691810 "MAPHACK3" 1691954 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1691203 1691276 1691390 "MAPHACK2" 1691555 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690629 1690744 1690886 "MAPHACK1" 1691094 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688552 1689329 1689633 "MAGMA" 1690357 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1687971 1688276 1688367 "MACROAST" 1688481 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1684214 1686210 1686671 "M3D" 1687543 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677686 1682525 1682566 "LZSTAGG" 1683348 NIL LZSTAGG (NIL T) -9 NIL 1683643 NIL) (-695 1673368 1674817 1676274 "LZSTAGG-" 1676279 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1670281 1671259 1671746 "LWORD" 1672913 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669803 1670085 1670160 "LSTAST" 1670226 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661731 1669574 1669708 "LSQM" 1669713 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1660949 1661094 1661322 "LSPP" 1661586 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657686 1658402 1659132 "LSMP1" 1660251 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655468 1655799 1656255 "LSMP" 1657375 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648596 1654558 1654599 "LSAGG" 1654661 NIL LSAGG (NIL T) -9 NIL 1654739 NIL) (-687 1645105 1646215 1647428 "LSAGG-" 1647433 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642400 1644249 1644498 "LPOLY" 1644900 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1641976 1642067 1642190 "LPEFRAC" 1642309 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641659 1641738 1641766 "LOGIC" 1641877 T LOGIC (NIL) -9 NIL 1641959 NIL) (-683 1641515 1641544 1641615 "LOGIC-" 1641620 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640690 1640848 1641041 "LODOOPS" 1641371 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1639214 1639463 1639816 "LODOF" 1640437 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1635090 1637849 1637890 "LODOCAT" 1638328 NIL LODOCAT (NIL T) -9 NIL 1638539 NIL) (-679 1634805 1634881 1635008 "LODOCAT-" 1635013 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631791 1634646 1634764 "LODO2" 1634769 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1628898 1631728 1631773 "LODO1" 1631778 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1625993 1628814 1628880 "LODO" 1628885 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1624862 1625039 1625344 "LODEEF" 1625816 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1623039 1623956 1624209 "LO" 1624694 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1618011 1621205 1621246 "LNAGG" 1622108 NIL LNAGG (NIL T) -9 NIL 1622543 NIL) (-672 1617104 1617372 1617714 "LNAGG-" 1617719 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1613084 1614029 1614668 "LMOPS" 1616519 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612383 1612861 1612902 "LMODULE" 1612907 NIL LMODULE (NIL T) -9 NIL 1612933 NIL) (-669 1609338 1612028 1612151 "LMDICT" 1612293 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608914 1609128 1609169 "LLINSET" 1609230 NIL LLINSET (NIL T) -9 NIL 1609274 NIL) (-667 1608559 1608822 1608882 "LITERAL" 1608887 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1608078 1608158 1608297 "LIST3" 1608479 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1606176 1606524 1606923 "LIST2MAP" 1607725 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1605165 1605361 1605589 "LIST2" 1605994 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597619 1604099 1604403 "LIST" 1604894 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1597202 1597438 1597479 "LINSET" 1597484 NIL LINSET (NIL T) -9 NIL 1597518 NIL) (-661 1596016 1596710 1596877 "LINFORM" 1597087 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1594315 1595043 1595084 "LINEXP" 1595574 NIL LINEXP (NIL T) -9 NIL 1595847 NIL) (-659 1592891 1593795 1593976 "LINELT" 1594186 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591448 1591728 1592039 "LINDEP" 1592643 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590584 1591180 1591290 "LINBASIS" 1591378 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587321 1588070 1588847 "LIMITRF" 1589839 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585606 1585920 1586329 "LIMITPS" 1587016 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584434 1585009 1585049 "LIECAT" 1585189 NIL LIECAT (NIL T) -9 NIL 1585340 NIL) (-653 1584269 1584302 1584390 "LIECAT-" 1584395 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1578289 1583780 1584008 "LIE" 1584090 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570474 1577829 1577985 "LIB" 1578153 T LIB (NIL) -8 NIL NIL NIL) (-650 1566043 1566992 1567927 "LGROBP" 1569591 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564667 1565575 1565603 "LFCAT" 1565810 T LFCAT (NIL) -9 NIL 1565949 NIL) (-648 1562605 1562939 1563289 "LF" 1564388 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559465 1560137 1560825 "LEXTRIPK" 1561969 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1556053 1557035 1557538 "LEXP" 1559045 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555469 1555774 1555866 "LETAST" 1555981 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553855 1554180 1554581 "LEADCDET" 1555151 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1553033 1553119 1553348 "LAZM3PK" 1553776 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547551 1551110 1551648 "LAUPOL" 1552545 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1547124 1547174 1547335 "LAPLACE" 1547501 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545972 1546688 1546729 "LALG" 1546791 NIL LALG (NIL T) -9 NIL 1546850 NIL) (-639 1545668 1545745 1545881 "LALG-" 1545886 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543405 1544769 1545020 "LA" 1545501 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1543234 1543264 1543305 "KVTFROM" 1543367 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541991 1542601 1542786 "KTVLOGIC" 1543069 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541820 1541850 1541891 "KRCFROM" 1541953 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540712 1540911 1541210 "KOVACIC" 1541620 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540541 1540571 1540612 "KONVERT" 1540674 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540370 1540400 1540441 "KOERCE" 1540503 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539854 1539947 1540079 "KERNEL2" 1540284 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537541 1538447 1538824 "KERNEL" 1539510 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1531012 1536018 1536072 "KDAGG" 1536449 NIL KDAGG (NIL T T) -9 NIL 1536655 NIL) (-628 1530523 1530665 1530870 "KDAGG-" 1530875 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1523223 1530184 1530339 "KAFILE" 1530401 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522827 1523112 1523175 "JVMOP" 1523180 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521563 1522067 1522316 "JVMMDACC" 1522598 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520499 1520953 1521158 "JVMFDACC" 1521378 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1519080 1519575 1519875 "JVMCSTTG" 1520219 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1518216 1518620 1518781 "JVMCFACC" 1518939 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517894 1518133 1518182 "JVMBCODE" 1518187 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511913 1517405 1517633 "JORDAN" 1517715 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1511226 1511562 1511683 "JOINAST" 1511812 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1507261 1509403 1509457 "IXAGG" 1510386 NIL IXAGG (NIL T T) -9 NIL 1510845 NIL) (-617 1506114 1506486 1506905 "IXAGG-" 1506910 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1501203 1506036 1506095 "IVECTOR" 1506100 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499928 1500206 1500472 "ITUPLE" 1500970 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498400 1498607 1498902 "ITRIGMNP" 1499750 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1497127 1497349 1497632 "ITFUN3" 1498176 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496725 1496788 1496911 "ITFUN2" 1497050 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495830 1496205 1496379 "ITFORM" 1496571 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493599 1494850 1495128 "ITAYLOR" 1495585 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481996 1487736 1488899 "ISUPS" 1492469 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1481088 1481240 1481476 "ISUMP" 1481843 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475938 1481033 1481074 "ISTRING" 1481079 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475354 1475659 1475751 "ISAST" 1475866 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474551 1474645 1474861 "IRURPK" 1475268 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473463 1473688 1473928 "IRSN" 1474331 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471508 1471889 1472318 "IRRF2F" 1473101 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1471249 1471293 1471369 "IRREDFFX" 1471464 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469822 1470123 1470422 "IROOT" 1470982 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468961 1469315 1469466 "IRFORM" 1469691 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1468043 1468174 1468388 "IR2F" 1468844 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465632 1466151 1466717 "IR2" 1467521 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1462072 1463316 1464008 "IR" 1464972 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461857 1461897 1461957 "IPRNTPK" 1462032 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457824 1461746 1461815 "IPF" 1461820 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455852 1457749 1457806 "IPADIC" 1457811 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1455110 1455412 1455542 "IP4ADDR" 1455742 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454448 1454739 1454871 "IOMODE" 1454998 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453419 1454045 1454172 "IOBFILE" 1454341 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452829 1453323 1453351 "IOBCON" 1453356 T IOBCON (NIL) -9 NIL 1453377 NIL) (-589 1452334 1452398 1452581 "INVLAPLA" 1452765 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441904 1444336 1446722 "INTTR" 1449998 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1438197 1438981 1439846 "INTTOOLS" 1441089 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437777 1437874 1437991 "INTSLPE" 1438100 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1435244 1437700 1437759 "INTRVL" 1437764 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432822 1433358 1433933 "INTRF" 1434729 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1432215 1432330 1432472 "INTRET" 1432720 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1430188 1430601 1431071 "INTRAT" 1431823 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427433 1428034 1428653 "INTPM" 1429673 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1424150 1424777 1425515 "INTPAF" 1426819 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1419251 1420291 1421342 "INTPACK" 1423119 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418497 1418655 1418863 "INTHERTR" 1419093 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417930 1418016 1418204 "INTHERAL" 1418411 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415698 1416219 1416676 "INTHEORY" 1417493 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1407030 1408725 1410497 "INTG0" 1414050 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387555 1392393 1397203 "INTFTBL" 1402240 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386780 1386942 1387115 "INTFACT" 1387414 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1384177 1384653 1385210 "INTEF" 1386334 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382374 1383269 1383297 "INTDOM" 1383598 T INTDOM (NIL) -9 NIL 1383805 NIL) (-570 1381713 1381917 1382159 "INTDOM-" 1382164 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377581 1380002 1380056 "INTCAT" 1380855 NIL INTCAT (NIL T) -9 NIL 1381176 NIL) (-568 1377035 1377156 1377284 "INTBIT" 1377473 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375716 1375888 1376195 "INTALG" 1376880 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1375193 1375289 1375446 "INTAF" 1375620 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1368160 1375003 1375143 "INTABL" 1375148 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367401 1367963 1368028 "INT8" 1368062 T INT8 (NIL) -8 NIL NIL 1368107) (-563 1366641 1367203 1367268 "INT64" 1367302 T INT64 (NIL) -8 NIL NIL 1367347) (-562 1365881 1366443 1366508 "INT32" 1366542 T INT32 (NIL) -8 NIL NIL 1366587) (-561 1365121 1365683 1365748 "INT16" 1365782 T INT16 (NIL) -8 NIL NIL 1365827) (-560 1361323 1364918 1365027 "INT" 1365032 T INT (NIL) -8 NIL NIL NIL) (-559 1355432 1358871 1358899 "INS" 1359833 T INS (NIL) -9 NIL 1360498 NIL) (-558 1352507 1353457 1354424 "INS-" 1354497 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1351264 1351509 1351807 "INPSIGN" 1352260 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350358 1350499 1350696 "INPRODPF" 1351144 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1349228 1349369 1349606 "INPRODFF" 1350238 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1348216 1348380 1348640 "INNMFACT" 1349064 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347395 1347510 1347698 "INMODGCD" 1348115 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345879 1346148 1346472 "INFSP" 1347140 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1345039 1345180 1345363 "INFPROD0" 1345759 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344637 1344709 1344807 "INFORM1" 1344974 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1341204 1342702 1343217 "INFORM" 1344130 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340709 1340816 1340930 "INFINITY" 1341110 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339783 1340429 1340530 "INETCLTS" 1340628 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338381 1338649 1338970 "INEP" 1339531 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337442 1338278 1338343 "INDE" 1338348 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1336994 1337074 1337191 "INCRMAPS" 1337369 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335716 1336263 1336469 "INBFILE" 1336808 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330895 1331952 1332896 "INBFF" 1334804 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329749 1330072 1330100 "INBCON" 1330613 T INBCON (NIL) -9 NIL 1330879 NIL) (-540 1328959 1329224 1329500 "INBCON-" 1329505 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328378 1328683 1328774 "INAST" 1328888 T INAST (NIL) -8 NIL NIL NIL) (-538 1327745 1328057 1328163 "IMPTAST" 1328292 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323666 1327589 1327693 "IMATRIX" 1327698 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322358 1322497 1322813 "IMATQF" 1323522 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320538 1320805 1321142 "IMATLIN" 1322114 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314453 1320462 1320520 "ILIST" 1320525 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1312119 1314313 1314426 "IIARRAY2" 1314431 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306933 1312030 1312094 "IFF" 1312099 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1306214 1306550 1306666 "IFAST" 1306837 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300726 1305506 1305694 "IFARRAY" 1306071 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299764 1300630 1300703 "IFAMON" 1300708 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299336 1299413 1299467 "IEVALAB" 1299674 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1298999 1299079 1299239 "IEVALAB-" 1299244 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1298063 1298888 1298963 "IDPOAMS" 1298968 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1297196 1297952 1298027 "IDPOAM" 1298032 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296577 1297111 1297173 "IDPO" 1297178 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1295057 1295584 1295636 "IDPC" 1296148 NIL IDPC (NIL T T) -9 NIL 1296429 NIL) (-522 1294389 1294949 1295022 "IDPAM" 1295027 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293604 1294281 1294354 "IDPAG" 1294359 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1293148 1293410 1293500 "IDENT" 1293534 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289367 1290251 1291146 "IDECOMP" 1292305 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1282002 1283290 1284337 "IDEAL" 1288403 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1281144 1281274 1281474 "ICDEN" 1281886 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1280119 1280624 1280771 "ICARD" 1281017 T ICARD (NIL) -8 NIL NIL NIL) (-515 1278149 1278492 1278897 "IBPTOOLS" 1279796 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1273264 1277769 1277882 "IBITS" 1278068 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269939 1270563 1271258 "IBATOOL" 1272681 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267700 1268180 1268713 "IBACHIN" 1269474 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1265290 1267546 1267649 "IARRAY2" 1267654 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1261003 1265216 1265273 "IARRAY1" 1265278 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1254020 1259415 1259896 "IAN" 1260542 T IAN (NIL) -8 NIL NIL NIL) (-508 1253525 1253588 1253761 "IALGFACT" 1253957 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1253017 1253166 1253194 "HYPCAT" 1253401 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252519 1252672 1252858 "HYPCAT-" 1252863 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1252066 1252314 1252397 "HOSTNAME" 1252456 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251899 1251948 1251989 "HOMOTOP" 1251994 NIL HOMOTOP (NIL T) -9 NIL 1252027 NIL) (-503 1248332 1249831 1249872 "HOAGG" 1250853 NIL HOAGG (NIL T) -9 NIL 1251582 NIL) (-502 1246848 1247325 1247851 "HOAGG-" 1247856 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239898 1246441 1246591 "HEXADEC" 1246718 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238610 1238868 1239131 "HEUGCD" 1239675 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237542 1238447 1238577 "HELLFDIV" 1238582 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235552 1237319 1237407 "HEAP" 1237486 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234749 1235104 1235238 "HEADAST" 1235438 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1228136 1234664 1234726 "HDP" 1234731 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1221148 1227771 1227923 "HDMP" 1228037 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220454 1220612 1220776 "HB" 1221004 T HB (NIL) -7 NIL NIL NIL) (-493 1213464 1220300 1220404 "HASHTBL" 1220409 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212880 1213185 1213277 "HASAST" 1213392 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210293 1212502 1212684 "HACKPI" 1212718 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205465 1210146 1210259 "GTSET" 1210264 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198504 1205343 1205441 "GSTBL" 1205446 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1190260 1197669 1197925 "GSERIES" 1198304 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189291 1189804 1189832 "GROUP" 1190035 T GROUP (NIL) -9 NIL 1190169 NIL) (-486 1188615 1188816 1189067 "GROUP-" 1189072 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186964 1187303 1187690 "GROEBSOL" 1188292 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185792 1186152 1186203 "GRMOD" 1186732 NIL GRMOD (NIL T T) -9 NIL 1186900 NIL) (-483 1185548 1185596 1185724 "GRMOD-" 1185729 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180688 1181902 1182902 "GRIMAGE" 1184568 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1179082 1179415 1179739 "GRDEF" 1180384 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178514 1178642 1178783 "GRAY" 1178961 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177591 1178093 1178144 "GRALG" 1178297 NIL GRALG (NIL T T) -9 NIL 1178390 NIL) (-478 1177228 1177325 1177488 "GRALG-" 1177493 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173709 1176811 1176990 "GPOLSET" 1177134 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1173057 1173120 1173378 "GOSPER" 1173646 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168627 1169495 1170021 "GMODPOL" 1172756 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167614 1167816 1168054 "GHENSEL" 1168439 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161686 1162613 1163633 "GENUPS" 1166698 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161377 1161434 1161523 "GENUFACT" 1161629 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160777 1160866 1161031 "GENPGCD" 1161295 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1160245 1160286 1160499 "GENMFACT" 1160736 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158781 1159068 1159375 "GENEEZ" 1159988 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151953 1158392 1158554 "GDMP" 1158704 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140691 1145724 1146830 "GCNAALG" 1150936 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138818 1139866 1139894 "GCDDOM" 1140149 T GCDDOM (NIL) -9 NIL 1140306 NIL) (-465 1138258 1138415 1138630 "GCDDOM-" 1138635 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126730 1129204 1131596 "GBINTERN" 1135949 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124531 1124859 1125280 "GBF" 1126405 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123288 1123477 1123744 "GBEUCLID" 1124347 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121938 1122145 1122449 "GB" 1123067 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121269 1121412 1121561 "GAUSSFAC" 1121809 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119590 1119938 1120252 "GALUTIL" 1120988 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117850 1118172 1118496 "GALPOLYU" 1119317 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1115149 1115505 1115912 "GALFACTU" 1117547 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106763 1108454 1110062 "GALFACT" 1113581 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1104049 1104809 1104837 "FVFUN" 1105993 T FVFUN (NIL) -9 NIL 1106713 NIL) (-454 1103279 1103497 1103525 "FVC" 1103816 T FVC (NIL) -9 NIL 1103999 NIL) (-453 1102880 1103104 1103172 "FUNDESC" 1103231 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102453 1102677 1102758 "FUNCTION" 1102832 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1101130 1101754 1101957 "FTEM" 1102270 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098760 1099452 1099918 "FT" 1100684 T FT (NIL) -8 NIL NIL NIL) (-449 1097029 1097340 1097737 "FSUPFACT" 1098451 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095348 1095715 1096047 "FST" 1096717 T FST (NIL) -8 NIL NIL NIL) (-447 1094529 1094653 1094841 "FSRED" 1095230 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1093218 1093484 1093831 "FSPRMELT" 1094244 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090428 1090962 1091448 "FSPECF" 1092781 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089950 1090010 1090180 "FSINT" 1090369 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1088086 1088943 1089246 "FSERIES" 1089729 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1087110 1087244 1087468 "FSCINT" 1087966 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1086134 1086295 1086522 "FSAGG2" 1086963 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081998 1085078 1085119 "FSAGG" 1085489 NIL FSAGG (NIL T) -9 NIL 1085748 NIL) (-439 1079598 1080361 1081157 "FSAGG-" 1081252 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1077258 1077556 1078104 "FS2UPS" 1079316 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1076124 1076307 1076609 "FS2EXPXP" 1077083 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075752 1075801 1075930 "FS2" 1076075 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055983 1065526 1065567 "FS" 