diff options
| -rw-r--r-- | src/ChangeLog | 5 | ||||
| -rw-r--r-- | src/algebra/op.spad.pamphlet | 6 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 640 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1212 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1310 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8896 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 27249 |
7 files changed, 19662 insertions, 19656 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 35b83293..4ebe27a5 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,8 @@ +2009-05-15 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/op.spad.pamphlet (assert$BasicOperator): Overload for + Identifier. + 2009-05-14 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/any.spad.pamphlet (RuntimeValue): New domain. diff --git a/src/algebra/op.spad.pamphlet b/src/algebra/op.spad.pamphlet index b5d9da45..617ea416 100644 --- a/src/algebra/op.spad.pamphlet +++ b/src/algebra/op.spad.pamphlet @@ -91,6 +91,9 @@ BasicOperator(): Exports == Implementation where assert : ($, String) -> $ ++ assert(op, s) attaches property s to op. ++ Argument op is modified "in place", i.e. no copy is made. + assert : (%, Identifier) -> $ + ++ \spad{assert(op, p)} attaches property \spad{p} to \spad{op}. + ++ Argument op is modified "in place", i.e. no copy is made. deleteProperty_!: ($, String) -> $ ++ deleteProperty!(op, s) unattaches property s from op. ++ Argument op is modified "in place", i.e. no copy is made. @@ -135,7 +138,8 @@ BasicOperator(): Exports == Implementation where case search(STRING(p)$Lisp, rep(op).props) is val@None => just val otherwise => nothing - assert(op, s) == setProperty(op, s, NIL$Lisp) + assert(op: %, s: String) == setProperty(op, s, NIL$Lisp) + assert(op: %, p: Identifier) == setProperty(op, p, NIL$Lisp) has?(op, name) == key?(name, rep(op).props) weight(op, n) == setProperty(op, WEIGHT, n pretend None) nullary? op == zero? rep(op).narg diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 78192ed0..db874e80 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2283254 . 3451299467) +(2283430 . 3451368717) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL @@ -56,7 +56,7 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -2286) +(-32 R -2308) ((|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 -1034) (QUOTE (-564))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -2286 UP UPUP -1487) +(-40 -2308 UP UPUP -1353) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2789 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2789 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2789 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2789 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2286) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2797 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2797 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2797 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -2308) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|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."))) ((-4406 . T) (-4407 . T)) -((-2789 (-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|))))))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|))))))) +((-2797 (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|))))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|))))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2286) +(-54 |Base| R -2308) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-61 -2420) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-61 -2446) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -2420) +(-62 -2446) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-63 -2420) +(-63 -2446) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -2420) +(-64 -2446) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -2420) +(-65 -2446) ((|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 -2420) +(-66 -2446) ((|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 -2420) +(-67 -2446) ((|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 -2420) +(-68 -2446) ((|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 -2420) +(-69 -2446) ((|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 -2420) +(-70 -2446) ((|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 -2420) +(-71 -2446) ((|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 -2420) +(-72 -2446) ((|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 -2420) +(-73 -2446) ((|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 -2420) +(-74 -2446) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -236,55 +236,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-77 -2420) +(-77 -2446) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2420) +(-78 -2446) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-79 -2420) +(-79 -2446) ((|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 -2420) +(-80 -2446) ((|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 -2420) +(-81 -2446) ((|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 -2420) +(-82 -2446) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2420) +(-83 -2446) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2420) +(-84 -2446) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2420) +(-85 -2446) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2420) +(-86 -2446) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2420) +(-87 -2446) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-88 -2420) +(-88 -2446) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-89 -2420) +(-89 -2446) ((|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}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-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."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2789 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -385,10 +385,10 @@ NIL NIL ((|HasCategory| |#1| (QUOTE (-846)))) (-114) -((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad}op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) +((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad}op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-115 -2286 UP) +(-115 -2308 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2789 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2797 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2789 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-2797 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2797 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -468,11 +468,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4408 "*") . T)) NIL -(-135 |minix| -2268 S T$) +(-135 |minix| -2291 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2268 R) +(-136 |minix| -2291 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4406 . T) (-4396 . T) (-4407 . T)) -((-2789 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2797 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4403 . T)) NIL -(-148 -2286 UP UPUP) +(-148 -2308 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -560,7 +560,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-158 R -2286) +(-158 R -2308) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4402)) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-846)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4399 -2789 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3570 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 -2797 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3609 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4399 -2789 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3570 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . 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(QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4402)) (|HasAttribute| |#1| (QUOTE -4405)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2286) +(-188 R -2308) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-215 -2286 UP UPUP R) +(-215 -2308 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f,{} ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-216 -2286 FP) +(-216 -2308 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2789 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2286) +(-219 R -2308) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4403 . T)) NIL -(-224 R -2286) +(-224 R -2308) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p,{} x,{} a,{} b,{} incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x,{} g,{} a,{} b,{} eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-225) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3564 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -2268 R) +(-237 S -2291 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -2268 R) +(-238 -2291 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . T)) NIL -(-239 -2268 A B) +(-239 -2291 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-240 -2268 R) +(-240 -2291 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."))) ((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . 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|#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-241) ((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -911,7 +911,7 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-246 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -987,7 +987,7 @@ NIL (-264 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"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1032,11 +1032,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-276 R -2286) +(-276 R -2308) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-277 R -2286) +(-277 R -2308) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1084,7 +1084,7 @@ 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 -(-289 S R |Mod| -2347 -2988 |exactQuo|) +(-289 S R |Mod| -1918 -1877 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4406 . T) (-4407 . 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Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-297 -2286 S) +(-297 -2308 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 -(-298 E -2286) +(-298 E -2308) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL @@ -1168,7 +1168,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-310 -2286) +(-310 -2308) ((|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 @@ -1183,7 +1183,7 @@ NIL (-313 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))}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2789 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2789 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2797 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2797 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) (-314 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 @@ -1194,9 +1194,9 @@ NIL NIL (-316 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4403 -2789 (-2342 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2789 (-2342 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) -((-2789 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-556))) (-2789 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1106)))) (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE 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(-2797 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2797 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2797 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2797 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) +(-317 R -2308) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1207,7 +1207,7 @@ NIL (-319 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."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2322) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2789 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3719) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2534) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2344) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2721) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1239,12 +1239,12 @@ NIL (-327 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."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2286) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -2308) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-368)))) -(-329 -2286) +(-329 -2308) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL @@ -1264,15 +1264,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-334 S -2286 UP UPUP R) +(-334 S -2308 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-335 -2286 UP UPUP R) +(-335 -2308 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-336 -2286 UP UPUP R) +(-336 -2308 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1292,26 +1292,26 @@ NIL ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-341 S -2286 UP UPUP) +(-341 S -2308 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-363)))) -(-342 -2286 UP UPUP) +(-342 -2308 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-343 |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."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1328,31 +1328,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-350 R UP -2286) +(-350 R UP -2308) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-351 |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."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |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}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2286 GF) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2308 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1360,14 +1360,14 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-358 -2286 FP FPP) +(-358 -2308 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4389 . T) (-4397 . T) (-3564 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4389 . T) (-4397 . T) (-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1496,7 +1496,7 @@ 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 -(-392 -2286 UP UPUP R) +(-392 -2308 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 @@ -1520,11 +1520,11 @@ NIL ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-398 -2420 |returnType| -1586 |symbols|) +(-398 -2446 |returnType| -1586 |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 -(-399 -2286 UP) +(-399 -2308 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4389)) (|HasAttribute| |#1| (QUOTE -4397))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3564 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-405 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."))) @@ -1559,7 +1559,7 @@ NIL (-407 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4393 -12 (|has| |#1| (-6 -4404)) (|has| |#1| (-452)) (|has| |#1| (-6 -4393))) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2789 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4393)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2797 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4393)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2286 UP A) +(-413 R -2308 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4403 . T)) NIL -(-414 R -2286 UP A |ibasis|) +(-414 R -2308 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 -1034) (|devaluate| |#2|)))) @@ -1603,7 +1603,7 @@ NIL (-418 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1632,7 +1632,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4406 . T) (-4396 . T) (-4407 . T)) NIL -(-426 R -2286) +(-426 R -2308) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4393 -12 (|has| |#1| (-6 -4393)) (|has| |#2| (-6 -4393))) (-4400 . T) (-4401 . T) (-4403 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4393)) (|HasAttribute| |#2| (QUOTE -4393)))) -(-428 R -2286) +(-428 R -2308) ((|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 @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4403 -2789 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) +((-4403 -2797 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) NIL -(-431 R -2286) +(-431 R -2308) ((|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 -(-432 R -2286) +(-432 R -2308) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-433 R -2286) +(-433 R -2308) ((|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 @@ -1668,7 +1668,7 @@ 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 -(-435 R -2286 UP) +(-435 R -2308 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 -1034) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-443 R UP -2286) +(-443 R UP -2308) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1747,7 +1747,7 @@ NIL (-454 |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"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -2286 R) +(-471 |lv| -2308 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 @@ -1827,11 +1827,11 @@ NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . 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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)}"))) ((-4407 . T) (-4406 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |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."))) ((-4406 . T) (-4407 . 