1069451 NIL FS (NIL T) -9 NIL 1071740 NIL) (-434 1044044 1047619 1051676 "FS-" 1051976 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043458 1043585 1043737 "FRUTIL" 1043924 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037969 1041147 1041187 "FRNAALG" 1042507 NIL FRNAALG (NIL T) -9 NIL 1043105 NIL) (-431 1033450 1034718 1035993 "FRNAALG-" 1036743 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1033082 1033131 1033258 "FRNAAF2" 1033401 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031369 1031931 1032227 "FRMOD" 1032894 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030554 1030647 1030938 "FRIDEAL2" 1031276 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1028159 1028929 1029247 "FRIDEAL" 1030345 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1027250 1027706 1027747 "FRETRCT" 1027752 NIL FRETRCT (NIL T) -9 NIL 1027928 NIL) (-425 1026308 1026593 1026944 "FRETRCT-" 1026949 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1023122 1024592 1024651 "FRAMALG" 1025533 NIL FRAMALG (NIL T T) -9 NIL 1025825 NIL) (-423 1021160 1021711 1022341 "FRAMALG-" 1022564 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020790 1020853 1020960 "FRAC2" 1021097 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013775 1020263 1020540 "FRAC" 1020545 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013405 1013468 1013575 "FR2" 1013712 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004322 1008900 1010258 "FR" 1012079 NIL FR (NIL T) -8 NIL NIL NIL) (-418 998241 1001701 1001729 "FPS" 1002848 T FPS (NIL) -9 NIL 1003405 NIL) (-417 997666 997799 997963 "FPS-" 998109 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994625 996623 996651 "FPC" 996876 T FPC (NIL) -9 NIL 997018 NIL) (-415 994406 994458 994555 "FPC-" 994560 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 993164 993894 993935 "FPATMAB" 993940 NIL FPATMAB (NIL T) -9 NIL 994092 NIL) (-413 991307 991906 992253 "FPARFRAC" 992880 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986599 987199 987881 "FORTRAN" 990739 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 984173 984837 984865 "FORTFN" 985925 T FORTFN (NIL) -9 NIL 986549 NIL) (-410 983925 983987 984015 "FORTCAT" 984074 T FORTCAT (NIL) -9 NIL 984136 NIL) (-409 981611 982141 982680 "FORT" 983406 T FORT (NIL) -7 NIL NIL NIL) (-408 981393 981429 981498 "FORMULA1" 981575 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979397 980009 980399 "FORMULA" 981023 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978914 978972 979145 "FORDER" 979339 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977974 978174 978367 "FOP" 978741 T FOP (NIL) -7 NIL NIL NIL) (-404 976387 977254 977428 "FNLA" 977856 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 975006 975517 975545 "FNCAT" 976005 T FNCAT (NIL) -9 NIL 976265 NIL) (-402 974449 974965 974993 "FNAME" 974998 T FNAME (NIL) -8 NIL NIL NIL) (-401 972775 973948 973976 "FMTC" 973981 T FMTC (NIL) -9 NIL 974017 NIL) (-400 971324 972711 972757 "FMONOID" 972762 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967913 969279 969320 "FMONCAT" 970537 NIL FMONCAT (NIL T) -9 NIL 971142 NIL) (-398 965235 965983 966011 "FMFUN" 967155 T FMFUN (NIL) -9 NIL 967863 NIL) (-397 962108 963160 963214 "FMCAT" 964409 NIL FMCAT (NIL T T) -9 NIL 964904 NIL) (-396 961341 961558 961586 "FMC" 961876 T FMC (NIL) -9 NIL 962058 NIL) (-395 960009 961107 961207 "FM1" 961286 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 959027 959751 959900 "FM" 959905 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956765 957217 957711 "FLOATRP" 958578 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 954167 954703 955281 "FLOATCP" 956232 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946830 951896 952517 "FLOAT" 953566 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945348 946422 946463 "FLINEXP" 946468 NIL FLINEXP (NIL T) -9 NIL 946561 NIL) (-389 944478 944737 945065 "FLINEXP-" 945070 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943536 943698 943922 "FLASORT" 944330 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940454 941506 941558 "FLALG" 942785 NIL FLALG (NIL T T) -9 NIL 943252 NIL) (-386 939478 939639 939866 "FLAGG2" 940307 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932733 936887 936928 "FLAGG" 938190 NIL FLAGG (NIL T) -9 NIL 938842 NIL) (-384 931387 931798 932288 "FLAGG-" 932293 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 928018 929232 929291 "FINRALG" 930419 NIL FINRALG (NIL T T) -9 NIL 930927 NIL) (-382 927142 927407 927746 "FINRALG-" 927751 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926448 926747 926775 "FINITE" 926971 T FINITE (NIL) -9 NIL 927078 NIL) (-380 918399 920978 921018 "FINAALG" 924685 NIL FINAALG (NIL T) -9 NIL 926138 NIL) (-379 913515 914781 915925 "FINAALG-" 917304 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 912075 912497 912551 "FILECAT" 913235 NIL FILECAT (NIL T T) -9 NIL 913451 NIL) (-377 911353 911830 911933 "FILE" 912005 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908756 910583 910611 "FIELD" 910651 T FIELD (NIL) -9 NIL 910731 NIL) (-375 907298 907761 908272 "FIELD-" 908277 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904981 905933 906280 "FGROUP" 906984 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 904053 904235 904455 "FGLMICPK" 904813 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899301 903978 904035 "FFX" 904040 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898896 898963 899098 "FFSLPE" 899234 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898394 898436 898645 "FFPOLY2" 898854 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894270 895166 895962 "FFPOLY" 897630 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889532 894189 894252 "FFP" 894257 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 884056 888875 889065 "FFNBX" 889386 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878382 883191 883449 "FFNBP" 883910 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872413 877666 877877 "FFNB" 878215 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871233 871443 871758 "FFINTBAS" 872210 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866819 869480 869508 "FFIELDC" 870128 T FFIELDC (NIL) -9 NIL 870504 NIL) (-362 865418 865866 866356 "FFIELDC-" 866361 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 864975 865033 865157 "FFHOM" 865360 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862634 863157 863674 "FFF" 864490 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857662 862376 862477 "FFCGX" 862577 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852694 857394 857501 "FFCGP" 857605 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847287 852421 852529 "FFCG" 852630 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846692 846741 846976 "FFCAT2" 847238 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825367 836424 836510 "FFCAT" 841675 NIL FFCAT (NIL T T T) -9 NIL 843126 NIL) (-354 820378 821612 822926 "FFCAT-" 824156 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815192 820289 820353 "FF" 820358 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803845 808164 809384 "FEXPR" 814044 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802773 803242 803283 "FEVALAB" 803367 NIL FEVALAB (NIL T) -9 NIL 803628 NIL) (-350 801890 802142 802480 "FEVALAB-" 802485 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798752 799637 799752 "FDIVCAT" 801320 NIL FDIVCAT (NIL T T T T) -9 NIL 801757 NIL) (-348 798508 798541 798711 "FDIVCAT-" 798716 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797722 797815 798092 "FDIV2" 798415 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796132 797105 797308 "FDIV" 797621 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 795040 795427 795629 "FCTRDATA" 795950 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793696 793985 794274 "FCPAK1" 794771 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792699 793196 793337 "FCOMP" 793587 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 776013 779849 783387 "FC" 789181 T FC (NIL) -8 NIL NIL NIL) (-341 767715 772334 772374 "FAXF" 774176 NIL FAXF (NIL T) -9 NIL 774868 NIL) (-340 764836 765649 766474 "FAXF-" 766939 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759405 764212 764388 "FARRAY" 764693 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753964 756352 756405 "FAMR" 757428 NIL FAMR (NIL T T) -9 NIL 757888 NIL) (-337 752788 753156 753591 "FAMR-" 753596 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751815 752710 752763 "FAMONOID" 752768 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749445 750297 750350 "FAMONC" 751291 NIL FAMONC (NIL T T) -9 NIL 751677 NIL) (-334 747919 749199 749336 "FAGROUP" 749341 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745672 746033 746436 "FACUTIL" 747600 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744759 744956 745178 "FACTFUNC" 745482 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736524 744062 744261 "EXPUPXS" 744615 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 733977 734547 735133 "EXPRTUBE" 735958 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730188 730840 731570 "EXPRODE" 733316 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724622 725329 726135 "EXPR2UPS" 729486 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724248 724311 724420 "EXPR2" 724559 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708549 722897 723326 "EXPR" 723852 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698880 707700 707991 "EXPEXPAN" 708385 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698300 698604 698695 "EXITAST" 698809 T EXITAST (NIL) -8 NIL NIL NIL) (-323 698064 698257 698286 "EXIT" 698291 T EXIT (NIL) -8 NIL NIL NIL) (-322 697685 697753 697866 "EVALCYC" 697996 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697202 697344 697385 "EVALAB" 697555 NIL EVALAB (NIL T) -9 NIL 697659 NIL) (-320 696659 696805 697026 "EVALAB-" 697031 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693774 695315 695343 "EUCDOM" 695898 T EUCDOM (NIL) -9 NIL 696248 NIL) (-318 692134 692635 693218 "EUCDOM-" 693223 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691760 691823 691932 "ESTOOLS2" 692071 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691505 691553 691633 "ESTOOLS1" 691712 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678822 681803 684553 "ESTOOLS" 688775 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678561 678599 678681 "ESCONT1" 678784 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674869 675696 676476 "ESCONT" 677801 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674538 674594 674694 "ES2" 674813 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674162 674226 674335 "ES1" 674474 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667863 669793 669821 "ES" 672589 T ES (NIL) -9 NIL 673999 NIL) (-309 662540 664097 665914 "ES-" 666078 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661732 661885 662061 "ERROR" 662384 T ERROR (NIL) -7 NIL NIL NIL) (-307 654748 661591 661682 "EQTBL" 661687 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654374 654437 654546 "EQ2" 654685 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646633 649688 651137 "EQ" 652958 NIL -1506 (NIL T) -8 NIL NIL NIL) (-304 641876 642971 644064 "EP" 645572 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640416 640767 641073 "ENV" 641590 T ENV (NIL) -8 NIL NIL NIL) (-302 639376 640050 640078 "ENTIRER" 640083 T ENTIRER (NIL) -9 NIL 640129 NIL) (-301 635795 637558 637919 "EMR" 639184 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634899 635110 635164 "ELTAGG" 635544 NIL ELTAGG (NIL T T) -9 NIL 635755 NIL) (-299 634606 634680 634821 "ELTAGG-" 634826 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634364 634399 634453 "ELTAB" 634537 NIL ELTAB (NIL T T) -9 NIL 634589 NIL) (-297 633466 633636 633835 "ELFUTS" 634215 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633190 633264 633292 "ELEMFUN" 633397 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 633054 633081 633149 "ELEMFUN-" 633154 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627465 631096 631137 "ELAGG" 632077 NIL ELAGG (NIL T) -9 NIL 632540 NIL) (-293 625642 626184 626847 "ELAGG-" 626852 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624924 625091 625247 "ELABOR" 625506 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623530 623864 624158 "ELABEXPR" 624650 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 616042 618167 618996 "EFUPXS" 622805 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609168 611291 612102 "EFULS" 615317 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606605 607011 607483 "EFSTRUC" 608800 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 596042 597962 599510 "EF" 605120 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 595020 595527 595676 "EAB" 595913 T EAB (NIL) -8 NIL NIL NIL) (-285 594142 594979 595007 "E04UCFA" 595012 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593264 594101 594129 "E04NAFA" 594134 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592386 593223 593251 "E04MBFA" 593256 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591508 592345 592373 "E04JAFA" 592378 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590632 591467 591495 "E04GCFA" 591500 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589756 590591 590619 "E04FDFA" 590624 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588878 589715 589743 "E04DGFA" 589748 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582955 584403 585767 "E04AGNT" 587534 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581575 582256 582296 "DVARCAT" 582637 NIL DVARCAT (NIL T) -9 NIL 582800 NIL) (-276 580725 580991 581305 "DVARCAT-" 581310 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572686 580524 580653 "DSMP" 580658 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 571037 571828 571869 "DSEXT" 572232 NIL DSEXT (NIL T) -9 NIL 572526 NIL) (-273 569226 569750 570416 "DSEXT-" 570421 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568885 568950 569048 "DROPT1" 569161 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563904 565126 566263 "DROPT0" 567768 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558487 559849 560917 "DROPT" 562856 T DROPT (NIL) -8 NIL NIL NIL) (-269 556796 557157 557543 "DRAWPT" 558121 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556423 556482 556600 "DRAWHACK" 556737 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555124 555423 555714 "DRAWCX" 556152 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554633 554708 554859 "DRAWCURV" 555050 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 544951 547063 549178 "DRAWCFUN" 552538 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539442 540461 541540 "DRAW" 543925 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535913 538107 538148 "DQAGG" 538777 NIL DQAGG (NIL T) -9 NIL 539051 NIL) (-262 522489 530124 530207 "DPOLCAT" 532059 NIL DPOLCAT (NIL T T T T) -9 NIL 532604 NIL) (-261 517008 518674 520632 "DPOLCAT-" 520637 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509865 516869 516967 "DPMO" 516972 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502619 509645 509812 "DPMM" 509817 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502141 502403 502492 "DOMTMPLT" 502550 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501490 501943 502023 "DOMCTOR" 502081 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500642 500970 501121 "DOMAIN" 501359 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493654 500277 500429 "DMP" 500543 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491431 492721 492762 "DMEXT" 492767 NIL DMEXT (NIL T) -9 NIL 492943 NIL) (-253 491025 491087 491231 "DLP" 491369 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484148 490352 490542 "DLIST" 490867 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480686 482973 483014 "DLAGG" 483564 NIL DLAGG (NIL T) -9 NIL 483794 NIL) (-250 479198 480012 480040 "DIVRING" 480132 T DIVRING (NIL) -9 NIL 480215 NIL) (-249 478381 478625 478925 "DIVRING-" 478930 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476423 476840 477246 "DISPLAY" 477995 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475253 475474 475739 "DIRPROD2" 476216 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468660 475167 475230 "DIRPROD" 475235 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456872 463371 463424 "DIRPCAT" 463682 NIL DIRPCAT (NIL NIL T) -9 NIL 464557 NIL) (-244 454072 454840 455721 "DIRPCAT-" 456058 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453353 453519 453705 "DIOSP" 453906 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449767 452237 452278 "DIOPS" 452712 NIL DIOPS (NIL T) -9 NIL 452941 NIL) (-241 449286 449430 449621 "DIOPS-" 449626 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448193 448965 448993 "DIFRING" 448998 T DIFRING (NIL) -9 NIL 449020 NIL) (-239 447841 447939 447967 "DIFFSPC" 448086 T DIFFSPC (NIL) -9 NIL 448161 NIL) (-238 447462 447564 447716 "DIFFSPC-" 447721 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446398 446996 447037 "DIFFMOD" 447042 NIL DIFFMOD (NIL T) -9 NIL 447140 NIL) (-236 446094 446151 446192 "DIFFDOM" 446313 NIL DIFFDOM (NIL T) -9 NIL 446381 NIL) (-235 445941 445971 446055 "DIFFDOM-" 446060 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443681 445145 445186 "DIFEXT" 445191 NIL DIFEXT (NIL T) -9 NIL 445344 NIL) (-233 440715 443185 443226 "DIAGG" 443231 NIL DIAGG (NIL T) -9 NIL 443251 NIL) (-232 440063 440256 440508 "DIAGG-" 440513 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434913 439022 439299 "DHMATRIX" 439832 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430381 431434 432444 "DFSFUN" 433923 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424622 429312 429624 "DFLOAT" 430089 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422861 423166 423555 "DFINTTLS" 424330 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419680 420882 421282 "DERHAM" 422527 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417216 419455 419544 "DEQUEUE" 419624 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416458 416603 416786 "DEGRED" 417078 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412864 413633 414479 "DEFINTRF" 415686 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410401 410888 411480 "DEFINTEF" 412383 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409685 410021 410136 "DEFAST" 410306 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402735 409278 409428 "DECIMAL" 409555 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400193 400705 401211 "DDFACT" 402279 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399783 399832 399983 "DBLRESP" 400144 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398984 399553 399644 "DBASIS" 399732 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396768 397214 397575 "DBASE" 398750 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395956 396248 396394 "DATAARY" 396667 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 395014 395915 395943 "D03FAFA" 395948 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394073 394973 395001 "D03EEFA" 395006 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391999 392489 392978 "D03AGNT" 393604 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391240 391958 391986 "D02EJFA" 391991 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390481 391199 391227 "D02CJFA" 391232 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389722 390440 390468 "D02BHFA" 390473 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388963 389681 389709 "D02BBFA" 389714 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382094 383749 385355 "D02AGNT" 387377 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379844 380385 380931 "D01WGTS" 381568 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378851 379803 379831 "D01TRNS" 379836 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377859 378810 378838 "D01GBFA" 378843 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376867 377818 377846 "D01FCFA" 377851 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375875 376826 376854 "D01ASFA" 376859 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374883 375834 375862 "D01AQFA" 375867 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373891 374842 374870 "D01APFA" 374875 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372899 373850 373878 "D01ANFA" 373883 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371907 372858 372886 "D01AMFA" 372891 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370915 371866 371894 "D01ALFA" 371899 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369923 370874 370902 "D01AKFA" 370907 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368931 369882 369910 "D01AJFA" 369915 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362154 363779 365340 "D01AGNT" 367390 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361473 361619 361771 "CYCLOTOM" 362022 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358128 358921 359648 "CYCLES" 360766 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357428 357574 357745 "CVMP" 357989 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355215 355527 355896 "CTRIGMNP" 357156 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354688 354946 355047 "CTORKIND" 355134 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353893 354281 354309 "CTORCAT" 354491 T CTORCAT (NIL) -9 NIL 354604 NIL) (-188 353467 353602 353761 "CTORCAT-" 353766 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352881 353141 353249 "CTORCALL" 353391 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352239 352675 352748 "CTOR" 352828 T CTOR (NIL) -8 NIL NIL NIL) (-185 351595 351712 351865 "CSTTOOLS" 352136 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347292 348051 348809 "CRFP" 350907 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346707 347013 347105 "CRCEAST" 347220 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345730 345939 346167 "CRAPACK" 346511 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345110 345215 345419 "CPMATCH" 345606 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344829 344863 344969 "CPIMA" 345076 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341087 341849 342568 "COORDSYS" 344164 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340475 340620 340762 "CONTOUR" 340965 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335947 338478 338970 "CONTFRAC" 340015 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335821 335848 335876 "CONDUIT" 335913 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334775 335449 335477 "COMRING" 335482 T COMRING (NIL) -9 NIL 335534 NIL) (-174 333757 334133 334317 "COMPPROP" 334611 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333412 333453 333581 "COMPLPAT" 333716 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 333042 333105 333212 "COMPLEX2" 333349 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321439 332851 332960 "COMPLEX" 332965 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320760 320899 321059 "COMPILER" 321299 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320472 320513 320611 "COMPFACT" 320719 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301859 314176 314216 "COMPCAT" 315220 NIL COMPCAT (NIL T) -9 NIL 316568 NIL) (-167 290747 294298 297925 "COMPCAT-" 298281 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290470 290504 290607 "COMMUPC" 290713 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290258 290298 290357 "COMMONOP" 290431 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289780 290062 290137 "COMMAAST" 290203 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289287 289531 289618 "COMM" 289713 T COMM (NIL) -8 NIL NIL NIL) (-162 288482 288730 288758 "COMBOPC" 289096 T COMBOPC (NIL) -9 NIL 289271 NIL) (-161 287336 287588 287830 "COMBINAT" 288272 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283679 284367 284994 "COMBF" 286758 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282341 282795 283030 "COLOR" 283464 T COLOR (NIL) -8 NIL NIL NIL) (-158 281757 282062 282154 "COLONAST" 282269 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281391 281444 281569 "CMPLXRT" 281704 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280779 281091 281190 "CLLCTAST" 281312 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276238 277309 278389 "CLIP" 279719 T CLIP (NIL) -7 NIL NIL NIL) (-154 274411 275339 275579 "CLIF" 276065 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270393 272529 272570 "CLAGG" 273499 NIL CLAGG (NIL T) -9 NIL 274035 NIL) (-152 268737 269272 269855 "CLAGG-" 269860 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268275 268366 268506 "CINTSLPE" 268646 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265740 266247 266795 "CHVAR" 267803 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264780 265454 265482 "CHARZ" 265487 T CHARZ (NIL) -9 NIL 265502 NIL) (-148 264528 264574 264652 "CHARPOL" 264734 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263446 264159 264187 "CHARNZ" 264234 T CHARNZ (NIL) -9 NIL 264290 NIL) (-146 260390 261500 262029 "CHAR" 262937 T CHAR (NIL) -8 NIL NIL NIL) (-145 260098 260177 260205 "CFCAT" 260316 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259321 259450 259633 "CDEN" 259982 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254918 258474 258754 "CCLASS" 259061 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254139 254326 254503 "CATEGORY" 254761 T -10 (NIL) -8 NIL NIL NIL) (-141 253634 254058 254106 "CATCTOR" 254111 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 253025 253337 253435 "CATAST" 253556 T CATAST (NIL) -8 NIL NIL NIL) (-139 252441 252746 252838 "CASEAST" 252953 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251537 251697 251918 "CARTEN2" 252288 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246435 247694 248438 "CARTEN" 250849 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244565 245585 245842 "CARD" 246198 T CARD (NIL) -8 NIL NIL NIL) (-135 244087 244369 244444 "CAPSLAST" 244510 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243529 243785 243813 "CACHSET" 243945 T CACHSET (NIL) -9 NIL 244023 NIL) (-133 242919 243307 243335 "CABMON" 243385 T CABMON (NIL) -9 NIL 243441 NIL) (-132 242356 242623 242733 "BYTEORD" 242829 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237283 241861 242033 "BYTEBUF" 242204 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236041 236798 236947 "BYTE" 237110 T BYTE (NIL) -8 NIL NIL 237239) (-129 233303 235733 235840 "BTREE" 235967 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230505 232951 233073 "BTOURN" 233213 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227612 229947 229988 "BTCAT" 230056 NIL BTCAT (NIL T) -9 NIL 230133 NIL) (-126 227261 227359 227508 "BTCAT-" 227513 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222150 226507 226535 "BTAGG" 226649 T BTAGG (NIL) -9 NIL 226759 NIL) (-124 221604 221765 221971 "BTAGG-" 221976 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218340 220882 221097 "BSTREE" 221421 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217448 217604 217788 "BRILL" 218196 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213843 216146 216187 "BRAGG" 216836 NIL BRAGG (NIL T) -9 NIL 217094 NIL) (-120 212276 212778 213333 "BRAGG-" 213338 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204526 211620 211805 "BPADICRT" 212123 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202542 204463 204508 "BPADIC" 204513 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202234 202270 202384 "BOUNDZRO" 202506 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199961 200419 200894 "BOP1" 201792 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194943 196387 197299 "BOP" 199069 T BOP (NIL) -8 NIL NIL NIL) (-114 193608 194531 194673 "BOOLEAN" 194821 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193201 193358 193386 "BOOLE" 193497 T BOOLE (NIL) -9 NIL 193578 NIL) (-112 193069 193096 193162 "BOOLE-" 193167 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192238 192738 192792 "BMODULE" 192797 NIL BMODULE (NIL T T) -9 NIL 192862 NIL) (-110 187559 192036 192109 "BITS" 192185 T BITS (NIL) -8 NIL NIL NIL) (-109 186956 187099 187239 "BINDING" 187439 T BINDING (NIL) -8 NIL NIL NIL) (-108 180009 186551 186700 "BINARY" 186827 T BINARY (NIL) -8 NIL NIL NIL) (-107 177616 179236 179277 "BGAGG" 179537 NIL BGAGG (NIL T) -9 NIL 179674 NIL) (-106 177441 177479 177570 "BGAGG-" 177575 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176464 176825 177030 "BFUNCT" 177256 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175134 175332 175620 "BEZOUT" 176288 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171332 173986 174316 "BBTREE" 174837 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170915 171011 171039 "BASTYPE" 171216 T BASTYPE (NIL) -9 NIL 171315 NIL) (-101 170573 170672 170807 "BASTYPE-" 170812 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169995 170083 170235 "BALFACT" 170484 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168731 169410 169596 "AUTOMOR" 169840 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168457 168462 168488 "ATTREG" 168493 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166619 167154 167506 "ATTRBUT" 168123 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166173 166447 166513 "ATTRAST" 166571 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165673 165822 165848 "ATRIG" 166049 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165470 165523 165610 "ATRIG-" 165615 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165053 165287 165313 "ASTCAT" 165318 T ASTCAT (NIL) -9 NIL 165348 NIL) (-92 164762 164839 164958 "ASTCAT-" 164963 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162736 164538 164626 "ASTACK" 164705 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161225 161538 161903 "ASSOCEQ" 162418 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160149 160884 161008 "ASP9" 161132 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158909 159754 159896 "ASP80" 160038 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158636 158857 158896 "ASP8" 158901 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157482 158313 158431 "ASP78" 158549 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156343 157162 157279 "ASP77" 157396 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155147 155981 156112 "ASP74" 156243 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153939 154782 154914 "ASP73" 155046 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152729 153574 153706 "ASP7" 153838 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151725 152555 152655 "ASP6" 152660 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150564 151402 151520 "ASP55" 151638 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149405 150238 150357 "ASP50" 150476 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148385 149106 149216 "ASP49" 149326 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147061 147924 148092 "ASP42" 148274 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145730 146594 146764 "ASP41" 146948 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144710 145431 145541 "ASP4" 145651 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143552 144387 144505 "ASP35" 144623 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143281 143500 143539 "ASP34" 143544 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 143000 143085 143161 "ASP33" 143236 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141786 142635 142767 "ASP31" 142899 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141515 141734 141773 "ASP30" 141778 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141232 141319 141395 "ASP29" 141470 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140961 141180 141219 "ASP28" 141224 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140690 140909 140948 "ASP27" 140953 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139666 140388 140499 "ASP24" 140610 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138635 139468 139580 "ASP20" 139585 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137470 138309 138428 "ASP19" 138547 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137189 137274 137350 "ASP12" 137425 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135933 136788 136932 "ASP10" 137076 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134913 135634 135744 "ASP1" 135854 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132525 134757 134848 "ARRAY2" 134853 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131539 131730 131951 "ARRAY12" 132348 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126899 131187 131301 "ARRAY1" 131456 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120944 123101 123176 "ARR2CAT" 125806 NIL ARR2CAT (NIL T T T) -9 NIL 126564 NIL) (-56 118234 119122 120076 "ARR2CAT-" 120081 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117485 117861 117986 "ARITY" 118127 T ARITY (NIL) -8 NIL NIL NIL) (-54 116243 116413 116712 "APPRULE" 117321 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115888 115942 116061 "APPLYORE" 116189 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115142 115289 115446 "ANY1" 115762 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114442 114735 114855 "ANY" 115040 T ANY (NIL) -8 NIL NIL NIL) (-50 111768 112879 113206 "ANTISYM" 114166 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111212 111475 111571 "ANON" 111690 T ANON (NIL) -8 NIL NIL NIL) (-48 104375 109751 110205 "AN" 110776 T AN (NIL) -8 NIL NIL NIL) (-47 100031 101647 101698 "AMR" 102446 NIL AMR (NIL T T) -9 NIL 103046 NIL) (-46 99083 99364 99727 "AMR-" 99732 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82552 99000 99061 "ALIST" 99066 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78849 82146 82315 "ALGSC" 82470 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75299 75959 76566 "ALGPKG" 78289 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74564 74677 74861 "ALGMFACT" 75185 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70547 71178 71772 "ALGMANIP" 74148 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59900 70173 70323 "ALGFF" 70480 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59072 59227 59406 "ALGFACT" 59758 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57861 58599 58637 "ALGEBRA" 58642 NIL ALGEBRA (NIL T) -9 NIL 58683 NIL) (-37 57561 57638 57770 "ALGEBRA-" 57775 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38515 55398 55450 "ALAGG" 55586 NIL ALAGG (NIL T T) -9 NIL 55747 NIL) (-35 38015 38164 38190 "AHYP" 38391 T AHYP (NIL) -9 NIL NIL NIL) (-34 36900 37194 37220 "AGG" 37719 T AGG (NIL) -9 NIL 37998 NIL) (-33 36298 36496 36710 "AGG-" 36715 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34058 34527 34932 "AF" 35940 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33478 33783 33873 "ADDAST" 33986 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32710 33005 33161 "ACPLOT" 33340 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29642 29680 "ACFS" 30287 NIL ACFS (NIL T) -9 NIL 30526 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3471983 3471988 3471993 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3471968 3471973 3471978 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3471953 3471958 3471963 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3471938 3471943 3471948 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1328 3470931 3471813 3471890 "ZMOD" 3471895 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1327 3469967 3470149 3470372 "ZLINDEP" 3470763 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1326 3459129 3461035 3463007 "ZDSOLVE" 3468097 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1325 3458363 3458516 3458705 "YSTREAM" 3458975 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1324 3457723 3458032 3458147 "YDIAGRAM" 3458270 T YDIAGRAM (NIL) -8 NIL NIL NIL) (-1323 3455171 3457024 3457228 "XRPOLY" 3457566 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1322 3451438 3453042 3453617 "XPR" 3454643 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1321 3448769 3450445 3450500 "XPOLYC" 3450788 NIL XPOLYC (NIL T T) -9 NIL 3450901 NIL) (-1320 3446164 3448100 3448304 "XPOLY" 3448600 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1319 3442110 3444681 3445069 "XPBWPOLY" 3445822 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1318 3437002 3438581 3438636 "XFALG" 3440808 NIL XFALG (NIL T T) -9 NIL 3441597 NIL) (-1317 3432278 3434978 3435020 "XF" 3435641 NIL XF (NIL T) -9 NIL 3436041 NIL) (-1316 3431875 3431987 3432156 "XF-" 3432161 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1315 3430990 3431112 3431317 "XEXPPKG" 3431767 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1314 3428731 3430840 3430936 "XDPOLY" 3430941 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1313 3427386 3428124 3428167 "XALG" 3428172 NIL XALG (NIL T) -9 NIL 3428283 NIL) (-1312 3420296 3425363 3425857 "WUTSET" 3426978 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1311 3418398 3419348 3419671 "WP" 3420107 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1310 3417946 3418220 3418290 "WHILEAST" 3418350 T WHILEAST (NIL) -8 NIL NIL NIL) (-1309 3417358 3417663 3417757 "WHEREAST" 3417874 T WHEREAST (NIL) -8 NIL NIL NIL) (-1308 3416232 3416442 3416737 "WFFINTBS" 3417155 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1307 3414100 3414563 3415025 "WEIER" 3415804 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1306 3413024 3413582 3413624 "VSPACE" 3413760 NIL VSPACE (NIL T) -9 NIL 3413834 NIL) (-1305 3412856 3412889 3412980 "VSPACE-" 3412985 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1304 3412653 3412707 3412775 "VOID" 3412810 T VOID (NIL) -8 NIL NIL NIL) (-1303 3408921 3409716 3410453 "VIEWDEF" 3411938 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1302 3397865 3400469 3402642 "VIEW3D" 3406770 T VIEW3D (NIL) -8 NIL NIL NIL) (-1301 3389882 3391776 3393355 "VIEW2D" 3396308 T VIEW2D (NIL) -8 NIL NIL NIL) (-1300 3387982 3388377 3388783 "VIEW" 3389498 T VIEW (NIL) -7 NIL NIL NIL) (-1299 3386535 3386818 3387136 "VECTOR2" 3387712 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1298 3381441 3386305 3386397 "VECTOR" 3386478 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1297 3374386 3379145 3379188 "VECTCAT" 3380183 NIL VECTCAT (NIL T) -9 NIL 3380770 NIL) (-1296 3373328 3373654 3374044 "VECTCAT-" 3374049 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1295 3372734 3372979 3373099 "VARIABLE" 3373243 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1294 3372667 3372672 3372702 "UTYPE" 3372707 T UTYPE (NIL) -9 NIL NIL NIL) (-1293 3371475 3371651 3371913 "UTSODETL" 3372493 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1292 3368867 3369375 3369899 "UTSODE" 3371016 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1291 3358877 3364800 3364843 "UTSCAT" 3365955 NIL UTSCAT (NIL T) -9 NIL 3366713 NIL) (-1290 3356003 3356947 3357936 "UTSCAT-" 3357941 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1289 3355624 3355673 3355806 "UTS2" 3355954 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1288 3346941 3353385 3353865 "UTS" 3355202 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1287 3340808 3343751 3343794 "URAGG" 3345864 NIL URAGG (NIL T) -9 NIL 3346587 NIL) (-1286 3337531 3338610 3339733 "URAGG-" 3339738 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1285 3332907 3336166 3336631 "UPXSSING" 3337195 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1284 3325336 3332811 3332883 "UPXSCONS" 3332888 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1283 3314094 3321538 3321600 "UPXSCCA" 3322174 NIL UPXSCCA (NIL T T) -9 NIL 3322407 NIL) (-1282 3313714 3313817 3313991 "UPXSCCA-" 3313996 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1281 3302372 3309541 3309584 "UPXSCAT" 3310232 NIL UPXSCAT (NIL T) -9 NIL 3310841 NIL) (-1280 3301796 3301881 3302060 "UPXS2" 3302287 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1279 3293288 3301178 3301442 "UPXS" 3301590 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1278 3291924 3292195 3292546 "UPSQFREE" 3293031 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1277 3284755 3288190 3288245 "UPSCAT" 3289325 NIL UPSCAT (NIL T T) -9 NIL 3290091 NIL) (-1276 3283911 3284166 3284493 "UPSCAT-" 3284498 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1275 3283532 3283581 3283714 "UPOLYC2" 3283862 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1274 3267680 3276659 3276702 "UPOLYC" 3278803 NIL UPOLYC (NIL T) -9 NIL 3280024 NIL) (-1273 3258549 3261448 3264588 "UPOLYC-" 3264593 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1272 3257870 3257995 3258159 "UPMP" 3258438 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1271 3257417 3257504 3257643 "UPDIVP" 3257783 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1270 3255955 3256234 3256550 "UPDECOMP" 3257166 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1269 3255168 3255298 3255484 "UPCDEN" 3255839 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1268 3254681 3254756 3254905 "UP2" 3255093 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1267 3245277 3254364 3254493 "UP" 3254600 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1266 3244482 3244619 3244824 "UNISEG2" 3245120 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1265 3242835 3243686 3243963 "UNISEG" 3244240 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1264 3241877 3242075 3242301 "UNIFACT" 3242651 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1263 3228608 3241781 3241853 "ULSCONS" 3241858 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1262 3208425 3221688 3221750 "ULSCCAT" 3222388 NIL ULSCCAT (NIL T T) -9 NIL 3222677 NIL) (-1261 3207421 3207720 3208108 "ULSCCAT-" 3208113 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1260 3195876 3202967 3203010 "ULSCAT" 3203873 NIL ULSCAT (NIL T) -9 NIL 3204604 NIL) (-1259 3195300 3195385 3195564 "ULS2" 3195791 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1258 3177131 3194612 3194854 "ULS" 3195116 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1257 3176050 3176750 3176864 "UINT8" 3176975 T UINT8 (NIL) -8 NIL NIL 3177067) (-1256 3174968 3175668 3175782 "UINT64" 3175893 T UINT64 (NIL) -8 NIL NIL 3175985) (-1255 3173886 3174586 3174700 "UINT32" 3174811 T UINT32 (NIL) -8 NIL NIL 3174903) (-1254 3172804 3173504 3173618 "UINT16" 3173729 T UINT16 (NIL) -8 NIL NIL 3173821) (-1253 3170883 3172050 3172080 "UFD" 3172292 T UFD (NIL) -9 NIL 3172406 NIL) (-1252 3170665 3170723 3170818 "UFD-" 3170823 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1251 3169723 3169930 3170146 "UDVO" 3170471 T UDVO (NIL) -7 NIL NIL NIL) (-1250 3167489 3167948 3168419 "UDPO" 3169287 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1249 3167201 3167444 3167475 "TYPEAST" 3167480 T TYPEAST (NIL) -8 NIL NIL NIL) (-1248 3167134 3167139 3167169 "TYPE" 3167174 T TYPE (NIL) -9 NIL NIL NIL) (-1247 3166087 3166307 3166547 "TWOFACT" 3166928 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1246 3165062 3165496 3165731 "TUPLE" 3165887 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1245 3162699 3163272 3163811 "TUBETOOL" 3164545 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1244 3161505 3161746 3161988 "TUBE" 3162492 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1243 3149640 3154262 3154359 "TSETCAT" 3159628 NIL TSETCAT (NIL T T T T) -9 NIL 3161160 NIL) (-1242 3144108 3145972 3147863 "TSETCAT-" 3147868 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1241 3138294 3143080 3143363 "TS" 3143860 NIL TS (NIL T) -8 NIL NIL NIL) (-1240 3132767 3133780 3134709 "TRMANIP" 3137430 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1239 3132196 3132271 3132434 "TRIMAT" 3132699 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1238 3130008 3130299 3130656 "TRIGMNIP" 3131945 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1237 3129492 3129641 3129671 "TRIGCAT" 3129884 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1236 3129137 3129240 3129381 "TRIGCAT-" 3129386 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1235 3125751 3127995 3128276 "TREE" 3128891 NIL TREE (NIL T) -8 NIL NIL NIL) (-1234 3124857 3125553 3125583 "TRANFUN" 3125618 T TRANFUN (NIL) -9 NIL 3125684 NIL) (-1233 3124076 3124327 3124607 "TRANFUN-" 3124612 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1232 3123874 3123912 3123973 "TOPSP" 3124037 T TOPSP (NIL) -7 NIL NIL NIL) (-1231 3123204 3123337 3123491 "TOOLSIGN" 3123755 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1230 3121718 3122381 3122620 "TEXTFILE" 3122987 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1229 3121493 3121530 3121602 "TEX1" 3121681 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1228 3119297 3119946 3120375 "TEX" 3121086 T TEX (NIL) -8 NIL NIL NIL) (-1227 3118933 3119008 3119098 "TEMUTL" 3119229 T TEMUTL (NIL) -7 NIL NIL NIL) (-1226 3117027 3117367 3117692 "TBCMPPK" 3118656 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1225 3108347 3115113 3115169 "TBAGG" 3115569 NIL TBAGG (NIL T T) -9 NIL 3115780 NIL) (-1224 3103231 3104905 3106659 "TBAGG-" 3106664 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1223 3102597 3102722 3102867 "TANEXP" 3103120 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1222 3102048 3102372 3102462 "TALGOP" 3102542 NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1221 3101442 3101559 3101697 "TABLEAU" 3101945 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1220 3094456 3101299 3101392 "TABLE" 3101397 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1219 3088986 3090284 3091532 "TABLBUMP" 3093242 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1218 3088196 3088355 3088536 "SYSTEM" 3088827 T SYSTEM (NIL) -8 NIL NIL NIL) (-1217 3084601 3085354 3086137 "SYSSOLP" 3087447 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1216 3084363 3084556 3084587 "SYSPTR" 3084592 T SYSPTR (NIL) -8 NIL NIL NIL) (-1215 3083202 3083894 3084020 "SYSNNI" 3084206 NIL SYSNNI (NIL NIL) -8 NIL NIL 3084298) (-1214 3082409 3082964 3083043 "SYSINT" 3083103 NIL SYSINT (NIL NIL) -8 NIL NIL 3083148) (-1213 3078507 3079687 3080397 "SYNTAX" 3081721 T SYNTAX (NIL) -8 NIL NIL NIL) (-1212 3075587 3076267 3076899 "SYMTAB" 3077897 T SYMTAB (NIL) -8 NIL NIL NIL) (-1211 3070686 3071738 3072721 "SYMS" 3074626 T SYMS (NIL) -8 NIL NIL NIL) (-1210 3067592 3070137 3070370 "SYMPOLY" 3070488 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1209 3067097 3067184 3067307 "SYMFUNC" 3067504 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1208 3062895 3064409 3065222 "SYMBOL" 3066306 T SYMBOL (NIL) -8 NIL NIL NIL) (-1207 3056368 3058123 3059843 "SWITCH" 3061197 T SWITCH (NIL) -8 NIL NIL NIL) (-1206 3049129 3055324 3055618 "SUTS" 3056132 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1205 3040621 3048511 3048775 "SUPXS" 3048923 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1204 3039768 3039907 3040124 "SUPFRACF" 3040489 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1203 3039383 3039448 3039561 "SUP2" 3039703 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1202 3029927 3039001 3039127 "SUP" 3039292 NIL SUP (NIL T) -8 NIL NIL NIL) (-1201 3028351 3028649 3029005 "SUMRF" 3029626 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1200 3027674 3027752 3027944 "SUMFS" 3028272 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1199 3009540 3026986 3027228 "SULS" 3027490 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1198 3009088 3009362 3009432 "SUCHTAST" 3009492 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1197 3008329 3008613 3008753 "SUCH" 3008996 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1196 3001968 3003235 3004194 "SUBSPACE" 3007417 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1195 3001388 3001488 3001652 "SUBRESP" 3001856 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1194 2995399 2996681 2997828 "STTFNC" 3000288 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1193 2988593 2990064 2991375 "STTF" 2994135 NIL STTF (NIL T) -7 NIL NIL NIL) (-1192 2979710 2981775 2983569 "STTAYLOR" 2986834 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1191 2972464 2979574 2979657 "STRTBL" 2979662 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1190 2966861 2972173 2972272 "STRING" 2972387 T STRING (NIL) -8 NIL NIL NIL) (-1189 2966365 2966448 2966592 "STREAM3" 2966778 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1188 2965329 2965530 2965765 "STREAM2" 2966178 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1187 2965011 2965069 2965162 "STREAM1" 2965271 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1186 2957125 2962630 2963241 "STREAM" 2964435 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1185 2956117 