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1855,11 +1855,11 @@ NIL (-481 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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|#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1867,8 +1867,8 @@ NIL (-484 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-485 -2286 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-485 -2308 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1879,7 +1879,7 @@ NIL (-487) ((|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."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2789 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,7 +1904,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -2286 UP |AlExt| |AlPol|) +(-494 -2308 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1915,16 +1915,16 @@ NIL (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-498 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 -(-499 R UP -2286) +(-499 R UP -2308) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2286 |Expon| |VarSet| |DPoly|) +(-504 -2308 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1995,7 +1995,7 @@ NIL (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|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 @@ -2003,15 +2003,15 @@ NIL (-518 |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}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2789 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-2797 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-520 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."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2023,7 +2023,7 @@ NIL (-523 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."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-524) ((|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 @@ -2056,7 +2056,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-532 K -2286 |Par|) +(-532 K -2308 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -2080,7 +2080,7 @@ 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 -(-538 K -2286 |Par|) +(-538 K -2308 |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 @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2286) +((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +(-551 R -2308) ((|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 -(-552 R0 -2286 UP UPUP R) +(-552 R0 -2308 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 @@ -2146,7 +2146,7 @@ NIL NIL (-554 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3564 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3599 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-555 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."))) @@ -2156,7 +2156,7 @@ 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."))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-557 R -2286) +(-557 R -2308) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2168,7 +2168,7 @@ 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 -(-560 R -2286 L) +(-560 R -2308 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -652) (|devaluate| |#2|)))) @@ -2176,11 +2176,11 @@ 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 -(-562 -2286 UP UPUP R) +(-562 -2308 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 -(-563 -2286 UP) +(-563 -2308 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 @@ -2192,15 +2192,15 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-566 R -2286 L) +(-566 R -2308 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -652) (|devaluate| |#2|)))) -(-567 R -2286) +(-567 R -2308) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2286 UP) +(-568 -2308 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2208,27 +2208,27 @@ 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 -(-570 -2286) +(-570 -2308) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-571 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."))) -((-3564 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3599 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-572) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-573 R -2286) +(-573 R -2308) ((|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 -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2286 UP) +(-574 -2308 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-575 R -2286) +(-575 R -2308) ((|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 @@ -2260,15 +2260,15 @@ 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 -(-583 R -2286) +(-583 R -2308) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-584 E -2286) +(-584 E -2308) ((|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 -(-585 -2286) +(-585 -2308) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4401 . T) (-4400 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) @@ -2299,7 +2299,7 @@ NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2789 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2797 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2797 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 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 @@ -2307,7 +2307,7 @@ NIL (-594 |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}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2322) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2344) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4401 |has| |#1| (-556)) (-4400 |has| |#1| (-556)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4403 . T)) @@ -2320,7 +2320,7 @@ 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 -(-598 R -2286 FG) +(-598 R -2308 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2331,7 +2331,7 @@ NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,12 +2350,12 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4403 -2789 (-2342 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2789 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4403 -2797 (-2366 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) +((-2797 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |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."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-607 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 @@ -2380,7 +2380,7 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2286 UP) +(-613 -2308 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2408,7 +2408,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-620 R -2286) +(-620 R -2308) ((|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 @@ -2440,18 +2440,18 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-628 R -2286) +(-628 R -2308) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-629 |lv| -2286) +(-629 |lv| -2308) ((|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 (-630) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-52))))))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094)))) (-631 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,8 +2462,8 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4403 -2789 (-2342 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2789 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4403 -2797 (-2366 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) +((-2797 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-634 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2475,7 +2475,7 @@ NIL (-636 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2329 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2352 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4403 . T)) @@ -2495,7 +2495,7 @@ NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2503,7 +2503,7 @@ NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-648 R -2286 L) +(-648 R -2308 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 @@ -2540,11 +2540,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-653 -2286 UP) +(-653 -2308 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)))) -(-654 A -3546) +(-654 A -3521) ((|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}}"))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2580,11 +2580,11 @@ 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}."))) ((-4407 . T) (-4406 . T)) NIL -(-663 -2286) +(-663 -2308) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-664 -2286 |Row| |Col| M) +(-664 -2308 |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 @@ -2595,7 +2595,7 @@ NIL (-666 |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."))) ((-4403 . T) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2789 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2797 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|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 @@ -2615,7 +2615,7 @@ NIL (-671 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 -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2671,7 +2671,7 @@ NIL (-685 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."))) ((-4406 . T) (-4407 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2680,7 +2680,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-688 S -2286 FLAF FLAS) +(-688 S -2308 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2690,8 +2690,8 @@ NIL NIL (-690) ((|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"))) -((-4399 . T) (-4404 |has| (-695) (-363)) (-4398 |has| (-695) (-363)) (-3570 . T) (-4405 |has| (-695) (-6 -4405)) (-4402 |has| (-695) (-6 -4402)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2789 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2789 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2789 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2789 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2789 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2789 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2789 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4405)) (|HasAttribute| (-695) (QUOTE -4402)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4399 . T) (-4404 |has| (-695) (-363)) (-4398 |has| (-695) (-363)) (-3609 . T) (-4405 |has| (-695) (-6 -4405)) (-4402 |has| (-695) (-6 -4402)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2797 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2797 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2797 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4405)) (|HasAttribute| (-695) (QUOTE -4402)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 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}."))) ((-4407 . T)) @@ -2704,13 +2704,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-694 OV E -2286 PG) +(-694 OV E -2308 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 (-695) ((|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}"))) -((-3564 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-696 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."))) @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-702 S -3917 I) +(-702 S -3932 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 @@ -2756,14 +2756,14 @@ 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 -(-707 R |Mod| -2347 -2988 |exactQuo|) +(-707 R |Mod| -1918 -1877 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-709 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -2347 -2988 |exactQuo|) +(-711 R |Mod| -1918 -1877 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4403 . T)) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4401 . T) (-4400 . T)) NIL -(-714 -2286) +(-714 -2308) ((|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]]}."))) ((-4403 . T)) NIL @@ -2820,7 +2820,7 @@ 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 -(-723 -2286 UP) +(-723 -2308 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 @@ -2839,7 +2839,7 @@ NIL (-727 |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."))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-728 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 @@ -2972,11 +2972,11 @@ 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 -(-761 -2286) +(-761 -2308) ((|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 -(-762 P -2286) +(-762 P -2308) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -2286) +(-764 UP -2308) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3000,7 +3000,7 @@ 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."))) (((-4408 "*") . T)) NIL -(-768 R -2286) +(-768 R -2308) ((|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 @@ -3020,7 +3020,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-773 -2286 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2308 |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 @@ -3035,7 +3035,7 @@ NIL (-776 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . 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|#1| (QUOTE (-545)))) (-2352 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2352 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2352 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2352 (|HasCategory| |#1| (LIST (QUOTE -988) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-777 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3043,7 +3043,7 @@ NIL (-778 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-779 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3104,23 +3104,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-794 -2789 R OS S) +(-794 -2797 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2789 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2789 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2797 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-796) ((|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 -(-797 R -2286 L) +(-797 R -2308 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-798 R -2286) +(-798 R -2308) ((|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 @@ -3128,7 +3128,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-800 R -2286) +(-800 R -2308) ((|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 @@ -3136,11 +3136,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-802 -2286 UP UPUP R) +(-802 -2308 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 -(-803 -2286 UP L LQ) +(-803 -2308 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3148,38 +3148,38 @@ 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 -(-805 -2286 UP L LQ) +(-805 -2308 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-806 -2286 UP) +(-806 -2308 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-807 -2286 L UP A LO) +(-807 -2308 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 -(-808 -2286 UP) +(-808 -2308 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-809 -2286 LO) +(-809 -2308 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-813 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4408 "*") |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4398 |has| |#2| (-363)) (-4403 . T) (-4401 . T) (-4400 . T)) @@ -3247,7 +3247,7 @@ NIL (-829 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."))) ((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2789 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2789 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-830 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3287,12 +3287,12 @@ NIL (-839 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2789 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2789 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -2268 S) +(-841 -2291 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 @@ -3328,11 +3328,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -2551) +(-850 R |sigma| -2564) ((|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."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-851 |x| R |sigma| -2551) +(-851 |x| R |sigma| -2564) ((|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}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3399,15 +3399,15 @@ NIL (-867 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2789 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2797 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) (-868 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2789 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2797 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-869 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-870) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3463,7 +3463,7 @@ NIL (-883 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2329 (|HasCategory| |#2| (QUOTE (-1045)))) (-2329 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2329 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) +((-12 (-2352 (|HasCategory| |#2| (QUOTE (-1045)))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-884 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3472,7 +3472,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-886 R -3917) +(-886 R -3932) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3496,7 +3496,7 @@ 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 -(-892 UP -2286) +(-892 UP -2308) ((|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 @@ -3519,7 +3519,7 @@ NIL (-897 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-898 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3535,7 +3535,7 @@ NIL (-901 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4403 . T)) -((-2789 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +((-2797 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (-902 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3556,7 +3556,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -2286 UP UPUP R) +(-907 R0 -2308 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 @@ -3584,7 +3584,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-914 -2286) +(-914 -2308) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3600,11 +3600,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4408 "*") . T)) NIL -(-918 -2286 P) +(-918 -2308 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2286) +(-919 |xx| -2308) ((|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 @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925 R -2286) +(-925 R -2308) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3640,7 +3640,7 @@ 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 -(-928 S R -2286) +(-928 S R -2308) ((|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 @@ -3660,11 +3660,11 @@ 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 -882) (|devaluate| |#1|)))) -(-933 R -2286 -3917) +(-933 R -2308 -3932) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-934 -3917) +(-934 -3932) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3687,7 +3687,7 @@ NIL (-939 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-940 |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 @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) NIL -(-946 E V R P -2286) +(-946 E V R P -2308) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3723,8 +3723,8 @@ NIL (-948 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}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2286) +((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-949 E V R P -2308) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3747,12 +3747,12 @@ NIL (-954 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-955) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-956 -2286) +(-956 -2308) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3767,11 +3767,11 @@ NIL (-959 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}"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4404))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4404))) (-960 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"))) ((-4403 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-961) ((|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| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3852,7 +3852,7 @@ 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 -(-981 K R UP -2286) +(-981 K R UP -2308) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3911,11 +3911,11 @@ NIL (-995 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.}"))) ((-4399 |has| |#1| (-290)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2789 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) (-996 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}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-997 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3924,14 +3924,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-999 -2286 UP UPUP |radicnd| |n|) +(-999 -2308 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2789 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2789 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2789 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2789 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2797 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2797 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2797 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1000 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2789 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1001) ((|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 @@ -3964,19 +3964,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) NIL -(-1009 R -2286) +(-1009 R -2308) ((|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 -(-1010 R -2286) +(-1010 R -2308) ((|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 -(-1011 -2286 UP) +(-1011 -2308 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 -(-1012 -2286 UP) +(-1012 -2308 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 @@ -4011,8 +4011,8 @@ NIL (-1020 |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"))) ((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) -((-2789 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) -(-1021 -2286 L) +((-2797 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) +(-1021 -2308 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4048,14 +4048,14 @@ 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 -(-1030 -2286 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2308 |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"))) (((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-1031) ((|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.}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-52))))))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4112,7 +4112,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4403 . T)) NIL -(-1046 |xx| -2286) +(-1046 |xx| -2308) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4127,7 +4127,7 @@ NIL (-1049 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4406 . T) (-4401 . T) (-4400 . T)) -((-2789 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) +((-2797 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) (-1050 |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 @@ -4159,7 +4159,7 @@ NIL (-1057) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2511) (QUOTE (-52))))))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1058 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -2286) +(-1070 |Base| R -2308) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-1071 |Base| R -2286) +(-1071 |Base| R -2308) ((|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 @@ -4227,7 +4227,7 @@ NIL (-1074 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."))) ((-4399 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4255,7 +4255,7 @@ NIL (-1081 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"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1082 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 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)}}"))) ((-4406 . T) (-4396 . T) (-4407 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4359,7 +4359,7 @@ NIL (-1107 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2797 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1108 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1110 R -2286) +(-1110 R -2308) ((|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 @@ -4407,16 +4407,16 @@ NIL (-1119 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."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1120 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 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}"))) ((-4407 . T) (-4406 . T)) NIL -(-1122 UP -2286) +(-1122 UP -2308) ((|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 @@ -4471,11 +4471,11 @@ NIL (-1135 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2789 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2797 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4403 . T) (-4395 |has| |#2| (-6 (-4408 "*"))) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2789 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2797 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4495,7 +4495,7 @@ NIL (-1141 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|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}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1142 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 @@ -4507,7 +4507,7 @@ NIL (-1144 |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."))) ((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094)))) (-1145) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4531,7 +4531,7 @@ NIL (-1150 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."))) ((-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4407 . T) (-4406 . T)) @@ -4539,11 +4539,11 @@ NIL (-1152) NIL ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2797 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#1|)))))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#1|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1154 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4408 "*") -2789 (-2342 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-172)) (-2342 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4399 -2789 (-2342 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-556)) (-2342 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2789 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4404))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4404))) (-1173) ((|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 @@ -4659,7 +4659,7 @@ NIL (-1182 |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}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3076) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2511) (|devaluate| |#2|)))))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2789 (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4711,7 +4711,7 @@ NIL (-1195 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4407 . T) (-4406 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -2286) +(-1198 R -2308) ((|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 @@ -4728,7 +4728,7 @@ NIL ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1200 R -2286) +(-1200 R -2308) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4743,7 +4743,7 @@ NIL (-1203 |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}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4756,7 +4756,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-1207 -2286) +(-1207 -2308) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) 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(LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1224 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4859,7 +4859,7 @@ NIL (-1232 |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}"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4402 |has| |#2| (-363)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2789 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2789 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2789 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1233 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2322) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2344) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) @@ -4903,15 +4903,15 @@ NIL (-1243 |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)}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2322) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2789 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3719) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2534) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2344) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2721) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2789 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2322) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2789 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3719) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2534) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2344) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2721) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 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))}."))) (((-4408 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4399 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2789 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2797 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -2534) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3719) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2721) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |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."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) @@ -4935,12 +4935,12 @@ NIL (-1251 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2789 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2322) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2789 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -3719) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2534) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2344) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2721) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1252 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,{}f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,{}y[1],{}y[2],{}...,{}y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,{}cl)} is the solution to \\spad{y<n>=f(y,{}y',{}..,{}y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,{}c0,{}c1)} is the solution to \\spad{y'' = f(y,{}y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,{}c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,{}g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1253 -2286 UP L UTS) +(-1253 -2308 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 (-556)))) @@ -4967,7 +4967,7 @@ NIL (-1259 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."))) ((-4407 . T) (-4406 . T)) -((-2789 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2789 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2789 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5000,7 +5000,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1268 K R UP -2286) +(-1268 K R UP -2308) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5036,11 +5036,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) NIL -(-1277 S -2286) +(-1277 S -2308) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2286) +(-1278 -2308) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2283234 2283239 2283244 2283249) (-2 NIL 2283214 2283219 2283224 2283229) (-1 NIL 2283194 2283199 2283204 2283209) (0 NIL 2283174 2283179 2283184 2283189) (-1287 "ZMOD.spad" 2282983 2282996 2283112 2283169) (-1286 "ZLINDEP.spad" 2282027 2282038 2282973 2282978) (-1285 "ZDSOLVE.spad" 2271876 2271898 2282017 2282022) (-1284 "YSTREAM.spad" 2271369 2271380 2271866 2271871) (-1283 "XRPOLY.spad" 2270589 2270609 2271225 2271294) (-1282 "XPR.spad" 2268380 2268393 2270307 2270406) (-1281 "XPOLY.spad" 2267935 2267946 2268236 2268305) (-1280 "XPOLYC.spad" 2267252 2267268 2267861 2267930) (-1279 "XPBWPOLY.spad" 2265689 2265709 2267032 2267101) (-1278 "XF.spad" 2264150 2264165 2265591 2265684) (-1277 "XF.spad" 2262591 2262608 2264034 2264039) (-1276 "XFALG.spad" 2259615 2259631 2262517 2262586) (-1275 "XEXPPKG.spad" 2258866 2258892 2259605 2259610) (-1274 "XDPOLY.spad" 2258480 2258496 2258722 2258791) (-1273 "XALG.spad" 2258140 2258151 2258436 2258475) (-1272 "WUTSET.spad" 2253979 2253996 2257786 2257813) (-1271 "WP.spad" 2253178 2253222 2253837 2253904) (-1270 "WHILEAST.spad" 2252976 2252985 2253168 2253173) (-1269 "WHEREAST.spad" 2252647 2252656 2252966 2252971) (-1268 "WFFINTBS.spad" 2250210 2250232 2252637 2252642) (-1267 "WEIER.spad" 2248424 2248435 2250200 2250205) (-1266 "VSPACE.spad" 2248097 2248108 2248392 2248419) (-1265 "VSPACE.spad" 2247790 2247803 2248087 2248092) (-1264 "VOID.spad" 2247467 2247476 2247780 2247785) (-1263 "VIEW.spad" 2245089 2245098 2247457 2247462) (-1262 "VIEWDEF.spad" 2240286 2240295 2245079 2245084) (-1261 "VIEW3D.spad" 2224121 2224130 2240276 2240281) (-1260 "VIEW2D.spad" 2211858 2211867 2224111 2224116) (-1259 "VECTOR.spad" 2210533 2210544 2210784 2210811) (-1258 "VECTOR2.spad" 2209160 2209173 2210523 2210528) (-1257 "VECTCAT.spad" 2207060 2207071 2209128 2209155) (-1256 "VECTCAT.spad" 2204768 2204781 2206838 2206843) (-1255 "VARIABLE.spad" 2204548 2204563 2204758 2204763) (-1254 "UTYPE.spad" 2204192 2204201 2204538 2204543) (-1253 "UTSODETL.spad" 2203485 2203509 2204148 2204153) (-1252 "UTSODE.spad" 2201673 2201693 2203475 2203480) (-1251 "UTS.spad" 2196462 2196490 2200140 2200237) (-1250 "UTSCAT.spad" 2193913 2193929 2196360 2196457) (-1249 "UTSCAT.spad" 2191008 2191026 2193457 2193462) (-1248 "UTS2.spad" 2190601 2190636 2190998 2191003) (-1247 "URAGG.spad" 2185233 2185244 2190591 2190596) (-1246 "URAGG.spad" 2179829 2179842 2185189 2185194) (-1245 "UPXSSING.spad" 2177472 2177498 2178910 2179043) (-1244 "UPXS.spad" 2174620 2174648 2175604 2175753) (-1243 "UPXSCONS.spad" 2172377 2172397 2172752 2172901) (-1242 "UPXSCCA.spad" 2170942 2170962 2172223 2172372) (-1241 "UPXSCCA.spad" 2169649 2169671 2170932 2170937) (-1240 "UPXSCAT.spad" 2168230 