2956322 2956553 "STINPROD" 2956941 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1184 2955232 2955606 2955754 "STEPAST" 2955991 T STEPAST (NIL) -8 NIL NIL NIL) (-1183 2954728 2954973 2955003 "STEP" 2955097 T STEP (NIL) -9 NIL 2955168 NIL) (-1182 2947784 2954627 2954704 "STBL" 2954709 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1181 2942334 2946947 2946990 "STAGG" 2947143 NIL STAGG (NIL T) -9 NIL 2947232 NIL) (-1180 2939886 2940638 2941510 "STAGG-" 2941515 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1179 2937858 2939656 2939748 "STACK" 2939829 NIL STACK (NIL T) -8 NIL NIL NIL) (-1178 2937175 2937688 2937718 "SRING" 2937723 T SRING (NIL) -9 NIL 2937743 NIL) (-1177 2929182 2935316 2935772 "SREGSET" 2936805 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1176 2921529 2922976 2924489 "SRDCMPK" 2927788 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1175 2913829 2918888 2918918 "SRAGG" 2920221 T SRAGG (NIL) -9 NIL 2920829 NIL) (-1174 2912780 2913101 2913480 "SRAGG-" 2913485 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1173 2906364 2911727 2912148 "SQMATRIX" 2912406 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1172 2899776 2903082 2903809 "SPLTREE" 2905709 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1171 2895601 2896432 2897078 "SPLNODE" 2899202 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1170 2894576 2894881 2894911 "SPFCAT" 2895355 T SPFCAT (NIL) -9 NIL NIL NIL) (-1169 2893271 2893523 2893787 "SPECOUT" 2894334 T SPECOUT (NIL) -7 NIL NIL NIL) (-1168 2883917 2886235 2886265 "SPADXPT" 2890943 T SPADXPT (NIL) -9 NIL 2893109 NIL) (-1167 2883672 2883718 2883787 "SPADPRSR" 2883870 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1166 2881275 2883627 2883658 "SPADAST" 2883663 T SPADAST (NIL) -8 NIL NIL NIL) (-1165 2872876 2874979 2875022 "SPACEC" 2879395 NIL SPACEC (NIL T) -9 NIL 2881211 NIL) (-1164 2870676 2872808 2872857 "SPACE3" 2872862 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1163 2869408 2869599 2869890 "SORTPAK" 2870481 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1162 2867470 2867803 2868215 "SOLVETRA" 2869072 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1161 2866508 2866742 2867003 "SOLVESER" 2867243 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1160 2861740 2862700 2863695 "SOLVERAD" 2865560 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1159 2857465 2858164 2858893 "SOLVEFOR" 2861107 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1158 2851069 2856813 2856910 "SNTSCAT" 2856915 NIL SNTSCAT (NIL T T T T) -9 NIL 2856985 NIL) (-1157 2844620 2849392 2849783 "SMTS" 2850759 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1156 2838342 2844508 2844585 "SMP" 2844590 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1155 2836471 2836802 2837200 "SMITH" 2838039 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1154 2827996 2833050 2833153 "SMATCAT" 2834504 NIL SMATCAT (NIL NIL T T T) -9 NIL 2835054 NIL) (-1153 2824768 2825759 2826937 "SMATCAT-" 2826942 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1152 2822237 2823976 2824019 "SKAGG" 2824280 NIL SKAGG (NIL T) -9 NIL 2824415 NIL) (-1151 2817755 2821720 2821897 "SINT" 2822049 T SINT (NIL) -8 NIL NIL 2822204) (-1150 2817521 2817565 2817631 "SIMPAN" 2817711 T SIMPAN (NIL) -7 NIL NIL NIL) (-1149 2816341 2816580 2816855 "SIGNRF" 2817280 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1148 2815156 2815325 2815609 "SIGNEF" 2816170 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1147 2814396 2814739 2814863 "SIGAST" 2815054 T SIGAST (NIL) -8 NIL NIL NIL) (-1146 2813621 2813931 2814071 "SIG" 2814278 T SIG (NIL) -8 NIL NIL NIL) (-1145 2811273 2811765 2812271 "SHP" 2813162 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1144 2804646 2811174 2811250 "SHDP" 2811255 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1143 2804157 2804397 2804427 "SGROUP" 2804520 T SGROUP (NIL) -9 NIL 2804582 NIL) (-1142 2804009 2804041 2804114 "SGROUP-" 2804119 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1141 2800728 2801498 2802221 "SGCF" 2803308 T SGCF (NIL) -7 NIL NIL NIL) (-1140 2794430 2800174 2800271 "SFRTCAT" 2800276 NIL SFRTCAT (NIL T T T T) -9 NIL 2800315 NIL) (-1139 2787749 2788869 2790005 "SFRGCD" 2793413 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1138 2780767 2781948 2783134 "SFQCMPK" 2786682 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1137 2780369 2780476 2780587 "SFORT" 2780708 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1136 2779295 2780209 2780330 "SEXOF" 2780335 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1135 2774884 2775791 2775886 "SEXCAT" 2778508 NIL SEXCAT (NIL T T T T T) -9 NIL 2779068 NIL) (-1134 2773799 2774765 2774833 "SEX" 2774838 T SEX (NIL) -8 NIL NIL NIL) (-1133 2771921 2772512 2772817 "SETMN" 2773540 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1132 2771451 2771639 2771669 "SETCAT" 2771786 T SETCAT (NIL) -9 NIL 2771871 NIL) (-1131 2771219 2771283 2771382 "SETCAT-" 2771387 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1130 2767322 2769680 2769723 "SETAGG" 2770593 NIL SETAGG (NIL T) -9 NIL 2770933 NIL) (-1129 2766744 2766896 2767133 "SETAGG-" 2767138 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1128 2763553 2766678 2766726 "SET" 2766731 NIL SET (NIL T) -8 NIL NIL NIL) (-1127 2762936 2763249 2763350 "SEQAST" 2763474 T SEQAST (NIL) -8 NIL NIL NIL) (-1126 2762063 2762429 2762490 "SEGXCAT" 2762776 NIL SEGXCAT (NIL T T) -9 NIL 2762896 NIL) (-1125 2760988 2761256 2761299 "SEGCAT" 2761821 NIL SEGCAT (NIL T) -9 NIL 2762042 NIL) (-1124 2760603 2760668 2760781 "SEGBIND2" 2760923 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1123 2759493 2759966 2760174 "SEGBIND" 2760430 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1122 2759012 2759294 2759371 "SEGAST" 2759438 T SEGAST (NIL) -8 NIL NIL NIL) (-1121 2758221 2758357 2758561 "SEG2" 2758856 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1120 2757137 2757887 2758069 "SEG" 2758074 NIL SEG (NIL T) -8 NIL NIL NIL) (-1119 2756370 2757072 2757119 "SDVAR" 2757124 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1118 2747728 2756140 2756270 "SDPOL" 2756275 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1117 2746297 2746587 2746906 "SCPKG" 2747443 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1116 2745419 2745633 2745825 "SCOPE" 2746127 T SCOPE (NIL) -8 NIL NIL NIL) (-1115 2744615 2744773 2744952 "SCACHE" 2745274 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1114 2744199 2744433 2744463 "SASTCAT" 2744468 T SASTCAT (NIL) -9 NIL 2744481 NIL) (-1113 2743602 2744034 2744110 "SAOS" 2744145 T SAOS (NIL) -8 NIL NIL NIL) (-1112 2743161 2743202 2743375 "SAERFFC" 2743561 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1111 2742748 2742789 2742948 "SAEFACT" 2743120 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1110 2735796 2742645 2742725 "SAE" 2742730 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1109 2734099 2734431 2734832 "RURPK" 2735462 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1108 2732676 2733042 2733347 "RULESET" 2733933 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1107 2732246 2732470 2732553 "RULECOLD" 2732628 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1106 2729361 2729999 2730457 "RULE" 2731927 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1105 2729145 2729179 2729250 "RTVALUE" 2729312 T RTVALUE (NIL) -8 NIL NIL NIL) (-1104 2728556 2728862 2728956 "RSTRCAST" 2729073 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1103 2723326 2724199 2725119 "RSETGCD" 2727755 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1102 2711890 2717634 2717731 "RSETCAT" 2721850 NIL RSETCAT (NIL T T T T) -9 NIL 2722947 NIL) (-1101 2709709 2710356 2711180 "RSETCAT-" 2711185 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1100 2702017 2703471 2704991 "RSDCMPK" 2708308 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1099 2699886 2700449 2700523 "RRCC" 2701609 NIL RRCC (NIL T T) -9 NIL 2701953 NIL) (-1098 2699207 2699411 2699690 "RRCC-" 2699695 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1097 2698590 2698903 2699004 "RPTAST" 2699128 T RPTAST (NIL) -8 NIL NIL NIL) (-1096 2670976 2681702 2681769 "RPOLCAT" 2692435 NIL RPOLCAT (NIL T T T) -9 NIL 2695595 NIL) (-1095 2661946 2664814 2667936 "RPOLCAT-" 2667941 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1094 2652399 2660157 2660639 "ROUTINE" 2661486 T ROUTINE (NIL) -8 NIL NIL NIL) (-1093 2648462 2652025 2652165 "ROMAN" 2652281 T ROMAN (NIL) -8 NIL NIL NIL) (-1092 2646574 2647322 2647582 "ROIRC" 2648267 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1091 2642294 2645063 2645093 "RNS" 2645397 T RNS (NIL) -9 NIL 2645671 NIL) (-1090 2640701 2641186 2641720 "RNS-" 2641795 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1089 2639662 2640066 2640268 "RNGBIND" 2640552 NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-1088 2638955 2639459 2639489 "RNG" 2639494 T RNG (NIL) -9 NIL 2639515 NIL) (-1087 2638250 2638728 2638771 "RMODULE" 2638776 NIL RMODULE (NIL T) -9 NIL 2638803 NIL) (-1086 2637074 2637180 2637516 "RMCAT2" 2638151 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1085 2633576 2636420 2636717 "RMATRIX" 2636836 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1084 2626075 2628663 2628778 "RMATCAT" 2632137 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2633119 NIL) (-1083 2625414 2625597 2625904 "RMATCAT-" 2625909 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1082 2624987 2625201 2625244 "RLINSET" 2625306 NIL RLINSET (NIL T) -9 NIL 2625350 NIL) (-1081 2624548 2624629 2624757 "RINTERP" 2624906 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1080 2623472 2624146 2624176 "RING" 2624232 T RING (NIL) -9 NIL 2624324 NIL) (-1079 2623252 2623308 2623405 "RING-" 2623410 NIL RING- (NIL T) -8 NIL NIL NIL) (-1078 2622063 2622330 2622588 "RIDIST" 2623016 T RIDIST (NIL) -7 NIL NIL NIL) (-1077 2612688 2621531 2621737 "RGCHAIN" 2621911 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1076 2611946 2612430 2612471 "RGBCSPC" 2612529 NIL RGBCSPC (NIL T) -9 NIL 2612581 NIL) (-1075 2611012 2611471 2611512 "RGBCMDL" 2611744 NIL RGBCMDL (NIL T) -9 NIL 2611858 NIL) (-1074 2610652 2610721 2610824 "RFFACTOR" 2610943 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1073 2610371 2610412 2610509 "RFFACT" 2610611 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1072 2608422 2608852 2609234 "RFDIST" 2610011 T RFDIST (NIL) -7 NIL NIL NIL) (-1071 2605362 2606030 2606700 "RF" 2607786 NIL RF (NIL T) -7 NIL NIL NIL) (-1070 2604809 2604907 2605070 "RETSOL" 2605264 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1069 2604427 2604525 2604568 "RETRACT" 2604701 NIL RETRACT (NIL T) -9 NIL 2604788 NIL) (-1068 2604270 2604301 2604388 "RETRACT-" 2604393 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1067 2603818 2604092 2604162 "RETAST" 2604222 T RETAST (NIL) -8 NIL NIL NIL) (-1066 2596168 2603471 2603598 "RESULT" 2603713 T RESULT (NIL) -8 NIL NIL NIL) (-1065 2594603 2595437 2595636 "RESRING" 2596071 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1064 2594227 2594288 2594386 "RESLATC" 2594540 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1063 2593926 2593967 2594074 "REPSQ" 2594186 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1062 2593617 2593658 2593769 "REPDB" 2593885 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1061 2587449 2588906 2590129 "REP2" 2592429 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1060 2583752 2584507 2585315 "REP1" 2586676 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1059 2581132 2581754 2582356 "REP" 2583172 T REP (NIL) -7 NIL NIL NIL) (-1058 2573140 2579273 2579729 "REGSET" 2580762 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1057 2571849 2572288 2572538 "REF" 2572925 NIL REF (NIL T) -8 NIL NIL NIL) (-1056 2571214 2571329 2571496 "REDORDER" 2571733 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1055 2566585 2570427 2570654 "RECLOS" 2571042 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1054 2565619 2565818 2566033 "REALSOLV" 2566392 T REALSOLV (NIL) -7 NIL NIL NIL) (-1053 2562066 2562904 2563788 "REAL0Q" 2564784 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1052 2557619 2558655 2559716 "REAL0" 2561047 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1051 2557453 2557506 2557536 "REAL" 2557541 T REAL (NIL) -9 NIL 2557576 NIL) (-1050 2556864 2557170 2557264 "RDUCEAST" 2557381 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1049 2556263 2556341 2556548 "RDIV" 2556786 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1048 2555313 2555505 2555718 "RDIST" 2556085 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1047 2553898 2554197 2554569 "RDETRS" 2555021 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1046 2551692 2552164 2552702 "RDETR" 2553440 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1045 2550311 2550595 2550992 "RDEEFS" 2551408 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1044 2548814 2549126 2549551 "RDEEF" 2549999 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1043 2542293 2545768 2545798 "RCFIELD" 2547093 T RCFIELD (NIL) -9 NIL 2547824 NIL) (-1042 2540249 2540861 2541557 "RCFIELD-" 2541632 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1041 2536301 2538322 2538365 "RCAGG" 2539449 NIL RCAGG (NIL T) -9 NIL 2539914 NIL) (-1040 2535911 2536023 2536186 "RCAGG-" 2536191 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1039 2535228 2535358 2535523 "RATRET" 2535795 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1038 2534769 2534848 2534969 "RATFACT" 2535156 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1037 2534047 2534197 2534349 "RANDSRC" 2534639 T RANDSRC (NIL) -7 NIL NIL NIL) (-1036 2533775 2533825 2533898 "RADUTIL" 2533996 T RADUTIL (NIL) -7 NIL NIL NIL) (-1035 2525920 2532606 2532917 "RADIX" 2533498 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1034 2515535 2525762 2525892 "RADFF" 2525897 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-1033 2515164 2515257 2515287 "RADCAT" 2515447 T RADCAT (NIL) -9 NIL NIL NIL) (-1032 2514934 2514994 2515094 "RADCAT-" 2515099 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-1031 2512845 2514704 2514796 "QUEUE" 2514877 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-1030 2512470 2512519 2512650 "QUATCT2" 2512796 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-1029 2504848 2508893 2508935 "QUATCAT" 2509726 NIL QUATCAT (NIL T) -9 NIL 2510492 NIL) (-1028 2500729 2502024 2503414 "QUATCAT-" 2503510 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-1027 2496575 2500662 2500710 "QUAT" 2500715 NIL QUAT (NIL T) -8 NIL NIL NIL) (-1026 2493831 2495623 2495666 "QUAGG" 2496047 NIL QUAGG (NIL T) -9 NIL 2496222 NIL) (-1025 2493379 2493653 2493723 "QQUTAST" 2493783 T QQUTAST (NIL) -8 NIL NIL NIL) (-1024 2492290 2492892 2493057 "QFORM" 2493260 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-1023 2491915 2491964 2492095 "QFCAT2" 2492241 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-1022 2481612 2487762 2487804 "QFCAT" 2488472 NIL QFCAT (NIL T) -9 NIL 2489473 NIL) (-1021 2476946 2478394 2479981 "QFCAT-" 2480077 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-1020 2476377 2476511 2476643 "QEQUAT" 2476836 T QEQUAT (NIL) -8 NIL NIL NIL) (-1019 2469395 2470576 2471762 "QCMPACK" 2475310 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2468624 2468806 2469042 "QALGSET2" 2469213 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-1017 2466074 2466610 2467040 "QALGSET" 2468279 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-1016 2464741 2464983 2465302 "PWFFINTB" 2465847 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-1015 2462886 2463084 2463440 "PUSHVAR" 2464555 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-1014 2458613 2459829 2459872 "PTRANFN" 2461783 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-1013 2456950 2457295 2457619 "PTPACK" 2458324 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-1012 2456573 2456636 2456747 "PTFUNC2" 2456887 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-1011 2450489 2455362 2455405 "PTCAT" 2455705 NIL PTCAT (NIL T) -9 NIL 2455858 NIL) (-1010 2450138 2450179 2450305 "PSQFR" 2450448 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-1009 2448710 2449026 2449362 "PSEUDLIN" 2449836 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-1008 2435230 2437805 2440131 "PSETPK" 2446470 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-1007 2427938 2430966 2431064 "PSETCAT" 2434105 NIL PSETCAT (NIL T T T T) -9 NIL 2434919 NIL) (-1006 2425663 2426405 2427229 "PSETCAT-" 2427234 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1005 2424976 2425171 2425201 "PSCURVE" 2425473 T PSCURVE (NIL) -9 NIL 2425640 NIL) (-1004 2420699 2422466 2422533 "PSCAT" 2423385 NIL PSCAT (NIL T T T) -9 NIL 2423625 NIL) (-1003 2419693 2419975 2420378 "PSCAT-" 2420383 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-1002 2417892 2418752 2419017 "PRTITION" 2419450 T PRTITION (NIL) -8 NIL NIL NIL) (-1001 2417303 2417609 2417703 "PRTDAST" 2417820 T PRTDAST (NIL) -8 NIL NIL NIL) (-1000 2406147 2408569 2410759 "PRS" 2415165 NIL PRS (NIL T T) -7 NIL NIL NIL) (-999 2403767 2405469 2405509 "PRQAGG" 2405692 NIL PRQAGG (NIL T) -9 NIL 2405794 NIL) (-998 2402946 2403395 2403423 "PROPLOG" 2403562 T PROPLOG (NIL) -9 NIL 2403677 NIL) (-997 2402544 2402607 2402730 "PROPFUN2" 2402869 NIL PROPFUN2 (NIL T T) -8 NIL NIL NIL) (-996 2401841 2401980 2402152 "PROPFUN1" 2402405 NIL PROPFUN1 (NIL T) -8 NIL NIL NIL) (-995 2399822 2400588 2400885 "PROPFRML" 2401577 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-994 2399267 2399398 2399526 "PROPERTY" 2399714 T PROPERTY (NIL) -8 NIL NIL NIL) (-993 2393155 2397433 2398253 "PRODUCT" 2398493 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-992 2392945 2392983 2393042 "PRINT" 2393116 T PRINT (NIL) -7 NIL NIL NIL) (-991 2392261 2392402 2392554 "PRIMES" 2392825 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-990 2390308 2390727 2391193 "PRIMELT" 2391840 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-989 2390025 2390086 2390114 "PRIMCAT" 2390238 T PRIMCAT (NIL) -9 NIL NIL NIL) (-988 2389014 2389210 2389438 "PRIMARR2" 2389843 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-987 2384736 2388952 2388997 "PRIMARR" 2389002 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-986 2384373 2384435 2384546 "PREASSOC" 2384674 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-985 2381338 2383831 2384065 "PR" 2384184 NIL PR (NIL T T) -8 NIL NIL NIL) (-984 2380789 2380946 2380974 "PPCURVE" 2381179 T PPCURVE (NIL) -9 NIL 2381315 NIL) (-983 2380336 2380584 2380667 "PORTNUM" 2380726 T PORTNUM (NIL) -8 NIL NIL NIL) (-982 2377673 2378094 2378686 "POLYROOT" 2379917 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-981 2377050 2377114 2377348 "POLYLIFT" 2377609 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-980 2373271 2373774 2374403 "POLYCATQ" 2376595 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-979 2358919 2365018 2365083 "POLYCAT" 2368597 NIL POLYCAT (NIL T T T) -9 NIL 2370475 NIL) (-978 2352059 2354244 2356621 "POLYCAT-" 2356626 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-977 2351640 2351714 2351834 "POLY2UP" 2351985 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-976 2351266 2351329 2351438 "POLY2" 2351577 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-975 2344481 2350870 2351030 "POLY" 2351139 NIL POLY (NIL T) -8 NIL NIL NIL) (-974 2343142 2343405 2343681 "POLUTIL" 2344255 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-973 2341461 2341774 2342105 "POLTOPOL" 2342864 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-972 2336457 2341395 2341442 "POINT" 2341447 NIL POINT (NIL T) -8 NIL NIL NIL) (-971 2334590 2335001 2335376 "PNTHEORY" 2336102 T PNTHEORY (NIL) -7 NIL NIL NIL) (-970 2333036 2333345 2333744 "PMTOOLS" 2334288 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-969 2332623 2332707 2332824 "PMSYM" 2332952 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-968 2332125 2332200 2332375 "PMQFCAT" 2332548 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-967 2331506 2331604 2331766 "PMPREDFS" 2332026 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-966 2330849 2330971 2331127 "PMPRED" 2331383 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-965 2329503 2329721 2330099 "PMPLCAT" 2330611 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-964 2329029 2329114 2329266 "PMLSAGG" 2329418 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-963 2328496 2328578 2328760 "PMKERNEL" 2328947 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-962 2328107 2328188 2328301 "PMINS" 2328415 NIL PMINS (NIL T) -7 NIL NIL NIL) (-961 2327543 2327618 2327827 "PMFS" 2328032 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-960 2326759 2326889 2327094 "PMDOWN" 2327420 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-959 2326008 2326142 2326305 "PMASSFS" 2326646 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-958 2325151 2325333 2325514 "PMASS" 2325847 T PMASS (NIL) -7 NIL NIL NIL) (-957 2324800 2324874 2324968 "PLOTTOOL" 2325077 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-956 2320452 2321646 2322568 "PLOT3D" 2323898 T PLOT3D (NIL) -8 NIL NIL NIL) (-955 2319340 2319541 2319776 "PLOT1" 2320256 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-954 2313761 2315151 2316299 "PLOT" 2318212 T PLOT (NIL) -8 NIL NIL NIL) (-953 2288936 2293827 2298678 "PLEQN" 2309027 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-952 2288623 2288676 2288779 "PINTERPA" 2288883 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-951 2287929 2288063 2288243 "PINTERP" 2288488 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-950 2286013 2287179 2287207 "PID" 2287404 T PID (NIL) -9 NIL 2287531 NIL) (-949 2285758 2285801 2285876 "PICOERCE" 2285970 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-948 2284854 2285522 2285609 "PI" 2285649 T PI (NIL) -8 NIL NIL 2285716) (-947 2284162 2284313 2284489 "PGROEB" 2284710 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-946 2279601 2280560 2281466 "PGE" 2283276 T PGE (NIL) -7 NIL NIL NIL) (-945 2277682 2277971 2278337 "PGCD" 2279318 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-944 2277008 2277123 2277284 "PFRPAC" 2277566 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-943 2273266 2275556 2275909 "PFR" 2276687 NIL PFR (NIL T) -8 NIL NIL NIL) (-942 2271619 2271899 2272224 "PFOTOOLS" 2273013 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-941 2270134 2270391 2270742 "PFOQ" 2271376 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-940 2268617 2268847 2269203 "PFO" 2269918 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-939 2265701 2267207 2267235 "PFECAT" 2267828 T PFECAT (NIL) -9 NIL 2268205 NIL) (-938 2265149 2265314 2265521 "PFECAT-" 2265526 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-937 2263722 2264004 2264305 "PFBRU" 2264898 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-936 2261551 2261940 2262372 "PFBR" 2263373 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-935 2257497 2261440 2261509 "PF" 2261514 NIL PF (NIL NIL) -8 NIL NIL NIL) (-934 2252551 2253704 2254574 "PERMGRP" 2256660 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-933 2250463 2251575 2251616 "PERMCAT" 2252016 NIL PERMCAT (NIL T) -9 NIL 2252314 NIL) (-932 2250110 2250157 2250281 "PERMAN" 2250416 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-931 2245912 2247619 2248267 "PERM" 2249495 NIL PERM (NIL T) -8 NIL NIL NIL) (-930 2243153 2245577 2245699 "PENDTREE" 2245823 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-929 2242034 2242297 2242338 "PDSPC" 2242871 NIL PDSPC (NIL T) -9 NIL 2243116 NIL) (-928 2241089 2241355 2241717 "PDSPC-" 2241722 NIL PDSPC- (NIL T T) -8 NIL NIL NIL) (-927 2239803 2240739 2240780 "PDRING" 2240785 NIL PDRING (NIL T) -9 NIL 2240813 NIL) (-926 2238546 2239308 2239362 "PDMOD" 2239367 NIL PDMOD (NIL T T) -9 NIL 2239471 NIL) (-925 2235713 2236539 2237207 "PDEPROB" 2237898 T PDEPROB (NIL) -8 NIL NIL NIL) (-924 2233222 2233762 2234317 "PDEPACK" 2235178 T PDEPACK (NIL) -7 NIL NIL NIL) (-923 2232110 2232324 2232575 "PDECOMP" 2233021 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-922 2229627 2230518 2230546 "PDECAT" 2231333 T PDECAT (NIL) -9 NIL 2232046 NIL) (-921 2229244 2229311 2229365 "PDDOM" 2229530 NIL PDDOM (NIL T T) -9 NIL 2229610 NIL) (-920 2229057 2229093 2229200 "PDDOM-" 2229205 NIL PDDOM- (NIL T T T) -8 NIL NIL NIL) (-919 2228802 2228841 2228931 "PCOMP" 2229018 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-918 2226842 2227603 2227900 "PBWLB" 2228531 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-917 2226468 2226531 2226640 "PATTERN2" 2226779 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-916 2224177 2224613 2225070 "PATTERN1" 2226057 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-915 2216356 2218250 2219588 "PATTERN" 2222860 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-914 2215914 2215987 2216119 "PATRES2" 2216283 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-913 2213180 2213863 2214344 "PATRES" 2215479 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-912 2211033 2211468 2211875 "PATMATCH" 2212847 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-911 2210487 2210738 2210779 "PATMAB" 2210886 NIL PATMAB (NIL T) -9 NIL 2210969 NIL) (-910 2208933 2209341 2209599 "PATLRES" 2210292 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-909 2208471 2208602 2208643 "PATAB" 2208648 NIL PATAB (NIL T) -9 NIL 2208820 NIL) (-908 2206611 2207048 2207471 "PARTPERM" 2208068 T PARTPERM (NIL) -7 NIL NIL NIL) (-907 2206220 2206295 2206397 "PARSURF" 2206542 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-906 2205846 2205909 2206018 "PARSU2" 2206157 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-905 2205604 2205650 2205717 "PARSER" 2205799 T PARSER (NIL) -7 NIL NIL NIL) (-904 2205213 2205288 2205390 "PARSCURV" 2205535 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-903 2204839 2204902 2205011 "PARSC2" 2205150 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-902 2204466 2204536 2204633 "PARPCURV" 2204775 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-901 2204092 2204155 2204264 "PARPC2" 2204403 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-900 2203081 2203465 2203647 "PARAMAST" 2203930 T PARAMAST (NIL) -8 NIL NIL NIL) (-899 2202589 2202687 2202806 "PAN2EXPR" 2202982 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-898 2201282 2201710 2201938 "PALETTE" 2202381 T PALETTE (NIL) -8 NIL NIL NIL) (-897 2199627 2200287 2200647 "PAIR" 2200968 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-896 2192560 2198884 2199079 "PADICRC" 2199481 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-895 2184817 2191904 2192089 "PADICRAT" 2192407 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-894 2181614 2183477 2183517 "PADICCT" 2184098 NIL PADICCT (NIL NIL) -9 NIL 2184380 NIL) (-893 2179630 2181551 2181596 "PADIC" 2181601 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-892 2178575 2178787 2179055 "PADEPAC" 2179417 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-891 2177775 2177920 2178126 "PADE" 2178437 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-890 2176008 2176983 2177263 "OWP" 2177579 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-889 2175453 2175714 2175811 "OVERSET" 2175931 T OVERSET (NIL) -8 NIL NIL NIL) (-888 2174373 2175058 2175230 "OVAR" 2175321 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-887 2162609 2165482 2167682 "OUTFORM" 2172193 T OUTFORM (NIL) -8 NIL NIL NIL) (-886 2161891 2162206 2162333 "OUTBFILE" 2162502 T OUTBFILE (NIL) -8 NIL NIL NIL) (-885 2161168 2161363 2161391 "OUTBCON" 2161709 T OUTBCON (NIL) -9 NIL 2161875 NIL) (-884 2160751 2160881 2161038 "OUTBCON-" 2161043 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-883 2159991 2160136 2160297 "OUT" 2160610 T OUT (NIL) -7 NIL NIL NIL) (-882 2159287 2159720 2159809 "OSI" 2159922 T OSI (NIL) -8 NIL NIL NIL) (-881 2158706 2159128 2159156 "OSGROUP" 2159161 T OSGROUP (NIL) -9 NIL 2159183 NIL) (-880 2157417 2157678 2157963 "ORTHPOL" 2158453 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-879 2154668 2157252 2157373 "OREUP" 2157378 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-878 2151771 2154359 2154486 "ORESUP" 2154610 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-877 2149271 2149799 2150360 "OREPCTO" 2151260 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-876 2142649 2145144 2145185 "OREPCAT" 2147533 NIL OREPCAT (NIL T) -9 NIL 2148637 NIL) (-875 2139622 2140578 2141636 "OREPCAT-" 2141641 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-874 2138814 2139092 2139120 "ORDTYPE" 2139429 T ORDTYPE (NIL) -9 NIL 2139592 NIL) (-873 2138115 2138331 2138586 "ORDTYPE-" 2138591 NIL ORDTYPE- (NIL T) -8 NIL NIL NIL) (-872 2137471 2137854 2138012 "ORDSTRCT" 2138017 NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-871 2136969 2137339 2137367 "ORDSET" 2137372 T ORDSET (NIL) -9 NIL 2137394 NIL) (-870 2135327 2136298 2136326 "ORDRING" 2136528 T ORDRING (NIL) -9 NIL 2136653 NIL) (-869 2134948 2135066 2135210 "ORDRING-" 2135215 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-868 2134199 2134764 2134792 "ORDMON" 2134797 T ORDMON (NIL) -9 NIL 2134818 NIL) (-867 2133343 2133508 2133703 "ORDFUNS" 2134048 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-866 2132558 2133073 2133101 "ORDFIN" 2133166 T ORDFIN (NIL) -9 NIL 2133240 NIL) (-865 2131812 2131951 2132137 "ORDCOMP2" 2132418 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-864 2128159 2130398 2130807 "ORDCOMP" 2131436 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-863 2124680 2125650 2126464 "OPTPROB" 2127365 T OPTPROB (NIL) -8 NIL NIL NIL) (-862 2121422 2122121 2122825 "OPTPACK" 2123996 T OPTPACK (NIL) -7 NIL NIL NIL) (-861 2119035 2119861 2119889 "OPTCAT" 2120708 T OPTCAT (NIL) -9 NIL 2121358 NIL) (-860 2118353 2118712 2118817 "OPSIG" 2118950 T OPSIG (NIL) -8 NIL NIL NIL) (-859 2118115 2118160 2118226 "OPQUERY" 2118307 T OPQUERY (NIL) -7 NIL NIL NIL) (-858 2117421 2117701 2117742 "OPERCAT" 2117954 NIL OPERCAT (NIL T) -9 NIL 2118051 NIL) (-857 2117164 2117232 2117349 "OPERCAT-" 2117354 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-856 2114080 2115475 2115979 "OP" 2116693 NIL OP (NIL T) -8 NIL NIL NIL) (-855 2113373 2113500 2113674 "ONECOMP2" 2113952 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-854 2109986 2112170 2112539 "ONECOMP" 2113037 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-853 2109387 2109511 2109641 "OMSERVER" 2109876 T OMSERVER (NIL) -7 NIL NIL NIL) (-852 2105901 2108827 2108867 "OMSAGG" 2108928 NIL OMSAGG (NIL T) -9 NIL 2108992 NIL) (-851 2104476 2104787 2105069 "OMPKG" 2105639 T OMPKG (NIL) -7 NIL NIL NIL) (-850 2102823 2104025 2104194 "OMLO" 2104357 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-849 2101759 2101930 2102150 "OMEXPR" 2102649 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-848 2100844 2101180 2101340 "OMERRK" 2101619 T OMERRK (NIL) -8 NIL NIL NIL) (-847 2100081 2100390 2100526 "OMERR" 2100728 T OMERR (NIL) -8 NIL NIL NIL) (-846 2099472 2099758 2099866 "OMENC" 2099993 T OMENC (NIL) -8 NIL NIL NIL) (-845 2093109 2094552 2095723 "OMDEV" 2098321 T OMDEV (NIL) -8 NIL NIL NIL) (-844 2092142 2092349 2092543 "OMCONN" 2092935 T OMCONN (NIL) -8 NIL NIL NIL) (-843 2091548 2091675 2091703 "OM" 2092002 T OM (NIL) -9 NIL NIL NIL) (-842 2089826 2091018 2091046 "OINTDOM" 2091051 T OINTDOM (NIL) -9 NIL 2091072 NIL) (-841 2086901 2088514 2088851 "OFMONOID" 2089521 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-840 2086135 2086838 2086883 "ODVAR" 2086888 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-839 2083279 2085880 2086035 "ODR" 2086040 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-838 2074691 2083055 2083181 "ODPOL" 2083186 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-837 2068034 2074563 2074668 "ODP" 2074673 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-836 2066776 2067015 2067290 "ODETOOLS" 2067808 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-835 2063719 2064401 2065117 "ODESYS" 2066109 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-834 2058549 2059509 2060534 "ODERTRIC" 2062794 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-833 2057969 2058057 2058251 "ODERED" 2058461 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-832 2054821 2055405 2056082 "ODERAT" 2057392 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-831 2051737 2052245 2052842 "ODEPRRIC" 2054350 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-830 2049632 2050276 2050762 "ODEPROB" 2051271 T ODEPROB (NIL) -8 NIL NIL NIL) (-829 2046098 2046637 2047284 "ODEPRIM" 2049111 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-828 2045341 2045449 2045709 "ODEPAL" 2045990 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-827 2041443 2042294 2043158 "ODEPACK" 2044497 T ODEPACK (NIL) -7 NIL NIL NIL) (-826 2040486 2040611 2040833 "ODEINT" 2041332 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-825 2034551 2036012 2037459 "ODEIFTBL" 2039059 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-824 2029901 2030735 2031687 "ODEEF" 2033710 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-823 2029244 2029339 2029562 "ODECONST" 2029806 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-822 2027307 2028016 2028044 "ODECAT" 2028649 T ODECAT (NIL) -9 NIL 2029180 NIL) (-821 2026939 2026988 2027115 "OCTCT2" 2027258 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-820 2023439 2026644 2026766 "OCT" 2026849 NIL OCT (NIL T) -8 NIL NIL NIL) (-819 2022662 2023232 2023260 "OCAMON" 2023265 T OCAMON (NIL) -9 NIL 2023286 NIL) (-818 2016933 2019705 2019745 "OC" 2020842 NIL OC (NIL T) -9 NIL 2021700 NIL) (-817 2013968 2014908 2015898 "OC-" 2015992 NIL OC- (NIL T T) -8 NIL NIL NIL) (-816 2013388 2013813 2013841 "OASGP" 2013846 T OASGP (NIL) -9 NIL 2013866 NIL) (-815 2012514 2013111 2013139 "OAMONS" 2013179 T OAMONS (NIL) -9 NIL 2013222 NIL) (-814 2011805 2012334 2012362 "OAMON" 2012367 T OAMON (NIL) -9 NIL 2012387 NIL) (-813 2010916 2011554 2011582 "OAGROUP" 2011587 T OAGROUP (NIL) -9 NIL 2011607 NIL) (-812 2010598 2010654 2010743 "NUMTUBE" 2010860 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-811 2004117 2005689 2007225 "NUMQUAD" 2009082 T NUMQUAD (NIL) -7 NIL NIL NIL) (-810 1999797 2000831 2001866 "NUMODE" 2003102 T NUMODE (NIL) -7 NIL NIL NIL) (-809 1997078 1998018 1998046 "NUMINT" 1998969 T NUMINT (NIL) -9 NIL 1999733 NIL) (-808 1995990 1996223 1996441 "NUMFMT" 1996880 T NUMFMT (NIL) -7 NIL NIL NIL) (-807 1982173 1985294 1987826 "NUMERIC" 1993497 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-806 1975877 1981621 1981716 "NTSCAT" 1981721 NIL NTSCAT (NIL T T T T) -9 NIL 1981760 NIL) (-805 1975057 1975236 1975429 "NTPOLFN" 1975716 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-804 1974683 1974746 1974855 "NSUP2" 1974994 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-803 1961465 1971508 1972320 "NSUP" 1973904 NIL NSUP (NIL T) -8 NIL NIL NIL) (-802 1950308 1961239 1961372 "NSMP" 1961377 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-801 1948716 1949041 1949398 "NREP" 1949996 NIL NREP (NIL T) -7 NIL NIL NIL) (-800 1947295 1947559 1947917 "NPCOEF" 1948459 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-799 1946343 1946476 1946692 "NORMRETR" 1947176 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-798 1944354 1944674 1945083 "NORMPK" 1946051 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-797 1944033 1944067 1944191 "NORMMA" 1944320 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-796 1943816 1943851 1943920 "NONE1" 1943997 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-795 1943580 1943773 1943802 "NONE" 1943807 T NONE (NIL) -8 NIL NIL NIL) (-794 1943071 1943139 1943318 "NODE1" 1943512 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-793 1941163 1942194 1942449 "NNI" 1942796 T NNI (NIL) -8 NIL NIL 1943031) (-792 1939559 1939896 1940260 "NLINSOL" 1940831 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-791 1935740 1936795 1937694 "NIPROB" 1938680 T NIPROB (NIL) -8 NIL NIL NIL) (-790 1934479 1934731 1935033 "NFINTBAS" 1935502 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-789 1933563 1934129 1934170 "NETCLT" 1934342 NIL NETCLT (NIL T) -9 NIL 1934424 NIL) (-788 1932235 1932502 1932783 "NCODIV" 1933331 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-787 1931991 1932034 1932109 "NCNTFRAC" 1932192 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-786 1930147 1930535 1930955 "NCEP" 1931616 NIL NCEP (NIL T) -7 NIL NIL NIL) (-785 1928810 1929757 1929785 "NASRING" 1929895 T NASRING (NIL) -9 NIL 1929975 NIL) (-784 1928593 1928649 1928743 "NASRING-" 1928748 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-783 1927560 1928211 1928239 "NARNG" 1928356 T NARNG (NIL) -9 NIL 1928447 NIL) (-782 1927234 1927319 1927453 "NARNG-" 1927458 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-781 1926071 1926320 1926555 "NAGSP" 1927019 T NAGSP (NIL) -7 NIL NIL NIL) (-780 1917115 1919027 1920700 "NAGS" 1924418 T NAGS (NIL) -7 NIL NIL NIL) (-779 1915639 1915971 1916302 "NAGF07" 1916804 T NAGF07 (NIL) -7 NIL NIL NIL) (-778 1910111 1911468 1912775 "NAGF04" 1914352 T NAGF04 (NIL) -7 NIL NIL NIL) (-777 1902983 1904693 1906326 "NAGF02" 1908498 T NAGF02 (NIL) -7 NIL NIL NIL) (-776 1898147 1899307 1900424 "NAGF01" 1901886 T NAGF01 (NIL) -7 NIL NIL NIL) (-775 1891727 1893341 1894926 "NAGE04" 1896582 T NAGE04 (NIL) -7 NIL NIL NIL) (-774 1882788 1885017 1887147 "NAGE02" 1889617 T NAGE02 (NIL) -7 NIL NIL NIL) (-773 1878681 1879688 1880652 "NAGE01" 1881844 T NAGE01 (NIL) -7 NIL NIL NIL) (-772 1876458 1877010 1877568 "NAGD03" 1878143 T NAGD03 (NIL) -7 NIL NIL NIL) (-771 1868154 1870136 1872090 "NAGD02" 1874524 T NAGD02 (NIL) -7 NIL NIL NIL) (-770 1861893 1863390 1864830 "NAGD01" 1866734 T NAGD01 (NIL) -7 NIL NIL NIL) (-769 1858030 1858924 1859761 "NAGC06" 1861076 T NAGC06 (NIL) -7 NIL NIL NIL) (-768 1856477 1856827 1857183 "NAGC05" 1857694 T NAGC05 (NIL) -7 NIL NIL NIL) (-767 1855841 1855972 1856116 "NAGC02" 1856353 T NAGC02 (NIL) -7 NIL NIL NIL) (-766 1854642 1855369 1855409 "NAALG" 1855488 NIL NAALG (NIL T) -9 NIL 1855549 NIL) (-765 1854471 1854506 1854596 "NAALG-" 1854601 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-764 1848343 1849529 1850716 "MULTSQFR" 1853367 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-763 1847650 1847737 1847921 "MULTFACT" 1848255 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-762 1839795 1844233 1844286 "MTSCAT" 1845356 NIL MTSCAT (NIL T T) -9 NIL 1845872 NIL) (-761 1839501 1839561 1839653 "MTHING" 1839735 NIL MTHING (NIL T) -7 NIL NIL NIL) (-760 1839287 1839326 1839386 "MSYSCMD" 1839461 T MSYSCMD (NIL) -7 NIL NIL NIL) (-759 1836032 1838848 1838889 "MSETAGG" 1838894 NIL MSETAGG (NIL T) -9 NIL 1838928 NIL) (-758 1831746 1834787 1835107 "MSET" 1835745 NIL MSET (NIL T) -8 NIL NIL NIL) (-757 1827345 1829125 1829870 "MRING" 1831046 NIL MRING (NIL T T) -8 NIL NIL NIL) (-756 1826905 1826978 1827109 "MRF2" 1827272 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-755 1826517 1826558 1826702 "MRATFAC" 1826864 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-754 1824087 1824424 1824855 "MPRFF" 1826222 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-753 1817421 1823941 1824038 "MPOLY" 1824043 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-752 1816905 1816946 1817154 "MPCPF" 1817380 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-751 1816413 1816462 1816646 "MPC3" 1816856 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-750 1815596 1815689 1815910 "MPC2" 1816328 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-749 1813873 1814234 1814624 "MONOTOOL" 1815256 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-748 1813018 1813401 1813429 "MONOID" 1813648 T MONOID (NIL) -9 NIL 1813795 NIL) (-747 1812534 1812683 1812864 "MONOID-" 1812869 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-746 1801507 1808354 1808413 "MONOGEN" 1809087 NIL MONOGEN (NIL T T) -9 NIL 1809543 NIL) (-745 1798557 1799460 1800460 "MONOGEN-" 1800579 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-744 1797274 1797822 1797850 "MONADWU" 1798242 T MONADWU (NIL) -9 NIL 1798480 NIL) (-743 1796604 1796805 1797053 "MONADWU-" 1797058 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-742 1795889 1796193 1796221 "MONAD" 1796428 T MONAD (NIL) -9 NIL 1796540 NIL) (-741 1795556 1795652 1795784 "MONAD-" 1795789 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-740 1793695 1794469 1794748 "MOEBIUS" 1795309 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-739 1792863 1793363 1793403 "MODULE" 1793408 NIL MODULE (NIL T) -9 NIL 1793447 NIL) (-738 1792401 1792527 1792717 "MODULE-" 1792722 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-737 1789931 1790765 1791092 "MODRING" 1792225 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-736 1786660 1788036 1788557 "MODOP" 1789460 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-735 1785146 1785727 1786004 "MODMONOM" 1786523 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-734 1773907 1783437 1783851 "MODMON" 1784783 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-733 1770740 1772751 1773027 "MODFIELD" 1773782 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-732 1769651 1770021 1770211 "MMLFORM" 1770570 T MMLFORM (NIL) -8 NIL NIL NIL) (-731 1769171 1769220 1769399 "MMAP" 1769602 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-730 1767064 1768003 1768044 "MLO" 1768467 NIL MLO (NIL T) -9 NIL 1768709 NIL) (-729 1764412 1764946 1765548 "MLIFT" 1766545 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-728 1763791 1763887 1764041 "MKUCFUNC" 1764323 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-727 1763384 1763460 1763583 "MKRECORD" 1763714 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-726 1762407 1762593 1762821 "MKFUNC" 1763195 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-725 1761783 1761899 1762055 "MKFLCFN" 1762290 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-724 1761048 1761162 1761347 "MKBCFUNC" 1761676 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-723 1757045 1760602 1760738 "MINT" 1760932 T MINT (NIL) -8 NIL NIL NIL) (-722 1755827 1756100 1756377 "MHROWRED" 1756800 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-721 1750578 1754362 1754767 "MFLOAT" 1755442 T MFLOAT (NIL) -8 NIL NIL NIL) (-720 1749923 1750011 1750182 "MFINFACT" 1750490 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-719 1746202 1747086 1747970 "MESH" 1749059 T MESH (NIL) -7 NIL NIL NIL) (-718 1744556 1744904 1745257 "MDDFACT" 1745889 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-717 1741092 1743687 1743728 "MDAGG" 1743983 NIL MDAGG (NIL T) -9 NIL 1744126 NIL) (-716 1728815 1740385 1740592 "MCMPLX" 1740905 T MCMPLX (NIL) -8 NIL NIL NIL) (-715 1727934 1728098 1728299 "MCDEN" 1728664 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-714 1725782 1726094 1726474 "MCALCFN" 1727664 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-713 1724659 1724947 1725180 "MAYBE" 1725588 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-712 1722217 1722794 1723356 "MATSTOR" 1724130 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-711 1717639 1721589 1721837 "MATRIX" 1722002 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-710 1713339 1714112 1714848 "MATLIN" 1716996 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-709 1711915 1712086 1712419 "MATCAT2" 1713174 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-708 1701254 1704972 1705049 "MATCAT" 1710081 NIL MATCAT (NIL T T T) -9 NIL 1711553 NIL) (-707 1697207 1698517 1699930 "MATCAT-" 1699935 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-706 1695283 1695643 1696027 "MAPPKG3" 1696882 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-705 1694240 1694437 1694659 "MAPPKG2" 1695107 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-704 1692697 1693023 1693350 "MAPPKG1" 1693946 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-703 1691698 1692103 1692280 "MAPPAST" 1692540 T MAPPAST (NIL) -8 NIL NIL NIL) (-702 1691303 1691367 1691490 "MAPHACK3" 1691634 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-701 1690883 1690956 1691070 "MAPHACK2" 1691235 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-700 1690309 1690424 1690566 "MAPHACK1" 1690774 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-699 1688232 1689009 1689313 "MAGMA" 1690037 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-698 1687651 1687956 1688047 "MACROAST" 1688161 T MACROAST (NIL) -8 NIL NIL NIL) (-697 1683894 1685890 1686351 "M3D" 1687223 NIL M3D (NIL T) -8 NIL NIL NIL) (-696 1677366 1682205 1682246 "LZSTAGG" 1683028 NIL LZSTAGG (NIL T) -9 NIL 1683323 NIL) (-695 1673048 1674497 1675954 "LZSTAGG-" 1675959 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-694 1669961 1670939 1671426 "LWORD" 1672593 NIL LWORD (NIL T) -8 NIL NIL NIL) (-693 1669483 1669765 1669840 "LSTAST" 1669906 T LSTAST (NIL) -8 NIL NIL NIL) (-692 1661411 1669254 1669388 "LSQM" 1669393 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-691 1660629 1660774 1661002 "LSPP" 1661266 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-690 1657366 1658082 1658812 "LSMP1" 1659931 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-689 1655148 1655479 1655935 "LSMP" 1657055 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-688 1648276 1654238 1654279 "LSAGG" 1654341 NIL LSAGG (NIL T) -9 NIL 1654419 NIL) (-687 1644785 1645895 1647108 "LSAGG-" 1647113 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-686 1642080 1643929 1644178 "LPOLY" 1644580 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-685 1641656 1641747 1641870 "LPEFRAC" 1641989 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-684 1641339 1641418 1641446 "LOGIC" 1641557 T LOGIC (NIL) -9 NIL 1641639 NIL) (-683 1641195 1641224 1641295 "LOGIC-" 1641300 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-682 1640370 1640528 1640721 "LODOOPS" 1641051 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-681 1638894 1639143 1639496 "LODOF" 1640117 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-680 1634770 1637529 1637570 "LODOCAT" 1638008 NIL LODOCAT (NIL T) -9 NIL 1638219 NIL) (-679 1634485 1634561 1634688 "LODOCAT-" 1634693 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-678 1631471 1634326 1634444 "LODO2" 1634449 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-677 1628578 1631408 1631453 "LODO1" 1631458 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-676 1625673 1628494 1628560 "LODO" 1628565 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-675 1624542 1624719 1625024 "LODEEF" 1625496 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-674 1622719 1623636 1623889 "LO" 1624374 NIL LO (NIL T T T) -8 NIL NIL NIL) (-673 1617691 1620885 1620926 "LNAGG" 1621788 NIL LNAGG (NIL T) -9 NIL 1622223 NIL) (-672 1616784 1617052 1617394 "LNAGG-" 1617399 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-671 1612764 1613709 1614348 "LMOPS" 1616199 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-670 1612063 1612541 1612582 "LMODULE" 1612587 NIL LMODULE (NIL T) -9 NIL 1612613 NIL) (-669 1609018 1611708 1611831 "LMDICT" 1611973 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-668 1608594 1608808 1608849 "LLINSET" 1608910 NIL LLINSET (NIL T) -9 NIL 1608954 NIL) (-667 1608239 1608502 1608562 "LITERAL" 1608567 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-666 1607758 1607838 1607977 "LIST3" 1608159 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-665 1605856 1606204 1606603 "LIST2MAP" 1607405 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-664 1604845 1605041 1605269 "LIST2" 1605674 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-663 1597299 1603779 1604083 "LIST" 1604574 NIL LIST (NIL T) -8 NIL NIL NIL) (-662 1596882 1597118 1597159 "LINSET" 1597164 NIL LINSET (NIL T) -9 NIL 1597198 NIL) (-661 1595696 1596390 1596557 "LINFORM" 1596767 NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-660 1593995 1594723 1594764 "LINEXP" 1595254 NIL LINEXP (NIL T) -9 NIL 1595527 NIL) (-659 1592571 1593475 1593656 "LINELT" 1593866 NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-658 1591128 1591408 1591719 "LINDEP" 1592323 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-657 1590264 1590860 1590970 "LINBASIS" 1591058 NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-656 1587001 1587750 1588527 "LIMITRF" 1589519 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-655 1585286 1585600 1586009 "LIMITPS" 1586696 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-654 1584114 1584689 1584729 "LIECAT" 1584869 NIL LIECAT (NIL T) -9 NIL 1585020 NIL) (-653 1583949 1583982 1584070 "LIECAT-" 1584075 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-652 1577969 1583460 1583688 "LIE" 1583770 NIL LIE (NIL T T) -8 NIL NIL NIL) (-651 1570154 1577509 1577665 "LIB" 1577833 T LIB (NIL) -8 NIL NIL NIL) (-650 1565723 1566672 1567607 "LGROBP" 1569271 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-649 1564347 1565255 1565283 "LFCAT" 1565490 T LFCAT (NIL) -9 NIL 1565629 NIL) (-648 1562285 1562619 1562969 "LF" 1564068 NIL LF (NIL T T) -7 NIL NIL NIL) (-647 1559145 1559817 1560505 "LEXTRIPK" 1561649 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-646 1555733 1556715 1557218 "LEXP" 1558725 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-645 1555149 1555454 1555546 "LETAST" 1555661 T LETAST (NIL) -8 NIL NIL NIL) (-644 1553535 1553860 1554261 "LEADCDET" 1554831 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-643 1552713 1552799 1553028 "LAZM3PK" 1553456 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-642 1547238 1550790 1551328 "LAUPOL" 1552225 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-641 1546811 1546861 1547022 "LAPLACE" 1547188 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-640 1545659 1546375 1546416 "LALG" 1546478 NIL LALG (NIL T) -9 NIL 1546537 NIL) (-639 1545355 1545432 1545568 "LALG-" 1545573 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-638 1543092 1544456 1544707 "LA" 1545188 NIL LA (NIL T T T) -8 NIL NIL NIL) (-637 1542921 1542951 1542992 "KVTFROM" 1543054 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-636 1541678 1542288 1542473 "KTVLOGIC" 1542756 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-635 1541507 1541537 1541578 "KRCFROM" 1541640 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-634 1540399 1540598 1540897 "KOVACIC" 1541307 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-633 1540228 1540258 1540299 "KONVERT" 1540361 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-632 1540057 1540087 1540128 "KOERCE" 1540190 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-631 1539541 1539634 1539766 "KERNEL2" 1539971 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-630 1537228 1538134 1538511 "KERNEL" 1539197 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-629 1530699 1535705 1535759 "KDAGG" 1536136 NIL KDAGG (NIL T T) -9 NIL 1536342 NIL) (-628 1530210 1530352 1530557 "KDAGG-" 1530562 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-627 1522910 1529871 1530026 "KAFILE" 1530088 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-626 1522514 1522799 1522862 "JVMOP" 1522867 T JVMOP (NIL) -8 NIL NIL NIL) (-625 1521250 1521754 1522003 "JVMMDACC" 1522285 T JVMMDACC (NIL) -8 NIL NIL NIL) (-624 1520186 1520640 1520845 "JVMFDACC" 1521065 T JVMFDACC (NIL) -8 NIL NIL NIL) (-623 1518767 1519262 1519562 "JVMCSTTG" 1519906 T JVMCSTTG (NIL) -8 NIL NIL NIL) (-622 1517903 1518307 1518468 "JVMCFACC" 1518626 T JVMCFACC (NIL) -8 NIL NIL NIL) (-621 1517581 1517820 1517869 "JVMBCODE" 1517874 T JVMBCODE (NIL) -8 NIL NIL NIL) (-620 1511600 1517092 1517320 "JORDAN" 1517402 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-619 1510913 1511249 1511370 "JOINAST" 1511499 T JOINAST (NIL) -8 NIL NIL NIL) (-618 1506948 1509090 1509144 "IXAGG" 1510073 NIL IXAGG (NIL T T) -9 NIL 1510532 NIL) (-617 1505801 1506173 1506592 "IXAGG-" 1506597 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-616 1500890 1505723 1505782 "IVECTOR" 1505787 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-615 1499615 1499893 1500159 "ITUPLE" 1500657 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-614 1498087 1498294 1498589 "ITRIGMNP" 1499437 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-613 1496814 1497036 1497319 "ITFUN3" 1497863 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-612 1496412 1496475 1496598 "ITFUN2" 1496737 NIL ITFUN2 (NIL T T) -8 NIL NIL NIL) (-611 1495517 1495892 1496066 "ITFORM" 1496258 T ITFORM (NIL) -8 NIL NIL NIL) (-610 1493286 1494537 1494815 "ITAYLOR" 1495272 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-609 1481690 1487423 1488586 "ISUPS" 1492156 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-608 1480782 1480934 1481170 "ISUMP" 1481537 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-607 1475632 1480727 1480768 "ISTRING" 1480773 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-606 1475048 1475353 1475445 "ISAST" 1475560 T ISAST (NIL) -8 NIL NIL NIL) (-605 1474245 1474339 1474555 "IRURPK" 1474962 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-604 1473157 1473382 1473622 "IRSN" 1474025 T IRSN (NIL) -7 NIL NIL NIL) (-603 1471202 1471583 1472012 "IRRF2F" 1472795 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-602 1470943 1470987 1471063 "IRREDFFX" 1471158 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-601 1469516 1469817 1470116 "IROOT" 1470676 NIL IROOT (NIL T) -7 NIL NIL NIL) (-600 1468655 1469009 1469160 "IRFORM" 1469385 T IRFORM (NIL) -8 NIL NIL NIL) (-599 1467737 1467868 1468082 "IR2F" 1468538 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-598 1465326 1465845 1466411 "IR2" 1467215 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-597 1461766 1463010 1463702 "IR" 1464666 NIL IR (NIL T) -8 NIL NIL NIL) (-596 1461551 1461591 1461651 "IPRNTPK" 1461726 T IPRNTPK (NIL) -7 NIL NIL NIL) (-595 1457525 1461440 1461509 "IPF" 1461514 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-594 1455553 1457450 1457507 "IPADIC" 1457512 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-593 1454811 1455113 1455243 "IP4ADDR" 1455443 T IP4ADDR (NIL) -8 NIL NIL NIL) (-592 1454149 1454440 1454572 "IOMODE" 1454699 T IOMODE (NIL) -8 NIL NIL NIL) (-591 1453120 1453746 1453873 "IOBFILE" 1454042 T IOBFILE (NIL) -8 NIL NIL NIL) (-590 1452530 1453024 1453052 "IOBCON" 1453057 T IOBCON (NIL) -9 NIL 1453078 NIL) (-589 1452035 1452099 1452282 "INVLAPLA" 1452466 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-588 1441605 1444037 1446423 "INTTR" 1449699 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-587 1437898 1438682 1439547 "INTTOOLS" 1440790 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-586 1437478 1437575 1437692 "INTSLPE" 1437801 T INTSLPE (NIL) -7 NIL NIL NIL) (-585 1434945 1437401 1437460 "INTRVL" 1437465 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-584 1432523 1433059 1433634 "INTRF" 1434430 NIL INTRF (NIL T) -7 NIL NIL NIL) (-583 1431916 1432031 1432173 "INTRET" 1432421 NIL INTRET (NIL T) -7 NIL NIL NIL) (-582 1429889 1430302 1430772 "INTRAT" 1431524 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-581 1427134 1427735 1428354 "INTPM" 1429374 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-580 1423851 1424478 1425216 "INTPAF" 1426520 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-579 1418952 1419992 1421043 "INTPACK" 1422820 T INTPACK (NIL) -7 NIL NIL NIL) (-578 1418198 1418356 1418564 "INTHERTR" 1418794 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-577 1417631 1417717 1417905 "INTHERAL" 1418112 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-576 1415399 1415920 1416377 "INTHEORY" 1417194 T INTHEORY (NIL) -7 NIL NIL NIL) (-575 1406731 1408426 1410198 "INTG0" 1413751 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-574 1387256 1392094 1396904 "INTFTBL" 1401941 T INTFTBL (NIL) -8 NIL NIL NIL) (-573 1386481 1386643 1386816 "INTFACT" 1387115 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-572 1383878 1384354 1384911 "INTEF" 1386035 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-571 1382075 1382970 1382998 "INTDOM" 1383299 T INTDOM (NIL) -9 NIL 1383506 NIL) (-570 1381414 1381618 1381860 "INTDOM-" 1381865 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-569 1377282 1379703 1379757 "INTCAT" 1380556 NIL INTCAT (NIL T) -9 NIL 1380877 NIL) (-568 1376736 1376857 1376985 "INTBIT" 1377174 T INTBIT (NIL) -7 NIL NIL NIL) (-567 1375417 1375589 1375896 "INTALG" 1376581 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-566 1374894 1374990 1375147 "INTAF" 1375321 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-565 1367861 1374704 1374844 "INTABL" 1374849 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-564 1367102 1367664 1367729 "INT8" 1367763 T INT8 (NIL) -8 NIL NIL 1367808) (-563 1366342 1366904 1366969 "INT64" 1367003 T INT64 (NIL) -8 NIL NIL 1367048) (-562 1365582 1366144 1366209 "INT32" 1366243 T INT32 (NIL) -8 NIL NIL 1366288) (-561 1364822 1365384 1365449 "INT16" 1365483 T INT16 (NIL) -8 NIL NIL 1365528) (-560 1361024 1364619 1364728 "INT" 1364733 T INT (NIL) -8 NIL NIL NIL) (-559 1355133 1358572 1358600 "INS" 1359534 T INS (NIL) -9 NIL 1360199 NIL) (-558 1352208 1353158 1354125 "INS-" 1354198 NIL INS- (NIL T) -8 NIL NIL NIL) (-557 1350965 1351210 1351508 "INPSIGN" 1351961 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-556 1350059 1350200 1350397 "INPRODPF" 1350845 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-555 1348929 1349070 1349307 "INPRODFF" 1349939 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-554 1347917 1348081 1348341 "INNMFACT" 1348765 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-553 1347096 1347211 1347399 "INMODGCD" 1347816 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-552 1345580 1345849 1346173 "INFSP" 1346841 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-551 1344740 1344881 1345064 "INFPROD0" 1345460 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-550 1344338 1344410 1344508 "INFORM1" 1344675 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-549 1340905 1342403 1342918 "INFORM" 1343831 T INFORM (NIL) -8 NIL NIL NIL) (-548 1340410 1340517 1340631 "INFINITY" 1340811 T INFINITY (NIL) -7 NIL NIL NIL) (-547 1339484 1340130 1340231 "INETCLTS" 1340329 T INETCLTS (NIL) -8 NIL NIL NIL) (-546 1338082 1338350 1338671 "INEP" 1339232 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-545 1337143 1337979 1338044 "INDE" 1338049 NIL INDE (NIL T) -8 NIL NIL NIL) (-544 1336695 1336775 1336892 "INCRMAPS" 1337070 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-543 1335417 1335964 1336170 "INBFILE" 1336509 T INBFILE (NIL) -8 NIL NIL NIL) (-542 1330596 1331653 1332597 "INBFF" 1334505 NIL INBFF (NIL T) -7 NIL NIL NIL) (-541 1329450 1329773 1329801 "INBCON" 1330314 T INBCON (NIL) -9 NIL 1330580 NIL) (-540 1328660 1328925 1329201 "INBCON-" 1329206 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-539 1328079 1328384 1328475 "INAST" 1328589 T INAST (NIL) -8 NIL NIL NIL) (-538 1327446 1327758 1327864 "IMPTAST" 1327993 T IMPTAST (NIL) -8 NIL NIL NIL) (-537 1323367 1327290 1327394 "IMATRIX" 1327399 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-536 1322059 1322198 1322514 "IMATQF" 1323223 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-535 1320239 1320506 1320843 "IMATLIN" 1321815 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-534 1314154 1320163 1320221 "ILIST" 1320226 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-533 1311820 1314014 1314127 "IIARRAY2" 1314132 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-532 1306641 1311731 1311795 "IFF" 1311800 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-531 1305922 1306258 1306374 "IFAST" 1306545 T IFAST (NIL) -8 NIL NIL NIL) (-530 1300434 1305214 1305402 "IFARRAY" 1305779 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-529 1299472 1300338 1300411 "IFAMON" 1300416 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-528 1299044 1299121 1299175 "IEVALAB" 1299382 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-527 1298707 1298787 1298947 "IEVALAB-" 1298952 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-526 1297771 1298596 1298671 "IDPOAMS" 1298676 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-525 1296904 1297660 1297735 "IDPOAM" 1297740 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-524 1296285 1296819 1296881 "IDPO" 1296886 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-523 1294765 1295292 1295344 "IDPC" 1295856 NIL IDPC (NIL T T) -9 NIL 1296137 NIL) (-522 1294097 1294657 1294730 "IDPAM" 1294735 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-521 1293312 1293989 1294062 "IDPAG" 1294067 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-520 1292856 1293118 1293208 "IDENT" 1293242 T IDENT (NIL) -8 NIL NIL NIL) (-519 1289075 1289959 1290854 "IDECOMP" 1292013 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-518 1281710 1282998 1284045 "IDEAL" 1288111 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-517 1280852 1280982 1281182 "ICDEN" 1281594 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-516 1279827 1280332 1280479 "ICARD" 1280725 T ICARD (NIL) -8 NIL NIL NIL) (-515 1277857 1278200 1278605 "IBPTOOLS" 1279504 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-514 1272972 1277477 1277590 "IBITS" 1277776 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-513 1269647 1270271 1270966 "IBATOOL" 1272389 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-512 1267408 1267888 1268421 "IBACHIN" 1269182 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-511 1264998 1267254 1267357 "IARRAY2" 1267362 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-510 1260711 1264924 1264981 "IARRAY1" 1264986 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-509 1253728 1259123 1259604 "IAN" 1260250 T IAN (NIL) -8 NIL NIL NIL) (-508 1253233 1253296 1253469 "IALGFACT" 1253665 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-507 1252725 1252874 1252902 "HYPCAT" 1253109 T HYPCAT (NIL) -9 NIL NIL NIL) (-506 1252227 1252380 1252566 "HYPCAT-" 1252571 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-505 1251774 1252022 1252105 "HOSTNAME" 1252164 T HOSTNAME (NIL) -8 NIL NIL NIL) (-504 1251607 1251656 1251697 "HOMOTOP" 1251702 NIL HOMOTOP (NIL T) -9 NIL 1251735 NIL) (-503 1248040 1249539 1249580 "HOAGG" 1250561 NIL HOAGG (NIL T) -9 NIL 1251290 NIL) (-502 1246556 1247033 1247559 "HOAGG-" 1247564 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-501 1239613 1246149 1246299 "HEXADEC" 1246426 T HEXADEC (NIL) -8 NIL NIL NIL) (-500 1238325 1238583 1238846 "HEUGCD" 1239390 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-499 1237257 1238162 1238292 "HELLFDIV" 1238297 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-498 1235267 1237034 1237122 "HEAP" 1237201 NIL HEAP (NIL T) -8 NIL NIL NIL) (-497 1234464 1234819 1234953 "HEADAST" 1235153 T HEADAST (NIL) -8 NIL NIL NIL) (-496 1227851 1234379 1234441 "HDP" 1234446 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-495 1220870 1227486 1227638 "HDMP" 1227752 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-494 1220176 1220334 1220498 "HB" 1220726 T HB (NIL) -7 NIL NIL NIL) (-493 1213186 1220022 1220126 "HASHTBL" 1220131 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-492 1212602 1212907 1212999 "HASAST" 1213114 T HASAST (NIL) -8 NIL NIL NIL) (-491 1210015 1212224 1212406 "HACKPI" 1212440 T HACKPI (NIL) -8 NIL NIL NIL) (-490 1205187 1209868 1209981 "GTSET" 1209986 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-489 1198226 1205065 1205163 "GSTBL" 1205168 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-488 1189989 1197391 1197647 "GSERIES" 1198026 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-487 1189020 1189533 1189561 "GROUP" 1189764 T GROUP (NIL) -9 NIL 1189898 NIL) (-486 1188344 1188545 1188796 "GROUP-" 1188801 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-485 1186693 1187032 1187419 "GROEBSOL" 1188021 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-484 1185521 1185881 1185932 "GRMOD" 1186461 NIL GRMOD (NIL T T) -9 NIL 1186629 NIL) (-483 1185277 1185325 1185453 "GRMOD-" 1185458 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-482 1180417 1181631 1182631 "GRIMAGE" 1184297 T GRIMAGE (NIL) -8 NIL NIL NIL) (-481 1178811 1179144 1179468 "GRDEF" 1180113 T GRDEF (NIL) -7 NIL NIL NIL) (-480 1178243 1178371 1178512 "GRAY" 1178690 T GRAY (NIL) -7 NIL NIL NIL) (-479 1177320 1177822 1177873 "GRALG" 1178026 NIL GRALG (NIL T T) -9 NIL 1178119 NIL) (-478 1176957 1177054 1177217 "GRALG-" 1177222 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-477 1173438 1176540 1176719 "GPOLSET" 1176863 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-476 1172786 1172849 1173107 "GOSPER" 1173375 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-475 1168356 1169224 1169750 "GMODPOL" 1172485 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-474 1167343 1167545 1167783 "GHENSEL" 1168168 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-473 1161415 1162342 1163362 "GENUPS" 1166427 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-472 1161106 1161163 1161252 "GENUFACT" 1161358 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-471 1160506 1160595 1160760 "GENPGCD" 1161024 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-470 1159974 1160015 1160228 "GENMFACT" 1160465 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-469 1158510 1158797 1159104 "GENEEZ" 1159717 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-468 1151689 1158121 1158283 "GDMP" 1158433 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-467 1140427 1145460 1146566 "GCNAALG" 1150672 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-466 1138554 1139602 1139630 "GCDDOM" 1139885 T GCDDOM (NIL) -9 NIL 1140042 NIL) (-465 1137994 1138151 1138366 "GCDDOM-" 1138371 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-464 1126466 1128940 1131332 "GBINTERN" 1135685 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-463 1124267 1124595 1125016 "GBF" 1126141 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-462 1123024 1123213 1123480 "GBEUCLID" 1124083 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-461 1121674 1121881 1122185 "GB" 1122803 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-460 1121005 1121148 1121297 "GAUSSFAC" 1121545 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-459 1119326 1119674 1119988 "GALUTIL" 1120724 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-458 1117586 1117908 1118232 "GALPOLYU" 1119053 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-457 1114885 1115241 1115648 "GALFACTU" 1117283 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-456 1106499 1108190 1109798 "GALFACT" 1113317 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-455 1103785 1104545 1104573 "FVFUN" 1105729 T FVFUN (NIL) -9 NIL 1106449 NIL) (-454 1103015 1103233 1103261 "FVC" 1103552 T FVC (NIL) -9 NIL 1103735 NIL) (-453 1102616 1102840 1102908 "FUNDESC" 1102967 T FUNDESC (NIL) -8 NIL NIL NIL) (-452 1102189 1102413 1102494 "FUNCTION" 1102568 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-451 1100866 1101490 1101693 "FTEM" 1102006 T FTEM (NIL) -8 NIL NIL NIL) (-450 1098496 1099188 1099654 "FT" 1100420 T FT (NIL) -8 NIL NIL NIL) (-449 1096765 1097076 1097473 "FSUPFACT" 1098187 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-448 1095084 1095451 1095783 "FST" 1096453 T FST (NIL) -8 NIL NIL NIL) (-447 1094265 1094389 1094577 "FSRED" 1094966 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-446 1092954 1093220 1093567 "FSPRMELT" 1093980 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-445 1090164 1090698 1091184 "FSPECF" 1092517 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-444 1089686 1089746 1089916 "FSINT" 1090105 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-443 1087822 1088679 1088982 "FSERIES" 1089465 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-442 1086846 1086980 1087204 "FSCINT" 1087702 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-441 1085870 1086031 1086258 "FSAGG2" 1086699 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-440 1081734 1084814 1084855 "FSAGG" 1085225 NIL FSAGG (NIL T) -9 NIL 1085484 NIL) (-439 1079334 1080097 1080893 "FSAGG-" 1080988 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-438 1076994 1077292 1077840 "FS2UPS" 1079052 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-437 1075860 1076043 1076345 "FS2EXPXP" 1076819 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-436 1075488 1075537 1075666 "FS2" 1075811 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-435 1055726 1065262 1065303 "FS" 1069187 NIL FS (NIL T) -9 NIL 1071476 NIL) (-434 1043787 1047362 1051419 "FS-" 1051719 NIL FS- (NIL T T) -8 NIL NIL NIL) (-433 1043201 1043328 1043480 "FRUTIL" 1043667 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-432 1037712 1040890 1040930 "FRNAALG" 1042250 NIL FRNAALG (NIL T) -9 NIL 1042848 NIL) (-431 1033193 1034461 1035736 "FRNAALG-" 1036486 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-430 1032825 1032874 1033001 "FRNAAF2" 1033144 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-429 1031112 1031674 1031970 "FRMOD" 1032637 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-428 1030297 1030390 1030681 "FRIDEAL2" 1031019 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-427 1027902 1028672 1028990 "FRIDEAL" 1030088 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-426 1026993 1027449 1027490 "FRETRCT" 1027495 NIL FRETRCT (NIL T) -9 NIL 1027671 NIL) (-425 1026051 1026336 1026687 "FRETRCT-" 1026692 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-424 1022872 1024335 1024394 "FRAMALG" 1025276 NIL FRAMALG (NIL T T) -9 NIL 1025568 NIL) (-423 1020910 1021461 1022091 "FRAMALG-" 1022314 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-422 1020540 1020603 1020710 "FRAC2" 1020847 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-421 1013532 1020013 1020290 "FRAC" 1020295 NIL FRAC (NIL T) -8 NIL NIL NIL) (-420 1013162 1013225 1013332 "FR2" 1013469 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-419 1004079 1008657 1010015 "FR" 1011836 NIL FR (NIL T) -8 NIL NIL NIL) (-418 997998 1001458 1001486 "FPS" 1002605 T FPS (NIL) -9 NIL 1003162 NIL) (-417 997423 997556 997720 "FPS-" 997866 NIL FPS- (NIL T) -8 NIL NIL NIL) (-416 994389 996380 996408 "FPC" 996633 T FPC (NIL) -9 NIL 996775 NIL) (-415 994170 994222 994319 "FPC-" 994324 NIL FPC- (NIL T) -8 NIL NIL NIL) (-414 992928 993658 993699 "FPATMAB" 993704 NIL FPATMAB (NIL T) -9 NIL 993856 NIL) (-413 991071 991670 992017 "FPARFRAC" 992644 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-412 986363 986963 987645 "FORTRAN" 990503 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-411 983937 984601 984629 "FORTFN" 985689 T FORTFN (NIL) -9 NIL 986313 NIL) (-410 983689 983751 983779 "FORTCAT" 983838 T FORTCAT (NIL) -9 NIL 983900 NIL) (-409 981375 981905 982444 "FORT" 983170 T FORT (NIL) -7 NIL NIL NIL) (-408 981157 981193 981262 "FORMULA1" 981339 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-407 979161 979773 980163 "FORMULA" 980787 T FORMULA (NIL) -8 NIL NIL NIL) (-406 978678 978736 978909 "FORDER" 979103 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-405 977738 977938 978131 "FOP" 978505 T FOP (NIL) -7 NIL NIL NIL) (-404 976151 977018 977192 "FNLA" 977620 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-403 974770 975281 975309 "FNCAT" 975769 T FNCAT (NIL) -9 NIL 976029 NIL) (-402 974213 974729 974757 "FNAME" 974762 T FNAME (NIL) -8 NIL NIL NIL) (-401 972539 973712 973740 "FMTC" 973745 T FMTC (NIL) -9 NIL 973781 NIL) (-400 971088 972475 972521 "FMONOID" 972526 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-399 967677 969043 969084 "FMONCAT" 970301 NIL FMONCAT (NIL T) -9 NIL 970906 NIL) (-398 964999 965747 965775 "FMFUN" 966919 T FMFUN (NIL) -9 NIL 967627 NIL) (-397 961872 962924 962978 "FMCAT" 964173 NIL FMCAT (NIL T T) -9 NIL 964668 NIL) (-396 961105 961322 961350 "FMC" 961640 T FMC (NIL) -9 NIL 961822 NIL) (-395 959773 960871 960971 "FM1" 961050 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-394 958791 959515 959664 "FM" 959669 NIL FM (NIL T T) -8 NIL NIL NIL) (-393 956529 956981 957475 "FLOATRP" 958342 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-392 953931 954467 955045 "FLOATCP" 955996 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-391 946594 951660 952281 "FLOAT" 953330 T FLOAT (NIL) -8 NIL NIL NIL) (-390 945112 946186 946227 "FLINEXP" 946232 NIL FLINEXP (NIL T) -9 NIL 946325 NIL) (-389 944242 944501 944829 "FLINEXP-" 944834 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-388 943300 943462 943686 "FLASORT" 944094 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-387 940218 941270 941322 "FLALG" 942549 NIL FLALG (NIL T T) -9 NIL 943016 NIL) (-386 939242 939403 939630 "FLAGG2" 940071 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-385 932497 936651 936692 "FLAGG" 937954 NIL FLAGG (NIL T) -9 NIL 938606 NIL) (-384 931151 931562 932052 "FLAGG-" 932057 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-383 927789 928996 929055 "FINRALG" 930183 NIL FINRALG (NIL T T) -9 NIL 930691 NIL) (-382 926913 927178 927517 "FINRALG-" 927522 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-381 926219 926518 926546 "FINITE" 926742 T FINITE (NIL) -9 NIL 926849 NIL) (-380 918170 920749 920789 "FINAALG" 924456 NIL FINAALG (NIL T) -9 NIL 925909 NIL) (-379 913286 914552 915696 "FINAALG-" 917075 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-378 911846 912268 912322 "FILECAT" 913006 NIL FILECAT (NIL T T) -9 NIL 913222 NIL) (-377 911124 911601 911704 "FILE" 911776 NIL FILE (NIL T) -8 NIL NIL NIL) (-376 908527 910354 910382 "FIELD" 910422 T FIELD (NIL) -9 NIL 910502 NIL) (-375 907069 907532 908043 "FIELD-" 908048 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-374 904752 905704 906051 "FGROUP" 906755 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-373 903824 904006 904226 "FGLMICPK" 904584 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-372 899079 903749 903806 "FFX" 903811 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-371 898674 898741 898876 "FFSLPE" 899012 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-370 898172 898214 898423 "FFPOLY2" 898632 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-369 894048 894944 895740 "FFPOLY" 897408 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-368 889317 893967 894030 "FFP" 894035 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-367 883848 888660 888850 "FFNBX" 889171 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-366 878181 882983 883241 "FFNBP" 883702 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-365 872219 877465 877676 "FFNB" 878014 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-364 871039 871249 871564 "FFINTBAS" 872016 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-363 866632 869286 869314 "FFIELDC" 869934 T FFIELDC (NIL) -9 NIL 870310 NIL) (-362 865252 865693 866176 "FFIELDC-" 866181 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-361 864809 864867 864991 "FFHOM" 865194 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-360 862468 862991 863508 "FFF" 864324 NIL FFF (NIL T) -7 NIL NIL NIL) (-359 857503 862210 862311 "FFCGX" 862411 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-358 852542 857235 857342 "FFCGP" 857446 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-357 847142 852269 852377 "FFCG" 852478 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-356 846547 846596 846831 "FFCAT2" 847093 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-355 825229 836279 836365 "FFCAT" 841530 NIL FFCAT (NIL T T T) -9 NIL 842981 NIL) (-354 820240 821474 822788 "FFCAT-" 824018 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-353 815061 820151 820215 "FF" 820220 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-352 803714 808033 809253 "FEXPR" 813913 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-351 802642 803111 803152 "FEVALAB" 803236 NIL FEVALAB (NIL T) -9 NIL 803497 NIL) (-350 801759 802011 802349 "FEVALAB-" 802354 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-349 798621 799506 799621 "FDIVCAT" 801189 NIL FDIVCAT (NIL T T T T) -9 NIL 801626 NIL) (-348 798377 798410 798580 "FDIVCAT-" 798585 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-347 797591 797684 797961 "FDIV2" 798284 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-346 796001 796974 797177 "FDIV" 797490 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-345 794909 795296 795498 "FCTRDATA" 795819 T FCTRDATA (NIL) -8 NIL NIL NIL) (-344 793565 793854 794143 "FCPAK1" 794640 T FCPAK1 (NIL) -7 NIL NIL NIL) (-343 792568 793065 793206 "FCOMP" 793456 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-342 775882 779718 783256 "FC" 789050 T FC (NIL) -8 NIL NIL NIL) (-341 767591 772203 772243 "FAXF" 774045 NIL FAXF (NIL T) -9 NIL 774737 NIL) (-340 764732 765539 766357 "FAXF-" 766822 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-339 759301 764108 764284 "FARRAY" 764589 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-338 753866 756248 756301 "FAMR" 757324 NIL FAMR (NIL T T) -9 NIL 757784 NIL) (-337 752690 753058 753493 "FAMR-" 753498 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-336 751717 752612 752665 "FAMONOID" 752670 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-335 749347 750199 750252 "FAMONC" 751193 NIL FAMONC (NIL T T) -9 NIL 751579 NIL) (-334 747821 749101 749238 "FAGROUP" 749243 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-333 745574 745935 746338 "FACUTIL" 747502 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-332 744661 744858 745080 "FACTFUNC" 745384 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-331 736433 743964 744163 "EXPUPXS" 744517 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-330 733886 734456 735042 "EXPRTUBE" 735867 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-329 730097 730749 731479 "EXPRODE" 733225 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-328 724531 725238 726044 "EXPR2UPS" 729395 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-327 724157 724220 724329 "EXPR2" 724468 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-326 708465 722806 723235 "EXPR" 723761 NIL EXPR (NIL T) -8 NIL NIL NIL) (-325 698803 707616 707907 "EXPEXPAN" 708301 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-324 698223 698527 698618 "EXITAST" 698732 T EXITAST (NIL) -8 NIL NIL NIL) (-323 697987 698180 698209 "EXIT" 698214 T EXIT (NIL) -8 NIL NIL NIL) (-322 697608 697676 697789 "EVALCYC" 697919 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-321 697125 697267 697308 "EVALAB" 697478 NIL EVALAB (NIL T) -9 NIL 697582 NIL) (-320 696582 696728 696949 "EVALAB-" 696954 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-319 693697 695238 695266 "EUCDOM" 695821 T EUCDOM (NIL) -9 NIL 696171 NIL) (-318 692057 692558 693141 "EUCDOM-" 693146 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-317 691683 691746 691855 "ESTOOLS2" 691994 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-316 691428 691476 691556 "ESTOOLS1" 691635 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-315 678745 681726 684476 "ESTOOLS" 688698 T ESTOOLS (NIL) -7 NIL NIL NIL) (-314 678484 678522 678604 "ESCONT1" 678707 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-313 674792 675619 676399 "ESCONT" 677724 T ESCONT (NIL) -7 NIL NIL NIL) (-312 674461 674517 674617 "ES2" 674736 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-311 674085 674149 674258 "ES1" 674397 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-310 667786 669716 669744 "ES" 672512 T ES (NIL) -9 NIL 673922 NIL) (-309 662463 664020 665837 "ES-" 666001 NIL ES- (NIL T) -8 NIL NIL NIL) (-308 661655 661808 661984 "ERROR" 662307 T ERROR (NIL) -7 NIL NIL NIL) (-307 654671 661514 661605 "EQTBL" 661610 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-306 654297 654360 654469 "EQ2" 654608 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-305 646556 649611 651060 "EQ" 652881 NIL -1500 (NIL T) -8 NIL NIL NIL) (-304 641799 642894 643987 "EP" 645495 NIL EP (NIL T) -7 NIL NIL NIL) (-303 640339 640690 640996 "ENV" 641513 T ENV (NIL) -8 NIL NIL NIL) (-302 639299 639973 640001 "ENTIRER" 640006 T ENTIRER (NIL) -9 NIL 640052 NIL) (-301 635718 637481 637842 "EMR" 639107 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-300 634822 635033 635087 "ELTAGG" 635467 NIL ELTAGG (NIL T T) -9 NIL 635678 NIL) (-299 634529 634603 634744 "ELTAGG-" 634749 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-298 634287 634322 634376 "ELTAB" 634460 NIL ELTAB (NIL T T) -9 NIL 634512 NIL) (-297 633389 633559 633758 "ELFUTS" 634138 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-296 633113 633187 633215 "ELEMFUN" 633320 T ELEMFUN (NIL) -9 NIL NIL NIL) (-295 632977 633004 633072 "ELEMFUN-" 633077 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-294 627388 631019 631060 "ELAGG" 632000 NIL ELAGG (NIL T) -9 NIL 632463 NIL) (-293 625565 626107 626770 "ELAGG-" 626775 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-292 624847 625014 625170 "ELABOR" 625429 T ELABOR (NIL) -8 NIL NIL NIL) (-291 623453 623787 624081 "ELABEXPR" 624573 T ELABEXPR (NIL) -8 NIL NIL NIL) (-290 615965 618090 618919 "EFUPXS" 622728 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-289 609091 611214 612025 "EFULS" 615240 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-288 606528 606934 607406 "EFSTRUC" 608723 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-287 595965 597885 599433 "EF" 605043 NIL EF (NIL T T) -7 NIL NIL NIL) (-286 594943 595450 595599 "EAB" 595836 T EAB (NIL) -8 NIL NIL NIL) (-285 594065 594902 594930 "E04UCFA" 594935 T E04UCFA (NIL) -8 NIL NIL NIL) (-284 593187 594024 594052 "E04NAFA" 594057 T E04NAFA (NIL) -8 NIL NIL NIL) (-283 592309 593146 593174 "E04MBFA" 593179 T E04MBFA (NIL) -8 NIL NIL NIL) (-282 591431 592268 592296 "E04JAFA" 592301 T E04JAFA (NIL) -8 NIL NIL NIL) (-281 590555 591390 591418 "E04GCFA" 591423 T E04GCFA (NIL) -8 NIL NIL NIL) (-280 589679 590514 590542 "E04FDFA" 590547 T E04FDFA (NIL) -8 NIL NIL NIL) (-279 588801 589638 589666 "E04DGFA" 589671 T E04DGFA (NIL) -8 NIL NIL NIL) (-278 582878 584326 585690 "E04AGNT" 587457 T E04AGNT (NIL) -7 NIL NIL NIL) (-277 581498 582179 582219 "DVARCAT" 582560 NIL DVARCAT (NIL T) -9 NIL 582723 NIL) (-276 580648 580914 581228 "DVARCAT-" 581233 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-275 572616 580447 580576 "DSMP" 580581 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-274 570967 571758 571799 "DSEXT" 572162 NIL DSEXT (NIL T) -9 NIL 572456 NIL) (-273 569156 569680 570346 "DSEXT-" 570351 NIL DSEXT- (NIL T T) -8 NIL NIL NIL) (-272 568815 568880 568978 "DROPT1" 569091 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-271 563834 565056 566193 "DROPT0" 567698 T DROPT0 (NIL) -7 NIL NIL NIL) (-270 558417 559779 560847 "DROPT" 562786 T DROPT (NIL) -8 NIL NIL NIL) (-269 556726 557087 557473 "DRAWPT" 558051 T DRAWPT (NIL) -7 NIL NIL NIL) (-268 556353 556412 556530 "DRAWHACK" 556667 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-267 555054 555353 555644 "DRAWCX" 556082 T DRAWCX (NIL) -7 NIL NIL NIL) (-266 554563 554638 554789 "DRAWCURV" 554980 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-265 544881 546993 549108 "DRAWCFUN" 552468 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-264 539372 540391 541470 "DRAW" 543855 NIL DRAW (NIL T) -7 NIL NIL NIL) (-263 535843 538037 538078 "DQAGG" 538707 NIL DQAGG (NIL T) -9 NIL 538981 NIL) (-262 522426 530054 530137 "DPOLCAT" 531989 NIL DPOLCAT (NIL T T T T) -9 NIL 532534 NIL) (-261 516945 518611 520569 "DPOLCAT-" 520574 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-260 509802 516806 516904 "DPMO" 516909 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-259 502556 509582 509749 "DPMM" 509754 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-258 502078 502340 502429 "DOMTMPLT" 502487 T DOMTMPLT (NIL) -8 NIL NIL NIL) (-257 501427 501880 501960 "DOMCTOR" 502018 T DOMCTOR (NIL) -8 NIL NIL NIL) (-256 500579 500907 501058 "DOMAIN" 501296 T DOMAIN (NIL) -8 NIL NIL NIL) (-255 493598 500214 500366 "DMP" 500480 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-254 491375 492665 492706 "DMEXT" 492711 NIL DMEXT (NIL T) -9 NIL 492887 NIL) (-253 490969 491031 491175 "DLP" 491313 NIL DLP (NIL T) -7 NIL NIL NIL) (-252 484092 490296 490486 "DLIST" 490811 NIL DLIST (NIL T) -8 NIL NIL NIL) (-251 480630 482917 482958 "DLAGG" 483508 NIL DLAGG (NIL T) -9 NIL 483738 NIL) (-250 479142 479956 479984 "DIVRING" 480076 T DIVRING (NIL) -9 NIL 480159 NIL) (-249 478325 478569 478869 "DIVRING-" 478874 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-248 476367 476784 477190 "DISPLAY" 477939 T DISPLAY (NIL) -7 NIL NIL NIL) (-247 475197 475418 475683 "DIRPROD2" 476160 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-246 468604 475111 475174 "DIRPROD" 475179 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-245 456816 463315 463368 "DIRPCAT" 463626 NIL DIRPCAT (NIL NIL T) -9 NIL 464501 NIL) (-244 454016 454784 455665 "DIRPCAT-" 456002 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-243 453297 453463 453649 "DIOSP" 453850 T DIOSP (NIL) -7 NIL NIL NIL) (-242 449711 452181 452222 "DIOPS" 452656 NIL DIOPS (NIL T) -9 NIL 452885 NIL) (-241 449230 449374 449565 "DIOPS-" 449570 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-240 448137 448909 448937 "DIFRING" 448942 T DIFRING (NIL) -9 NIL 448964 NIL) (-239 447785 447883 447911 "DIFFSPC" 448030 T DIFFSPC (NIL) -9 NIL 448105 NIL) (-238 447406 447508 447660 "DIFFSPC-" 447665 NIL DIFFSPC- (NIL T) -8 NIL NIL NIL) (-237 446342 446940 446981 "DIFFMOD" 446986 NIL DIFFMOD (NIL T) -9 NIL 447084 NIL) (-236 446038 446095 446136 "DIFFDOM" 446257 NIL DIFFDOM (NIL T) -9 NIL 446325 NIL) (-235 445885 445915 445999 "DIFFDOM-" 446004 NIL DIFFDOM- (NIL T T) -8 NIL NIL NIL) (-234 443625 445089 445130 "DIFEXT" 445135 NIL DIFEXT (NIL T) -9 NIL 445288 NIL) (-233 440659 443129 443170 "DIAGG" 443175 NIL DIAGG (NIL T) -9 NIL 443195 NIL) (-232 440007 440200 440452 "DIAGG-" 440457 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-231 434857 438966 439243 "DHMATRIX" 439776 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-230 430325 431378 432388 "DFSFUN" 433867 T DFSFUN (NIL) -7 NIL NIL NIL) (-229 424566 429256 429568 "DFLOAT" 430033 T DFLOAT (NIL) -8 NIL NIL NIL) (-228 422805 423110 423499 "DFINTTLS" 424274 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-227 419624 420826 421226 "DERHAM" 422471 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-226 417160 419399 419488 "DEQUEUE" 419568 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-225 416402 416547 416730 "DEGRED" 417022 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-224 412808 413577 414423 "DEFINTRF" 415630 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-223 410345 410832 411424 "DEFINTEF" 412327 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-222 409629 409965 410080 "DEFAST" 410250 T DEFAST (NIL) -8 NIL NIL NIL) (-221 402686 409222 409372 "DECIMAL" 409499 T DECIMAL (NIL) -8 NIL NIL NIL) (-220 400144 400656 401162 "DDFACT" 402230 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-219 399734 399783 399934 "DBLRESP" 400095 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-218 398935 399504 399595 "DBASIS" 399683 NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-217 396719 397165 397526 "DBASE" 398701 NIL DBASE (NIL T) -8 NIL NIL NIL) (-216 395907 396199 396345 "DATAARY" 396618 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-215 394965 395866 395894 "D03FAFA" 395899 T D03FAFA (NIL) -8 NIL NIL NIL) (-214 394024 394924 394952 "D03EEFA" 394957 T D03EEFA (NIL) -8 NIL NIL NIL) (-213 391950 392440 392929 "D03AGNT" 393555 T D03AGNT (NIL) -7 NIL NIL NIL) (-212 391191 391909 391937 "D02EJFA" 391942 T D02EJFA (NIL) -8 NIL NIL NIL) (-211 390432 391150 391178 "D02CJFA" 391183 T D02CJFA (NIL) -8 NIL NIL NIL) (-210 389673 390391 390419 "D02BHFA" 390424 T D02BHFA (NIL) -8 NIL NIL NIL) (-209 388914 389632 389660 "D02BBFA" 389665 T D02BBFA (NIL) -8 NIL NIL NIL) (-208 382045 383700 385306 "D02AGNT" 387328 T D02AGNT (NIL) -7 NIL NIL NIL) (-207 379795 380336 380882 "D01WGTS" 381519 T D01WGTS (NIL) -7 NIL NIL NIL) (-206 378802 379754 379782 "D01TRNS" 379787 T D01TRNS (NIL) -8 NIL NIL NIL) (-205 377810 378761 378789 "D01GBFA" 378794 T D01GBFA (NIL) -8 NIL NIL NIL) (-204 376818 377769 377797 "D01FCFA" 377802 T D01FCFA (NIL) -8 NIL NIL NIL) (-203 375826 376777 376805 "D01ASFA" 376810 T D01ASFA (NIL) -8 NIL NIL NIL) (-202 374834 375785 375813 "D01AQFA" 375818 T D01AQFA (NIL) -8 NIL NIL NIL) (-201 373842 374793 374821 "D01APFA" 374826 T D01APFA (NIL) -8 NIL NIL NIL) (-200 372850 373801 373829 "D01ANFA" 373834 T D01ANFA (NIL) -8 NIL NIL NIL) (-199 371858 372809 372837 "D01AMFA" 372842 T D01AMFA (NIL) -8 NIL NIL NIL) (-198 370866 371817 371845 "D01ALFA" 371850 T D01ALFA (NIL) -8 NIL NIL NIL) (-197 369874 370825 370853 "D01AKFA" 370858 T D01AKFA (NIL) -8 NIL NIL NIL) (-196 368882 369833 369861 "D01AJFA" 369866 T D01AJFA (NIL) -8 NIL NIL NIL) (-195 362105 363730 365291 "D01AGNT" 367341 T D01AGNT (NIL) -7 NIL NIL NIL) (-194 361424 361570 361722 "CYCLOTOM" 361973 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-193 358079 358872 359599 "CYCLES" 360717 T CYCLES (NIL) -7 NIL NIL NIL) (-192 357379 357525 357696 "CVMP" 357940 NIL CVMP (NIL T) -7 NIL NIL NIL) (-191 355166 355478 355847 "CTRIGMNP" 357107 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-190 354639 354897 354998 "CTORKIND" 355085 T CTORKIND (NIL) -8 NIL NIL NIL) (-189 353844 354232 354260 "CTORCAT" 354442 T CTORCAT (NIL) -9 NIL 354555 NIL) (-188 353418 353553 353712 "CTORCAT-" 353717 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-187 352832 353092 353200 "CTORCALL" 353342 NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-186 352190 352626 352699 "CTOR" 352779 T CTOR (NIL) -8 NIL NIL NIL) (-185 351546 351663 351816 "CSTTOOLS" 352087 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-184 347243 348002 348760 "CRFP" 350858 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-183 346658 346964 347056 "CRCEAST" 347171 T CRCEAST (NIL) -8 NIL NIL NIL) (-182 345681 345890 346118 "CRAPACK" 346462 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-181 345061 345166 345370 "CPMATCH" 345557 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-180 344780 344814 344920 "CPIMA" 345027 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-179 341038 341800 342519 "COORDSYS" 344115 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-178 340426 340571 340713 "CONTOUR" 340916 T CONTOUR (NIL) -8 NIL NIL NIL) (-177 335898 338429 338921 "CONTFRAC" 339966 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-176 335772 335799 335827 "CONDUIT" 335864 T CONDUIT (NIL) -9 NIL NIL NIL) (-175 334726 335400 335428 "COMRING" 335433 T COMRING (NIL) -9 NIL 335485 NIL) (-174 333708 334084 334268 "COMPPROP" 334562 T COMPPROP (NIL) -8 NIL NIL NIL) (-173 333363 333404 333532 "COMPLPAT" 333667 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-172 332993 333056 333163 "COMPLEX2" 333300 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-171 321397 332802 332911 "COMPLEX" 332916 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-170 320718 320857 321017 "COMPILER" 321257 T COMPILER (NIL) -8 NIL NIL NIL) (-169 320430 320471 320569 "COMPFACT" 320677 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-168 301824 314134 314174 "COMPCAT" 315178 NIL COMPCAT (NIL T) -9 NIL 316526 NIL) (-167 290712 294263 297890 "COMPCAT-" 298246 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-166 290435 290469 290572 "COMMUPC" 290678 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-165 290223 290263 290322 "COMMONOP" 290396 T COMMONOP (NIL) -7 NIL NIL NIL) (-164 289745 290027 290102 "COMMAAST" 290168 T COMMAAST (NIL) -8 NIL NIL NIL) (-163 289252 289496 289583 "COMM" 289678 T COMM (NIL) -8 NIL NIL NIL) (-162 288447 288695 288723 "COMBOPC" 289061 T COMBOPC (NIL) -9 NIL 289236 NIL) (-161 287301 287553 287795 "COMBINAT" 288237 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-160 283644 284332 284959 "COMBF" 286723 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-159 282306 282760 282995 "COLOR" 283429 T COLOR (NIL) -8 NIL NIL NIL) (-158 281722 282027 282119 "COLONAST" 282234 T COLONAST (NIL) -8 NIL NIL NIL) (-157 281356 281409 281534 "CMPLXRT" 281669 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-156 280744 281056 281155 "CLLCTAST" 281277 T CLLCTAST (NIL) -8 NIL NIL NIL) (-155 276203 277274 278354 "CLIP" 279684 T CLIP (NIL) -7 NIL NIL NIL) (-154 274376 275304 275544 "CLIF" 276030 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-153 270358 272494 272535 "CLAGG" 273464 NIL CLAGG (NIL T) -9 NIL 274000 NIL) (-152 268702 269237 269820 "CLAGG-" 269825 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-151 268240 268331 268471 "CINTSLPE" 268611 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-150 265705 266212 266760 "CHVAR" 267768 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-149 264745 265419 265447 "CHARZ" 265452 T CHARZ (NIL) -9 NIL 265467 NIL) (-148 264493 264539 264617 "CHARPOL" 264699 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-147 263411 264117 264145 "CHARNZ" 264206 T CHARNZ (NIL) -9 NIL 264255 NIL) (-146 260355 261465 261994 "CHAR" 262902 T CHAR (NIL) -8 NIL NIL NIL) (-145 260063 260142 260170 "CFCAT" 260281 T CFCAT (NIL) -9 NIL NIL NIL) (-144 259286 259415 259598 "CDEN" 259947 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-143 254883 258439 258719 "CCLASS" 259026 T CCLASS (NIL) -8 NIL NIL NIL) (-142 254104 254291 254468 "CATEGORY" 254726 T -10 (NIL) -8 NIL NIL NIL) (-141 253599 254023 254071 "CATCTOR" 254076 T CATCTOR (NIL) -8 NIL NIL NIL) (-140 252990 253302 253400 "CATAST" 253521 T CATAST (NIL) -8 NIL NIL NIL) (-139 252406 252711 252803 "CASEAST" 252918 T CASEAST (NIL) -8 NIL NIL NIL) (-138 251502 251662 251883 "CARTEN2" 252253 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-137 246400 247659 248403 "CARTEN" 250814 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-136 244530 245550 245807 "CARD" 246163 T CARD (NIL) -8 NIL NIL NIL) (-135 244052 244334 244409 "CAPSLAST" 244475 T CAPSLAST (NIL) -8 NIL NIL NIL) (-134 243494 243750 243778 "CACHSET" 243910 T CACHSET (NIL) -9 NIL 243988 NIL) (-133 242884 243272 243300 "CABMON" 243350 T CABMON (NIL) -9 NIL 243406 NIL) (-132 242321 242588 242698 "BYTEORD" 242794 T BYTEORD (NIL) -8 NIL NIL NIL) (-131 237248 241826 241998 "BYTEBUF" 242169 T BYTEBUF (NIL) -8 NIL NIL NIL) (-130 236006 236763 236912 "BYTE" 237075 T BYTE (NIL) -8 NIL NIL 237204) (-129 233268 235698 235805 "BTREE" 235932 NIL BTREE (NIL T) -8 NIL NIL NIL) (-128 230470 232916 233038 "BTOURN" 233178 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-127 227577 229912 229953 "BTCAT" 230021 NIL BTCAT (NIL T) -9 NIL 230098 NIL) (-126 227226 227324 227473 "BTCAT-" 227478 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-125 222115 226472 226500 "BTAGG" 226614 T BTAGG (NIL) -9 NIL 226724 NIL) (-124 221569 221730 221936 "BTAGG-" 221941 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-123 218305 220847 221062 "BSTREE" 221386 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-122 217413 217569 217753 "BRILL" 218161 NIL BRILL (NIL T) -7 NIL NIL NIL) (-121 213808 216111 216152 "BRAGG" 216801 NIL BRAGG (NIL T) -9 NIL 217059 NIL) (-120 212241 212743 213298 "BRAGG-" 213303 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-119 204498 211585 211770 "BPADICRT" 212088 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-118 202514 204435 204480 "BPADIC" 204485 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-117 202206 202242 202356 "BOUNDZRO" 202478 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-116 199933 200391 200866 "BOP1" 201764 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-115 194915 196359 197271 "BOP" 199041 T BOP (NIL) -8 NIL NIL NIL) (-114 193580 194503 194645 "BOOLEAN" 194793 T BOOLEAN (NIL) -8 NIL NIL NIL) (-113 193173 193330 193358 "BOOLE" 193469 T BOOLE (NIL) -9 NIL 193550 NIL) (-112 193041 193068 193134 "BOOLE-" 193139 NIL BOOLE- (NIL T) -8 NIL NIL NIL) (-111 192210 192710 192764 "BMODULE" 192769 NIL BMODULE (NIL T T) -9 NIL 192834 NIL) (-110 187531 192008 192081 "BITS" 192157 T BITS (NIL) -8 NIL NIL NIL) (-109 186928 187071 187211 "BINDING" 187411 T BINDING (NIL) -8 NIL NIL NIL) (-108 179988 186523 186672 "BINARY" 186799 T BINARY (NIL) -8 NIL NIL NIL) (-107 177595 179215 179256 "BGAGG" 179516 NIL BGAGG (NIL T) -9 NIL 179653 NIL) (-106 177420 177458 177549 "BGAGG-" 177554 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 176443 176804 177009 "BFUNCT" 177235 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 175113 175311 175599 "BEZOUT" 176267 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 171311 173965 174295 "BBTREE" 174816 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 170894 170990 171018 "BASTYPE" 171195 T BASTYPE (NIL) -9 NIL 171294 NIL) (-101 170552 170651 170786 "BASTYPE-" 170791 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 169974 170062 170214 "BALFACT" 170463 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 168710 169389 169575 "AUTOMOR" 169819 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 168436 168441 168467 "ATTREG" 168472 T ATTREG (NIL) -9 NIL NIL NIL) (-97 166598 167133 167485 "ATTRBUT" 168102 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 166152 166426 166492 "ATTRAST" 166550 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 165652 165801 165827 "ATRIG" 166028 T ATRIG (NIL) -9 NIL NIL NIL) (-94 165449 165502 165589 "ATRIG-" 165594 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 165032 165266 165292 "ASTCAT" 165297 T ASTCAT (NIL) -9 NIL 165327 NIL) (-92 164741 164818 164937 "ASTCAT-" 164942 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 162715 164517 164605 "ASTACK" 164684 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 161204 161517 161882 "ASSOCEQ" 162397 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 160128 160863 160987 "ASP9" 161111 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 158888 159733 159875 "ASP80" 160017 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-87 158615 158836 158875 "ASP8" 158880 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-86 157461 158292 158410 "ASP78" 158528 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-85 156322 157141 157258 "ASP77" 157375 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-84 155126 155960 156091 "ASP74" 156222 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-83 153918 154761 154893 "ASP73" 155025 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-82 152708 153553 153685 "ASP7" 153817 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-81 151704 152534 152634 "ASP6" 152639 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 150543 151381 151499 "ASP55" 151617 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 149384 150217 150336 "ASP50" 150455 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 148364 149085 149195 "ASP49" 149305 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-77 147040 147903 148071 "ASP42" 148253 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-76 145709 146573 146743 "ASP41" 146927 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 144689 145410 145520 "ASP4" 145630 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-74 143531 144366 144484 "ASP35" 144602 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 143260 143479 143518 "ASP34" 143523 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 142979 143064 143140 "ASP33" 143215 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 141765 142614 142746 "ASP31" 142878 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 141494 141713 141752 "ASP30" 141757 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 141211 141298 141374 "ASP29" 141449 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 140940 141159 141198 "ASP28" 141203 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 140669 140888 140927 "ASP27" 140932 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 139645 140367 140478 "ASP24" 140589 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 138614 139447 139559 "ASP20" 139564 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 137449 138288 138407 "ASP19" 138526 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-63 137168 137253 137329 "ASP12" 137404 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-62 135912 136767 136911 "ASP10" 137055 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-61 134892 135613 135723 "ASP1" 135833 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-60 132504 134736 134827 "ARRAY2" 134832 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 131518 131709 131930 "ARRAY12" 132327 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 126878 131166 131280 "ARRAY1" 131435 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 120923 123080 123155 "ARR2CAT" 125785 NIL ARR2CAT (NIL T T T) -9 NIL 126543 NIL) (-56 118213 119101 120055 "ARR2CAT-" 120060 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 117464 117840 117965 "ARITY" 118106 T ARITY (NIL) -8 NIL NIL NIL) (-54 116222 116392 116691 "APPRULE" 117300 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 115867 115921 116040 "APPLYORE" 116168 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 115121 115268 115425 "ANY1" 115741 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 114421 114714 114834 "ANY" 115019 T ANY (NIL) -8 NIL NIL NIL) (-50 111747 112858 113185 "ANTISYM" 114145 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 111191 111454 111550 "ANON" 111669 T ANON (NIL) -8 NIL NIL NIL) (-48 104354 109730 110184 "AN" 110755 T AN (NIL) -8 NIL NIL NIL) (-47 100017 101626 101677 "AMR" 102425 NIL AMR (NIL T T) -9 NIL 103025 NIL) (-46 99069 99350 99713 "AMR-" 99718 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 82538 98986 99047 "ALIST" 99052 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 78835 82132 82301 "ALGSC" 82456 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 75285 75945 76552 "ALGPKG" 78275 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 74550 74663 74847 "ALGMFACT" 75171 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 70533 71164 71758 "ALGMANIP" 74134 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 59893 70159 70309 "ALGFF" 70466 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 59065 59220 59399 "ALGFACT" 59751 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 57854 58592 58630 "ALGEBRA" 58635 NIL ALGEBRA (NIL T) -9 NIL 58676 NIL) (-37 57554 57631 57763 "ALGEBRA-" 57768 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 38508 55391 55443 "ALAGG" 55579 NIL ALAGG (NIL T T) -9 NIL 55740 NIL) (-35 38008 38157 38183 "AHYP" 38384 T AHYP (NIL) -9 NIL NIL NIL) (-34 36893 37187 37213 "AGG" 37712 T AGG (NIL) -9 NIL 37991 NIL) (-33 36291 36489 36703 "AGG-" 36708 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 34051 34520 34925 "AF" 35933 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 33471 33776 33866 "ADDAST" 33979 T ADDAST (NIL) -8 NIL NIL NIL) (-30 32703 32998 33154 "ACPLOT" 33333 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 20267 29635 29673 "ACFS" 30280 NIL ACFS (NIL T) -9 NIL 30519 NIL) (-28 18174 18784 19546 "ACFS-" 19551 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 13882 16207 16233 "ACF" 17112 T ACF (NIL) -9 NIL 17525 NIL) (-26 12514 12920 13413 "ACF-" 13418 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 12024 12267 12293 "ABELSG" 12385 T ABELSG (NIL) -9 NIL 12450 NIL) (-24 11885 11916 11982 "ABELSG-" 11987 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 11154 11501 11527 "ABELMON" 11697 T ABELMON (NIL) -9 NIL 11809 NIL) (-22 10794 10902 11040 "ABELMON-" 11045 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 10044 10500 10526 "ABELGRP" 10598 T ABELGRP (NIL) -9 NIL 10673 NIL) (-20 9471 9636 9852 "ABELGRP-" 9857 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4579 8733 8772 "A1AGG" 8777 NIL A1AGG (NIL T) -9 NIL 8817 NIL) (-18 30 1497 3059 "A1AGG-" 3064 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 7a639d78..4b97b17e 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,220 +1,187 @@ -(733391 . 3508696572) +(733414 . 3508766237) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-291)))) + ((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-915 *3)) (-4 *3 (-1132)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1318 *3 *4)) (-4 *3 (-871)) (-4 *4 (-1080)) + (-5 *2 (-114)))) + ((*1 *2 *1) + (-12 (-5 *2 (-114)) (-5 *1 (-1322 *3 *4)) (-4 *3 (-1080)) + (-4 *4 (-868))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-171 (-229))) (-5 *5 (-560)) (-5 *6 (-1190)) + (-5 *3 (-229)) (-5 *2 (-1066)) (-5 *1 (-780))))) (((*1 *2 *3 *3) - (-12 (-4 *4 (-571)) - (-5 *2 (-2 (|:| -1400 *4) (|:| -2647 *3) (|:| -3893 *3))) - (-5 *1 (-1000 *4 *3)) (-4 *3 (-1274 *4)))) - ((*1 *2 *1 *1) - (-12 (-4 *3 (-1080)) (-4 *4 (-815)) (-4 *5 (-871)) - (-5 *2 (-2 (|:| -2647 *1) (|:| -3893 *1))) (-4 *1 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|endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1186 (-229))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -2659 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| - "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated")))))))) - (-5 *1 (-574)))) - ((*1 *2 *1) - (-12 (-4 *1 (-618 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-1248)) - (-5 *2 (-663 *4))))) -(((*1 *2 *2) (-12 (-5 *2 (-1202 *3)) (-4 *3 (-363)) (-5 *1 (-369 *3))))) -(((*1 *2 *3 *4) - 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(-1 *5 *5)) (-4 *5 (-376)) + (-4 *1 (-746 *5 *6)) (-4 *5 (-175)) (-4 *6 (-1274 *5)) + (-5 *2 (-711 *5))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-229)) (-5 *4 (-560)) (-5 *2 (-1066)) (-5 *1 (-780))))) +(((*1 *2 *1) + (-12 (-5 *2 (-663 (-2 (|:| |gen| *3) (|:| -1920 (-560))))) + (-5 *1 (-374 *3)) (-4 *3 (-1132)))) + ((*1 *2 *1) + (-12 (-4 *1 (-399 *3)) (-4 *3 (-1132)) + (-5 *2 (-663 (-2 (|:| |gen| *3) (|:| -1920 (-793))))))) + ((*1 *2 *1) + (-12 (-5 *2 (-663 (-2 (|:| -3388 *3) (|:| -3881 (-560))))) + (-5 *1 (-419 *3)) (-4 *3 (-571))))) +(((*1 *2 *2 *2) + (-12 (-5 *2 (-663 *6)) (-4 *6 (-1096 *3 *4 *5)) (-4 *3 (-466)) + (-4 *3 (-571)) (-4 *4 (-815)) (-4 *5 (-871)) + (-5 *1 (-1008 *3 *4 *5 *6))))) (((*1 *2 *1 *2 *3) (-12 (-5 *3 (-663 (-1190))) (-5 *2 (-1190)) (-5 *1 (-1301)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1190)) (-5 *1 (-1301)))) @@ -2523,70 +2391,41 @@ (-12 (-5 *3 (-663 (-1190))) (-5 *2 (-1190)) (-5 *1 (-1302)))) ((*1 *2 *1 *2 *2) (-12 (-5 *2 (-1190)) (-5 *1 (-1302)))) ((*1 *2 *1 *2) (-12 (-5 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|notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-574))))) -(((*1 *2 *3) - (-12 (-5 *3 (-663 *2)) (-4 *2 (-1274 *4)) (-5 *1 (-553 *4 *2 *5 *6)) - (-4 *4 (-319)) (-14 *5 *4) (-14 *6 (-1 *4 *4 (-793)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-618 *2 *3)) (-4 *3 (-1248)) (-4 *2 (-1132)) - (-4 *2 (-871))))) -(((*1 *1) - (|partial| -12 (-4 *1 (-380 *2)) (-4 *2 (-571)) (-4 *2 (-175))))) +(((*1 *2 *1) (-12 (-5 *2 (-1134)) (-5 *1 (-342))))) +(((*1 *2) (-12 (-5 *2 (-1190)) (-5 *1 (-248))))) (((*1 *2 *3) (-12 (-5 *3 (-1208)) (-4 *4 (-13 (-466) (-1069 (-560)) (-660 (-560)))) (-5 *2 (-51)) @@ -3895,42 +4215,55 @@ ((*1 *1 *2 *3) (-12 (-5 *2 (-421 (-560))) (-4 *4 (-1080)) (-4 *1 (-1283 *4 *3)) (-4 *3 (-1260 *4))))) -(((*1 *2 *2) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4510)) (-4 *1 (-251 *2)) (-4 *2 (-1248))))) +(((*1 *2 *3 *4 *5 *5 *6) + (-12 (-5 *4 (-1208)) (-5 *6 (-114)) + (-4 *7 (-13 (-319) (-149) (-1069 (-560)) (-660 (-560)))) + (-4 *3 (-13 (-1234) (-989) (-29 *7))) + (-5 *2 + (-3 (|:| |f1| (-864 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(-149) (-1069 (-560)) (-660 (-560)))) + (-5 *2 (-2 (|:| -3735 *3) (|:| |coeff| *3))) + (-5 *1 (-572 *7 *3))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2178 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2814 (-663 (-229))))) (-5 *2 (-663 (-1208))) (-5 *1 (-278)))) ((*1 *2 *3) (-12 (-5 *3 (-1202 *7)) (-4 *7 (-979 *6 *4 *5)) (-4 *4 (-815)) @@ -4375,7 +4743,7 @@ (-5 *1 (-980 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-376) - (-10 -8 (-15 -2587 ($ *7)) (-15 -4416 (*7 $)) (-15 -4425 (*7 $))))))) + (-10 -8 (-15 -2539 ($ *7)) (-15 -4420 (*7 $)) (-15 -4429 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-1004 *3 *4 *5)) (-4 *3 (-1080)) (-4 *4 (-814)) (-4 *5 (-871)) (-5 *2 (-663 *5)))) @@ -4385,29 +4753,41 @@ ((*1 *2 *3) (-12 (-5 *3 (-421 (-975 *4))) (-4 *4 (-571)) (-5 *2 (-663 (-1208))) (-5 *1 (-1071 *4))))) -(((*1 *2 *1) (-12 (-5 *2 (-1304)) (-5 *1 (-845))))) +(((*1 *2 *3 *3) + (-12 (-5 *2 (-1186 (-663 (-560)))) (-5 *1 (-908)) + (-5 *3 (-663 (-560))))) + ((*1 *2 *3) + 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(-815)) (-4 *5 (-871)) (-5 *2 (-663 *1)) + (-4 *1 (-979 *3 *4 *5))))) (((*1 *2 *1) (-12 (-4 *1 (-263 *3)) (-4 *3 (-1248)) (-5 *2 (-793)))) ((*1 *2 *1) (-12 (-4 *1 (-310)) (-5 *2 (-793)))) ((*1 *2 *3) @@ -4417,35 +4797,35 @@ ((*1 *2 *1) (-12 (-5 *2 (-793)) (-5 *1 (-630 *3)) (-4 *3 (-1132)))) ((*1 *2) (-12 (-5 *2 (-560)) (-5 *1 (-887)))) ((*1 *2 *1) (-12 (-5 *2 (-560)) (-5 *1 (-887))))) -(((*1 *2 *3 *4 *5 *6 *3 *3 *3 *3 *6 *3 *7 *8) - (-12 (-5 *3 (-560)) (-5 *4 (-711 (-229))) (-5 *5 (-114)) - (-5 *6 (-229)) (-5 *7 (-3 (|:| |fn| (-402)) (|:| |fp| (-68 APROD)))) - (-5 *8 (-3 (|:| |fn| (-402)) (|:| |fp| (-73 MSOLVE)))) - (-5 *2 (-1066)) (-5 *1 (-778))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-1202 *9)) (-5 *4 (-663 *7)) (-5 *5 (-663 (-663 *8))) + (-4 *7 (-871)) (-4 *8 (-319)) (-4 *9 (-979 *8 *6 *7)) (-4 *6 (-815)) + (-5 *2 + (-2 (|:| |upol| (-1202 *8)) (|:| |Lval| (-663 *8)) + (|:| |Lfact| + (-663 (-2 (|:| -3388 (-1202 *8)) (|:| -3881 (-560))))) + (|:| |ctpol| *8))) + (-5 *1 (-764 *6 *7 *8 *9))))) (((*1 *2 *3) (-12 (-5 *2 (-1 *3 *3)) (-5 *1 (-544 *3)) (-4 *3 (-13 (-748) (-25)))))) -(((*1 *2 *1) (-12 (-5 *2 (-1304)) (-5 *1 (-845))))) -(((*1 *2 *2 *3 *3) - (-12 (-5 *2 (-1186 *4)) (-5 *3 (-560)) (-4 *4 (-1080)) - (-5 *1 (-1192 *4)))) - ((*1 *1 *1 *2 *2) - (-12 (-5 *2 (-560)) (-5 *1 (-1288 *3 *4 *5)) (-4 *3 (-1080)) - (-14 *4 (-1208)) (-14 *5 *3)))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1190)) (-5 *4 (-560)) (-5 *5 (-711 (-229))) - (-5 *2 (-1066)) (-5 *1 (-779))))) -(((*1 *2 *2) - (-12 (-4 *3 (-571)) (-4 *4 (-1022 *3)) (-5 *1 (-144 *3 *4 *2)) - (-4 *2 (-385 *4)))) - ((*1 *2 *3) - (-12 (-4 *4 (-571)) (-4 *5 (-1022 *4)) (-4 *2 (-385 *4)) - (-5 *1 (-517 *4 *5 *2 *3)) (-4 *3 (-385 *5)))) - ((*1 *2 *3) - (-12 (-5 *3 (-711 *5)) (-4 *5 (-1022 *4)) (-4 *4 (-571)) - (-5 *2 (-711 *4)) (-5 *1 (-715 *4 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-571)) (-4 *4 (-1022 *3)) (-5 *1 (-1269 *3 *4 *2)) - (-4 *2 (-1274 *4))))) +(((*1 *1 *1) + (-12 (-4 *1 (-1096 *2 *3 *4)) (-4 *2 (-1080)) (-4 *3 (-815)) + (-4 *4 (-871)) (-4 *2 (-466))))) +(((*1 *2 *2 *1) + (-12 (-5 *2 (-1323 *3 *4)) (-4 *1 (-387 *3 *4)) (-4 *3 (-871)) + (-4 *4 (-175)))) + ((*1 *1 *1 *1) (|partial| -12 (-4 *1 (-399 *2)) (-4 *2 (-1132)))) + ((*1 *1 *1 *2) (|partial| -12 (-5 *1 (-841 *2)) (-4 *2 (-871)))) + ((*1 *1 *1 *1) + (-12 (-4 *1 (-1318 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-841 *3)) (-4 *1 (-1318 *3 *4)) (-4 *3 (-871)) + (-4 *4 (-1080)))) + ((*1 *1 *1 *2) + (-12 (-4 *1 (-1318 *2 *3)) (-4 *2 (-871)) (-4 *3 (-1080))))) +(((*1 *2 *2 *2) + (|partial| -12 (-4 *3 (-13 (-571) (-149))) (-5 *1 (-1270 *3 *2)) + (-4 *2 (-1274 *3))))) (((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1202 (-421 (-1202 *2)))) (-5 *4 (-630 *2)) (-4 *2 (-13 (-435 *5) (-27) (-1234))) @@ -4462,112 +4842,46 @@ (-4 *6 (-1080)) (-4 *2 (-13 (-376) - (-10 -8 (-15 -2587 ($ *7)) (-15 -4416 (*7 $)) (-15 -4425 (*7 $))))) + (-10 -8 (-15 -2539 ($ *7)) (-15 -4420 (*7 $)) (-15 -4429 (*7 $))))) (-5 *1 (-980 *5 *4 *6 *7 *2)) (-4 *7 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(-12 (-5 *2 (-1208)) (-5 *3 (-1190)) (-5 *1 (-342)))) - ((*1 *1 *1 *1) (-5 *1 (-887)))) -(((*1 *2 *3 *2) (-12 (-5 *2 (-1190)) (-5 *3 (-560)) (-5 *1 (-248))))) -(((*1 *2 *3 *4 *5 *4 *4 *4) - (-12 (-4 *6 (-871)) (-5 *3 (-663 *6)) (-5 *5 (-663 *3)) - (-5 *2 - (-2 (|:| |f1| *3) (|:| |f2| (-663 *5)) (|:| |f3| *5) - (|:| |f4| (-663 *5)))) - (-5 *1 (-1219 *6)) (-5 *4 (-663 *5))))) + (-12 (-5 *3 (-793)) (-5 *4 (-560)) (-5 *1 (-459 *2)) (-4 *2 (-1080))))) +(((*1 *1 *1 *2 *3) + (-12 (-5 *2 (-663 (-1208))) (-5 *3 (-51)) (-5 *1 (-915 *4)) + (-4 *4 (-1132))))) +(((*1 *2 *3 *4 *4 *2 *2 *2 *2) + (-12 (-5 *2 (-560)) + (-5 *3 + (-2 (|:| |lcmfij| *6) (|:| |totdeg| (-793)) (|:| |poli| *4) + (|:| |polj| *4))) + (-4 *6 (-815)) (-4 *4 (-979 *5 *6 *7)) (-4 *5 (-466)) (-4 *7 (-871)) + (-5 *1 (-464 *5 *6 *7 *4))))) (((*1 *1 *2 *3) (-12 (-4 *1 (-47 *2 *3)) (-4 *2 (-1080)) (-4 *3 (-814)))) ((*1 *1 *2 *3) @@ -4575,10 +4889,10 @@ (-4 *2 (-376)) (-14 *5 (-1024 *4 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-735 *5 *6 *7)) 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*1 (-754 *4 *5 *6 *3)) (-4 *3 (-979 (-421 (-975 *6)) *4 *5)))) ((*1 *2 *3) @@ -5323,34 +5745,53 @@ ((*1 *2 *1) (-12 (-5 *2 (-419 *1)) (-4 *1 (-1253)))) ((*1 *2 *3) (-12 (-5 *2 (-419 *3)) (-5 *1 (-1264 *3)) (-4 *3 (-1274 (-560)))))) -(((*1 *1 *2 *3) (-12 (-5 *3 (-560)) (-5 *1 (-419 *2)) (-4 *2 (-571))))) -(((*1 *1 *1) (-12 (-5 *1 (-305 *2)) (-4 *2 (-21)) (-4 *2 (-1248))))) +(((*1 *2 *3) + (|partial| -12 (-5 *3 (-346 *5 *6 *7 *8)) (-4 *5 (-435 *4)) + (-4 *6 (-1274 *5)) (-4 *7 (-1274 (-421 *6))) + (-4 *8 (-355 *5 *6 *7)) (-4 *4 (-13 (-571) (-1069 (-560)))) + (-5 *2 (-2 (|:| -2252 (-793)) (|:| -2313 *8))) + (-5 *1 (-940 *4 *5 *6 *7 *8)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-346 (-421 (-560)) *4 *5 *6)) + (-4 *4 (-1274 (-421 (-560)))) (-4 *5 (-1274 (-421 *4))) + (-4 *6 (-355 (-421 (-560)) *4 *5)) + (-5 *2 (-2 (|:| -2252 (-793)) (|:| -2313 *6))) + (-5 *1 (-941 *4 *5 *6))))) +(((*1 *2 *3) + (-12 (-5 *2 (-419 (-1202 *1))) (-5 *1 (-326 *4)) (-5 *3 (-1202 *1)) + (-4 *4 (-466)) (-4 *4 (-571)) (-4 *4 (-1132)))) + ((*1 *2 *3) + (-12 (-4 *1 (-939)) (-5 *2 (-419 (-1202 *1))) (-5 *3 (-1202 *1))))) (((*1 *1 *2 *2) (-12 (-5 *2 - (-3 (|:| I (-326 (-560))) (|:| -1633 (-326 (-391))) + (-3 (|:| I (-326 (-560))) (|:| -1610 (-326 (-391))) (|:| CF (-326 (-171 (-391)))) (|:| |switch| (-1207)))) (-5 *1 (-1207))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-663 (-887))) (-5 *1 (-1208))))) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4510)) (-4 *1 (-1041 *2)) (-4 *2 (-1248))))) -(((*1 *1) (-5 *1 (-143))) ((*1 *1 *1) (-5 *1 (-146))) - ((*1 *1 *1) (-4 *1 (-1175)))) -(((*1 *2 *1) - (-12 (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1248)) (-4 *4 (-385 *3)) - (-4 *5 (-385 *3)) (-5 *2 (-663 *3)))) - ((*1 *2 *1) - (-12 (|has| *1 (-6 -4509)) (-4 *1 (-503 *3)) (-4 *3 (-1248)) - (-5 *2 (-663 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-663 (-948))) (-5 *1 (-1002))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *4 (-663 *7)) (-5 *5 (-663 (-663 *8))) (-4 *7 (-871)) - (-4 *8 (-319)) (-4 *6 (-815)) (-4 *9 (-979 *8 *6 *7)) - (-5 *2 - (-2 (|:| |unitPart| *9) - 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-(((*1 *1 *2 *3) - (-12 (-5 *2 (-913 *4 *5)) (-5 *3 (-913 *4 *6)) (-4 *4 (-1132)) - (-4 *5 (-1132)) (-4 *6 (-688 *5)) (-5 *1 (-910 *4 *5 *6))))) -(((*1 *2 *1) (-12 (-5 *2 (-611)) (-5 *1 (-292))))) -(((*1 *1 *1) (-4 *1 (-35))) - ((*1 *2 *2) +(((*1 *2 *3 *4 *5) + (|partial| -12 (-5 *4 (-1208)) (-5 *5 (-663 *3)) + (-4 *3 (-13 (-27) (-1234) (-435 *6))) + (-4 *6 (-13 (-466) (-149) (-1069 (-560)) (-660 (-560)))) + (-5 *2 + (-2 (|:| |mainpart| *3) + (|:| |limitedlogs| + (-663 (-2 (|:| |coeff| *3) (|:| |logand| *3)))))) + (-5 *1 (-572 *6 *3))))) +(((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) ((*1 *2 *2) @@ -7455,33 +8686,50 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-421 (-560)))) (-4 *4 (-1260 *3)) (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1283 *3 *4)) (-4 *5 (-1014 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1208))) + (-14 *3 (-663 (-1208))) (-4 *4 (-401)))) + ((*1 *1 *1) (-4 *1 (-507))) ((*1 *2 *2) (-12 (-5 *2 (-1186 *3)) (-4 *3 (-38 (-421 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(-4 *3 (-1132))))) -(((*1 *2 *3 *4) - (-12 (-5 *3 (-711 (-171 (-421 (-560))))) (-5 *2 (-663 (-171 *4))) - (-5 *1 (-786 *4)) (-4 *4 (-13 (-376) (-870)))))) -(((*1 *2) (-12 (-5 *2 (-1190)) (-5 *1 (-1218))))) -(((*1 *2) (-12 (-5 *2 (-1304)) (-5 *1 (-1208))))) -(((*1 *2 *1) (-12 (-5 *2 (-795)) (-5 *1 (-51))))) -(((*1 *1 *1) (-4 *1 (-35))) - ((*1 *2 *2) + (-12 (-4 *1 (-262 *3 *4 *5 *6)) (-4 *3 (-1080)) (-4 *4 (-871)) + (-4 *5 (-277 *4)) (-4 *6 (-815)) (-5 *2 (-663 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-114)) (-5 *1 (-1213))))) +(((*1 *2 *1) + (-12 (-4 *1 (-335 *3 *4)) (-4 *3 (-1132)) (-4 *4 (-133)) + (-5 *2 (-663 (-2 (|:| |gen| *3) (|:| -1920 *4)))))) + ((*1 *2 *1) + (-12 (-4 *1 (-523 *3 *4)) (-4 *3 (-102)) (-4 *4 (-874)) + (-5 *2 (-663 (-897 *4 *3))))) + ((*1 *2 *1) + (-12 (-5 *2 (-663 (-2 (|:| -1398 *3) (|:| -4002 *4)))) + (-5 *1 (-757 *3 *4)) (-4 *3 (-1080)) (-4 *4 (-748)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1277 *3 *4)) (-4 *3 (-1080)) (-4 *4 (-814)) + (-5 *2 (-1186 (-2 (|:| |k| *4) (|:| |c| *3))))))) +(((*1 *1 *1) + (-12 (|has| *1 (-6 -4510)) (-4 *1 (-1287 *2)) (-4 *2 (-1248))))) +(((*1 *1) (-12 (-4 *1 (-440 *2)) (-4 *2 (-381)) (-4 *2 (-1132))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1190)) (-5 *2 (-1304)) (-5 *1 (-1226 *4 *5)) + (-4 *4 (-1132)) (-4 *5 (-1132))))) +(((*1 *2 *1) + (-12 (-4 *3 (-1132)) (-4 *4 (-13 (-1080) (-911 *3) (-633 (-915 *3)))) + (-5 *2 (-663 (-1208))) (-5 *1 (-1106 *3 *4 *5)) + (-4 *5 (-13 (-435 *4) (-911 *3) (-633 (-915 *3))))))) +(((*1 *2 *2) (-12 (-4 *3 (-571)) (-5 *1 (-287 *3 *2)) (-4 *2 (-13 (-435 *3) (-1033))))) ((*1 *2 *2) @@ -7490,37 +8738,43 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-421 (-560)))) (-4 *4 (-1260 *3)) (-5 *1 (-290 *3 *4 *2 *5)) (-4 *2 (-1283 *3 *4)) (-4 *5 (-1014 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-352 *2 *3 *4)) (-14 *2 (-663 (-1208))) + (-14 *3 (-663 (-1208))) (-4 *4 (-401)))) + ((*1 *1 *1) (-4 *1 (-507))) ((*1 *2 *2) (-12 (-5 *2 (-1186 *3)) (-4 *3 (-38 (-421 (-560)))) (-5 *1 (-1193 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1186 *3)) (-4 *3 (-38 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-10178,14 +10655,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-448)) (-5 *1 (-450)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3400 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342))))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 (-5 *2 (-1298 (-721))) (-4 *1 (-454)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3400 (-663 (-342))))) + (-5 *2 (-2 (|:| |localSymbols| (-1212)) (|:| -3347 (-663 (-342))))) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-342)) (-4 *1 (-455)))) ((*1 *1 *2) (-12 (-5 *2 (-663 (-342))) (-4 *1 (-455)))) @@ -10254,7 +10731,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-663 (-2 (|:| -1400 *3) (|:| -4004 *4)))) + (-12 (-5 *2 (-663 (-2 (|:| -1398 *3) (|:| -4002 *4)))) (-4 *3 (-1080)) (-4 *4 (-748)) (-5 *1 (-757 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-560)) (-4 *1 (-785)))) ((*1 *1 *2) @@ -10263,25 +10740,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) - (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (|:| |mdnia| (-2 (|:| |fn| (-326 (-229))) - (|:| -2659 (-663 (-1120 (-864 (-229))))) + (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-326 (-229))) - (|:| -2659 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) + (|:| -2132 (-663 (-1120 (-864 (-229))))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1208)) (|:| |fn| (-326 (-229))) - (|:| -2659 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) + (|:| -2132 (-1120 (-864 (-229)))) (|:| |abserr| (-229)) (|:| |relerr| (-229)))) (-5 *1 (-791)))) ((*1 *2 *3) (-12 (-5 *2 (-795)) (-5 *1 (-796 *3)) (-4 *3 (-1248)))) @@ -10299,23 +10776,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-326 (-229))) (|:| -2178 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2814 (-663 (-229))) (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-864 (-229)))))) (|:| |lsa| (-2 (|:| |lfn| (-663 (-326 (-229)))) - (|:| -2178 (-663 (-229))))))) + (|:| -2814 (-663 (-229))))))) (-5 *1 (-863)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2178 (-663 (-229))))) + (-2 (|:| |lfn| (-663 (-326 (-229)))) (|:| -2814 (-663 (-229))))) (-5 *1 (-863)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-326 (-229))) (|:| -2178 (-663 (-229))) + (-2 (|:| |fn| (-326 (-229))) (|:| -2814 (-663 (-229))) (|:| |lb| (-663 (-864 (-229)))) (|:| |cf| (-663 (-326 (-229)))) (|:| |ub| (-663 (-864 (-229)))))) (-5 *1 (-863)))) @@ -10416,33 +10893,13 @@ ((*1 *1 *2) (-12 (-5 *2 (-686 *3 *4)) (-4 *3 (-871)) (-4 *4 (-175)) (-5 *1 (-1319 *3 *4))))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-663 *7)) (-4 *7 (-1096 *4 *5 *6)) 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+ (-5 *6 + (-2 (|:| |tryValue| (-391)) (|:| |did| (-391)) (|:| -2168 (-391)))) + (-5 *7 (-1 (-1304) (-1298 *5) (-1298 *5) (-391))) + (-5 *3 (-1298 (-391))) (-5 *5 (-391)) (-5 *2 (-1304)) + (-5 *1 (-810))))) +(((*1 *2 *3) + (-12 (-5 *2 (-114)) (-5 *1 (-39 *3)) (-4 *3 (-1274 (-48)))))) (((*1 *2 *1 *1) (-12 (-4 *1 (-102)) (-5 *2 (-114)))) ((*1 *1 *1 *1) (-5 *1 (-887)))) (((*1 *1 *2 *1) (-12 (-4 *1 (-23)) (-5 *2 (-793)))) @@ -11939,10 +12266,10 @@ ((*1 *1 *2 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1132)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-663 (-1208))) (-4 *4 (-175)) - (-4 *6 (-245 (-2340 *3) (-793))) + (-4 *6 (-245 (-2305 *3) (-793))) (-14 *7 - (-1 (-114) (-2 (|:| -4001 *5) (|:| -2440 *6)) - (-2 (|:| -4001 *5) (|:| -2440 *6)))) + (-1 (-114) (-2 (|:| -3998 *5) (|:| -3881 *6)) + (-2 (|:| -3998 *5) (|:| -3881 *6)))) (-5 *1 (-475 *3 *4 *5 *6 *7 *2)) (-4 *5 (-871)) (-4 *2 (-979 *4 *6 (-888 *3))))) ((*1 *1 *1 *2) @@ -12016,105 +12343,43 @@ (-12 (-4 *1 (-1318 *3 *2)) (-4 *3 (-871)) (-4 *2 (-1080)))) 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