2168246 2169495 2169644) (-1239 "UPXS2.spad" 2167771 2167824 2168220 2168225) (-1238 "UPSQFREE.spad" 2166183 2166197 2167761 2167766) (-1237 "UPSCAT.spad" 2163776 2163800 2166081 2166178) (-1236 "UPSCAT.spad" 2161075 2161101 2163382 2163387) (-1235 "UPOLYC.spad" 2156053 2156064 2160917 2161070) (-1234 "UPOLYC.spad" 2150923 2150936 2155789 2155794) (-1233 "UPOLYC2.spad" 2150392 2150411 2150913 2150918) (-1232 "UP.spad" 2147549 2147564 2147942 2148095) (-1231 "UPMP.spad" 2146439 2146452 2147539 2147544) (-1230 "UPDIVP.spad" 2146002 2146016 2146429 2146434) (-1229 "UPDECOMP.spad" 2144239 2144253 2145992 2145997) (-1228 "UPCDEN.spad" 2143446 2143462 2144229 2144234) (-1227 "UP2.spad" 2142808 2142829 2143436 2143441) (-1226 "UNISEG.spad" 2142161 2142172 2142727 2142732) (-1225 "UNISEG2.spad" 2141654 2141667 2142117 2142122) (-1224 "UNIFACT.spad" 2140755 2140767 2141644 2141649) (-1223 "ULS.spad" 2131307 2131335 2132400 2132829) (-1222 "ULSCONS.spad" 2123701 2123721 2124073 2124222) (-1221 "ULSCCAT.spad" 2121430 2121450 2123547 2123696) (-1220 "ULSCCAT.spad" 2119267 2119289 2121386 2121391) (-1219 "ULSCAT.spad" 2117483 2117499 2119113 2119262) (-1218 "ULS2.spad" 2116995 2117048 2117473 2117478) (-1217 "UINT8.spad" 2116872 2116881 2116985 2116990) (-1216 "UINT64.spad" 2116748 2116757 2116862 2116867) (-1215 "UINT32.spad" 2116624 2116633 2116738 2116743) (-1214 "UINT16.spad" 2116500 2116509 2116614 2116619) (-1213 "UFD.spad" 2115565 2115574 2116426 2116495) (-1212 "UFD.spad" 2114692 2114703 2115555 2115560) (-1211 "UDVO.spad" 2113539 2113548 2114682 2114687) (-1210 "UDPO.spad" 2110966 2110977 2113495 2113500) (-1209 "TYPE.spad" 2110898 2110907 2110956 2110961) (-1208 "TYPEAST.spad" 2110817 2110826 2110888 2110893) (-1207 "TWOFACT.spad" 2109467 2109482 2110807 2110812) (-1206 "TUPLE.spad" 2108951 2108962 2109366 2109371) (-1205 "TUBETOOL.spad" 2105788 2105797 2108941 2108946) (-1204 "TUBE.spad" 2104429 2104446 2105778 2105783) (-1203 "TS.spad" 2103018 2103034 2103994 2104091) (-1202 "TSETCAT.spad" 2090145 2090162 2102986 2103013) (-1201 "TSETCAT.spad" 2077258 2077277 2090101 2090106) (-1200 "TRMANIP.spad" 2071624 2071641 2076964 2076969) (-1199 "TRIMAT.spad" 2070583 2070608 2071614 2071619) (-1198 "TRIGMNIP.spad" 2069100 2069117 2070573 2070578) (-1197 "TRIGCAT.spad" 2068612 2068621 2069090 2069095) (-1196 "TRIGCAT.spad" 2068122 2068133 2068602 2068607) (-1195 "TREE.spad" 2066693 2066704 2067729 2067756) (-1194 "TRANFUN.spad" 2066524 2066533 2066683 2066688) (-1193 "TRANFUN.spad" 2066353 2066364 2066514 2066519) (-1192 "TOPSP.spad" 2066027 2066036 2066343 2066348) (-1191 "TOOLSIGN.spad" 2065690 2065701 2066017 2066022) (-1190 "TEXTFILE.spad" 2064247 2064256 2065680 2065685) (-1189 "TEX.spad" 2061379 2061388 2064237 2064242) (-1188 "TEX1.spad" 2060935 2060946 2061369 2061374) (-1187 "TEMUTL.spad" 2060490 2060499 2060925 2060930) (-1186 "TBCMPPK.spad" 2058583 2058606 2060480 2060485) (-1185 "TBAGG.spad" 2057619 2057642 2058563 2058578) (-1184 "TBAGG.spad" 2056663 2056688 2057609 2057614) (-1183 "TANEXP.spad" 2056039 2056050 2056653 2056658) (-1182 "TABLE.spad" 2054450 2054473 2054720 2054747) (-1181 "TABLEAU.spad" 2053931 2053942 2054440 2054445) (-1180 "TABLBUMP.spad" 2050714 2050725 2053921 2053926) (-1179 "SYSTEM.spad" 2049942 2049951 2050704 2050709) (-1178 "SYSSOLP.spad" 2047415 2047426 2049932 2049937) (-1177 "SYSNNI.spad" 2046595 2046606 2047405 2047410) (-1176 "SYSINT.spad" 2045999 2046010 2046585 2046590) (-1175 "SYNTAX.spad" 2042193 2042202 2045989 2045994) (-1174 "SYMTAB.spad" 2040249 2040258 2042183 2042188) (-1173 "SYMS.spad" 2036234 2036243 2040239 2040244) (-1172 "SYMPOLY.spad" 2035241 2035252 2035323 2035450) (-1171 "SYMFUNC.spad" 2034716 2034727 2035231 2035236) (-1170 "SYMBOL.spad" 2032143 2032152 2034706 2034711) (-1169 "SWITCH.spad" 2028900 2028909 2032133 2032138) (-1168 "SUTS.spad" 2025799 2025827 2027367 2027464) (-1167 "SUPXS.spad" 2022934 2022962 2023931 2024080) (-1166 "SUP.spad" 2019703 2019714 2020484 2020637) (-1165 "SUPFRACF.spad" 2018808 2018826 2019693 2019698) (-1164 "SUP2.spad" 2018198 2018211 2018798 2018803) (-1163 "SUMRF.spad" 2017164 2017175 2018188 2018193) (-1162 "SUMFS.spad" 2016797 2016814 2017154 2017159) (-1161 "SULS.spad" 2007336 2007364 2008442 2008871) (-1160 "SUCHTAST.spad" 2007105 2007114 2007326 2007331) (-1159 "SUCH.spad" 2006785 2006800 2007095 2007100) (-1158 "SUBSPACE.spad" 1998792 1998807 2006775 2006780) (-1157 "SUBRESP.spad" 1997952 1997966 1998748 1998753) (-1156 "STTF.spad" 1994051 1994067 1997942 1997947) (-1155 "STTFNC.spad" 1990519 1990535 1994041 1994046) (-1154 "STTAYLOR.spad" 1982917 1982928 1990400 1990405) (-1153 "STRTBL.spad" 1981422 1981439 1981571 1981598) (-1152 "STRING.spad" 1980831 1980840 1980845 1980872) (-1151 "STRICAT.spad" 1980619 1980628 1980799 1980826) (-1150 "STREAM.spad" 1977477 1977488 1980144 1980159) (-1149 "STREAM3.spad" 1977022 1977037 1977467 1977472) (-1148 "STREAM2.spad" 1976090 1976103 1977012 1977017) (-1147 "STREAM1.spad" 1975794 1975805 1976080 1976085) (-1146 "STINPROD.spad" 1974700 1974716 1975784 1975789) (-1145 "STEP.spad" 1973901 1973910 1974690 1974695) (-1144 "STBL.spad" 1972427 1972455 1972594 1972609) (-1143 "STAGG.spad" 1971502 1971513 1972417 1972422) (-1142 "STAGG.spad" 1970575 1970588 1971492 1971497) (-1141 "STACK.spad" 1969926 1969937 1970182 1970209) (-1140 "SREGSET.spad" 1967630 1967647 1969572 1969599) (-1139 "SRDCMPK.spad" 1966175 1966195 1967620 1967625) (-1138 "SRAGG.spad" 1961272 1961281 1966143 1966170) (-1137 "SRAGG.spad" 1956389 1956400 1961262 1961267) (-1136 "SQMATRIX.spad" 1954005 1954023 1954921 1955008) (-1135 "SPLTREE.spad" 1948557 1948570 1953441 1953468) (-1134 "SPLNODE.spad" 1945145 1945158 1948547 1948552) (-1133 "SPFCAT.spad" 1943922 1943931 1945135 1945140) (-1132 "SPECOUT.spad" 1942472 1942481 1943912 1943917) (-1131 "SPADXPT.spad" 1934611 1934620 1942462 1942467) (-1130 "spad-parser.spad" 1934076 1934085 1934601 1934606) (-1129 "SPADAST.spad" 1933777 1933786 1934066 1934071) (-1128 "SPACEC.spad" 1917790 1917801 1933767 1933772) (-1127 "SPACE3.spad" 1917566 1917577 1917780 1917785) (-1126 "SORTPAK.spad" 1917111 1917124 1917522 1917527) (-1125 "SOLVETRA.spad" 1914868 1914879 1917101 1917106) (-1124 "SOLVESER.spad" 1913388 1913399 1914858 1914863) (-1123 "SOLVERAD.spad" 1909398 1909409 1913378 1913383) (-1122 "SOLVEFOR.spad" 1907818 1907836 1909388 1909393) (-1121 "SNTSCAT.spad" 1907418 1907435 1907786 1907813) (-1120 "SMTS.spad" 1905678 1905704 1906983 1907080) (-1119 "SMP.spad" 1903117 1903137 1903507 1903634) (-1118 "SMITH.spad" 1901960 1901985 1903107 1903112) (-1117 "SMATCAT.spad" 1900070 1900100 1901904 1901955) (-1116 "SMATCAT.spad" 1898112 1898144 1899948 1899953) (-1115 "SKAGG.spad" 1897073 1897084 1898080 1898107) (-1114 "SINT.spad" 1895899 1895908 1896939 1897068) (-1113 "SIMPAN.spad" 1895627 1895636 1895889 1895894) (-1112 "SIG.spad" 1894955 1894964 1895617 1895622) (-1111 "SIGNRF.spad" 1894063 1894074 1894945 1894950) (-1110 "SIGNEF.spad" 1893332 1893349 1894053 1894058) (-1109 "SIGAST.spad" 1892713 1892722 1893322 1893327) (-1108 "SHP.spad" 1890631 1890646 1892669 1892674) (-1107 "SHDP.spad" 1880342 1880369 1880851 1880982) (-1106 "SGROUP.spad" 1879950 1879959 1880332 1880337) (-1105 "SGROUP.spad" 1879556 1879567 1879940 1879945) (-1104 "SGCF.spad" 1872437 1872446 1879546 1879551) (-1103 "SFRTCAT.spad" 1871365 1871382 1872405 1872432) (-1102 "SFRGCD.spad" 1870428 1870448 1871355 1871360) (-1101 "SFQCMPK.spad" 1865065 1865085 1870418 1870423) (-1100 "SFORT.spad" 1864500 1864514 1865055 1865060) (-1099 "SEXOF.spad" 1864343 1864383 1864490 1864495) (-1098 "SEX.spad" 1864235 1864244 1864333 1864338) (-1097 "SEXCAT.spad" 1861786 1861826 1864225 1864230) (-1096 "SET.spad" 1860086 1860097 1861207 1861246) (-1095 "SETMN.spad" 1858520 1858537 1860076 1860081) (-1094 "SETCAT.spad" 1858005 1858014 1858510 1858515) (-1093 "SETCAT.spad" 1857488 1857499 1857995 1858000) (-1092 "SETAGG.spad" 1854009 1854020 1857468 1857483) (-1091 "SETAGG.spad" 1850538 1850551 1853999 1854004) (-1090 "SEQAST.spad" 1850241 1850250 1850528 1850533) (-1089 "SEGXCAT.spad" 1849363 1849376 1850231 1850236) (-1088 "SEG.spad" 1849176 1849187 1849282 1849287) (-1087 "SEGCAT.spad" 1848083 1848094 1849166 1849171) (-1086 "SEGBIND.spad" 1847155 1847166 1848038 1848043) (-1085 "SEGBIND2.spad" 1846851 1846864 1847145 1847150) (-1084 "SEGAST.spad" 1846565 1846574 1846841 1846846) (-1083 "SEG2.spad" 1845990 1846003 1846521 1846526) (-1082 "SDVAR.spad" 1845266 1845277 1845980 1845985) (-1081 "SDPOL.spad" 1842656 1842667 1842947 1843074) (-1080 "SCPKG.spad" 1840735 1840746 1842646 1842651) (-1079 "SCOPE.spad" 1839888 1839897 1840725 1840730) (-1078 "SCACHE.spad" 1838570 1838581 1839878 1839883) (-1077 "SASTCAT.spad" 1838479 1838488 1838560 1838565) (-1076 "SAOS.spad" 1838351 1838360 1838469 1838474) (-1075 "SAERFFC.spad" 1838064 1838084 1838341 1838346) (-1074 "SAE.spad" 1836239 1836255 1836850 1836985) (-1073 "SAEFACT.spad" 1835940 1835960 1836229 1836234) (-1072 "RURPK.spad" 1833581 1833597 1835930 1835935) (-1071 "RULESET.spad" 1833022 1833046 1833571 1833576) (-1070 "RULE.spad" 1831226 1831250 1833012 1833017) (-1069 "RULECOLD.spad" 1831078 1831091 1831216 1831221) (-1068 "RTVALUE.spad" 1830811 1830820 1831068 1831073) (-1067 "RSTRCAST.spad" 1830528 1830537 1830801 1830806) (-1066 "RSETGCD.spad" 1826906 1826926 1830518 1830523) (-1065 "RSETCAT.spad" 1816690 1816707 1826874 1826901) (-1064 "RSETCAT.spad" 1806494 1806513 1816680 1816685) (-1063 "RSDCMPK.spad" 1804946 1804966 1806484 1806489) (-1062 "RRCC.spad" 1803330 1803360 1804936 1804941) (-1061 "RRCC.spad" 1801712 1801744 1803320 1803325) (-1060 "RPTAST.spad" 1801414 1801423 1801702 1801707) (-1059 "RPOLCAT.spad" 1780774 1780789 1801282 1801409) (-1058 "RPOLCAT.spad" 1759848 1759865 1780358 1780363) (-1057 "ROUTINE.spad" 1755711 1755720 1758495 1758522) (-1056 "ROMAN.spad" 1755039 1755048 1755577 1755706) (-1055 "ROIRC.spad" 1754119 1754151 1755029 1755034) (-1054 "RNS.spad" 1753022 1753031 1754021 1754114) (-1053 "RNS.spad" 1752011 1752022 1753012 1753017) (-1052 "RNG.spad" 1751746 1751755 1752001 1752006) (-1051 "RMODULE.spad" 1751384 1751395 1751736 1751741) (-1050 "RMCAT2.spad" 1750792 1750849 1751374 1751379) (-1049 "RMATRIX.spad" 1749616 1749635 1749959 1749998) (-1048 "RMATCAT.spad" 1745149 1745180 1749572 1749611) (-1047 "RMATCAT.spad" 1740572 1740605 1744997 1745002) (-1046 "RINTERP.spad" 1740460 1740480 1740562 1740567) (-1045 "RING.spad" 1739930 1739939 1740440 1740455) (-1044 "RING.spad" 1739408 1739419 1739920 1739925) (-1043 "RIDIST.spad" 1738792 1738801 1739398 1739403) (-1042 "RGCHAIN.spad" 1737371 1737387 1738277 1738304) (-1041 "RGBCSPC.spad" 1737152 1737164 1737361 1737366) (-1040 "RGBCMDL.spad" 1736682 1736694 1737142 1737147) (-1039 "RF.spad" 1734296 1734307 1736672 1736677) (-1038 "RFFACTOR.spad" 1733758 1733769 1734286 1734291) (-1037 "RFFACT.spad" 1733493 1733505 1733748 1733753) (-1036 "RFDIST.spad" 1732481 1732490 1733483 1733488) (-1035 "RETSOL.spad" 1731898 1731911 1732471 1732476) (-1034 "RETRACT.spad" 1731326 1731337 1731888 1731893) (-1033 "RETRACT.spad" 1730752 1730765 1731316 1731321) (-1032 "RETAST.spad" 1730564 1730573 1730742 1730747) (-1031 "RESULT.spad" 1728624 1728633 1729211 1729238) (-1030 "RESRING.spad" 1727971 1728018 1728562 1728619) (-1029 "RESLATC.spad" 1727295 1727306 1727961 1727966) (-1028 "REPSQ.spad" 1727024 1727035 1727285 1727290) (-1027 "REP.spad" 1724576 1724585 1727014 1727019) (-1026 "REPDB.spad" 1724281 1724292 1724566 1724571) (-1025 "REP2.spad" 1713853 1713864 1724123 1724128) (-1024 "REP1.spad" 1707843 1707854 1713803 1713808) (-1023 "REGSET.spad" 1705640 1705657 1707489 1707516) (-1022 "REF.spad" 1704969 1704980 1705595 1705600) (-1021 "REDORDER.spad" 1704145 1704162 1704959 1704964) (-1020 "RECLOS.spad" 1702928 1702948 1703632 1703725) (-1019 "REALSOLV.spad" 1702060 1702069 1702918 1702923) (-1018 "REAL.spad" 1701932 1701941 1702050 1702055) (-1017 "REAL0Q.spad" 1699214 1699229 1701922 1701927) (-1016 "REAL0.spad" 1696042 1696057 1699204 1699209) (-1015 "RDUCEAST.spad" 1695763 1695772 1696032 1696037) (-1014 "RDIV.spad" 1695414 1695439 1695753 1695758) (-1013 "RDIST.spad" 1694977 1694988 1695404 1695409) (-1012 "RDETRS.spad" 1693773 1693791 1694967 1694972) (-1011 "RDETR.spad" 1691880 1691898 1693763 1693768) (-1010 "RDEEFS.spad" 1690953 1690970 1691870 1691875) (-1009 "RDEEF.spad" 1689949 1689966 1690943 1690948) (-1008 "RCFIELD.spad" 1687135 1687144 1689851 1689944) (-1007 "RCFIELD.spad" 1684407 1684418 1687125 1687130) (-1006 "RCAGG.spad" 1682319 1682330 1684397 1684402) (-1005 "RCAGG.spad" 1680158 1680171 1682238 1682243) (-1004 "RATRET.spad" 1679518 1679529 1680148 1680153) (-1003 "RATFACT.spad" 1679210 1679222 1679508 1679513) (-1002 "RANDSRC.spad" 1678529 1678538 1679200 1679205) (-1001 "RADUTIL.spad" 1678283 1678292 1678519 1678524) (-1000 "RADIX.spad" 1675184 1675198 1676750 1676843) (-999 "RADFF.spad" 1673598 1673634 1673716 1673872) (-998 "RADCAT.spad" 1673192 1673200 1673588 1673593) (-997 "RADCAT.spad" 1672784 1672794 1673182 1673187) (-996 "QUEUE.spad" 1672127 1672137 1672391 1672418) (-995 "QUAT.spad" 1670709 1670719 1671051 1671116) (-994 "QUATCT2.spad" 1670328 1670346 1670699 1670704) (-993 "QUATCAT.spad" 1668493 1668503 1670258 1670323) (-992 "QUATCAT.spad" 1666409 1666421 1668176 1668181) (-991 "QUAGG.spad" 1665235 1665245 1666377 1666404) (-990 "QQUTAST.spad" 1665004 1665012 1665225 1665230) (-989 "QFORM.spad" 1664467 1664481 1664994 1664999) (-988 "QFCAT.spad" 1663170 1663180 1664369 1664462) (-987 "QFCAT.spad" 1661464 1661476 1662665 1662670) (-986 "QFCAT2.spad" 1661155 1661171 1661454 1661459) (-985 "QEQUAT.spad" 1660712 1660720 1661145 1661150) (-984 "QCMPACK.spad" 1655459 1655478 1660702 1660707) (-983 "QALGSET.spad" 1651534 1651566 1655373 1655378) (-982 "QALGSET2.spad" 1649530 1649548 1651524 1651529) (-981 "PWFFINTB.spad" 1646840 1646861 1649520 1649525) (-980 "PUSHVAR.spad" 1646169 1646188 1646830 1646835) (-979 "PTRANFN.spad" 1642295 1642305 1646159 1646164) (-978 "PTPACK.spad" 1639383 1639393 1642285 1642290) (-977 "PTFUNC2.spad" 1639204 1639218 1639373 1639378) (-976 "PTCAT.spad" 1638453 1638463 1639172 1639199) (-975 "PSQFR.spad" 1637760 1637784 1638443 1638448) (-974 "PSEUDLIN.spad" 1636618 1636628 1637750 1637755) (-973 "PSETPK.spad" 1622051 1622067 1636496 1636501) (-972 "PSETCAT.spad" 1615971 1615994 1622031 1622046) (-971 "PSETCAT.spad" 1609865 1609890 1615927 1615932) (-970 "PSCURVE.spad" 1608848 1608856 1609855 1609860) (-969 "PSCAT.spad" 1607615 1607644 1608746 1608843) (-968 "PSCAT.spad" 1606472 1606503 1607605 1607610) (-967 "PRTITION.spad" 1605417 1605425 1606462 1606467) (-966 "PRTDAST.spad" 1605136 1605144 1605407 1605412) (-965 "PRS.spad" 1594698 1594715 1605092 1605097) (-964 "PRQAGG.spad" 1594129 1594139 1594666 1594693) (-963 "PROPLOG.spad" 1593532 1593540 1594119 1594124) (-962 "PROPFRML.spad" 1592340 1592351 1593522 1593527) (-961 "PROPERTY.spad" 1591834 1591842 1592330 1592335) (-960 "PRODUCT.spad" 1589514 1589526 1589800 1589855) (-959 "PR.spad" 1587900 1587912 1588605 1588732) (-958 "PRINT.spad" 1587652 1587660 1587890 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"FORMULA.spad" 645869 645877 648395 648400) (-393 "FORMULA1.spad" 645348 645358 645859 645864) (-392 "FORDER.spad" 645039 645063 645338 645343) (-391 "FOP.spad" 644240 644248 645029 645034) (-390 "FNLA.spad" 643664 643686 644208 644235) (-389 "FNCAT.spad" 642251 642259 643654 643659) (-388 "FNAME.spad" 642143 642151 642241 642246) (-387 "FMTC.spad" 641941 641949 642069 642138) (-386 "FMONOID.spad" 638996 639006 641897 641902) (-385 "FM.spad" 638691 638703 638930 638957) (-384 "FMFUN.spad" 635721 635729 638681 638686) (-383 "FMC.spad" 634773 634781 635711 635716) (-382 "FMCAT.spad" 632427 632445 634741 634768) (-381 "FM1.spad" 631784 631796 632361 632388) (-380 "FLOATRP.spad" 629505 629519 631774 631779) (-379 "FLOAT.spad" 622793 622801 629371 629500) (-378 "FLOATCP.spad" 620210 620224 622783 622788) (-377 "FLINEXP.spad" 619922 619932 620190 620205) (-376 "FLINEXP.spad" 619588 619600 619858 619863) (-375 "FLASORT.spad" 618908 618920 619578 619583) (-374 "FLALG.spad" 616554 616573 618834 618903) (-373 "FLAGG.spad" 613572 613582 616534 616549) (-372 "FLAGG.spad" 610491 610503 613455 613460) (-371 "FLAGG2.spad" 609172 609188 610481 610486) (-370 "FINRALG.spad" 607201 607214 609128 609167) (-369 "FINRALG.spad" 605156 605171 607085 607090) (-368 "FINITE.spad" 604308 604316 605146 605151) (-367 "FINAALG.spad" 593289 593299 604250 604303) (-366 "FINAALG.spad" 582282 582294 593245 593250) (-365 "FILE.spad" 581865 581875 582272 582277) (-364 "FILECAT.spad" 580383 580400 581855 581860) (-363 "FIELD.spad" 579789 579797 580285 580378) (-362 "FIELD.spad" 579281 579291 579779 579784) (-361 "FGROUP.spad" 577890 577900 579261 579276) (-360 "FGLMICPK.spad" 576677 576692 577880 577885) (-359 "FFX.spad" 576052 576067 576393 576486) (-358 "FFSLPE.spad" 575541 575562 576042 576047) (-357 "FFPOLY.spad" 566793 566804 575531 575536) (-356 "FFPOLY2.spad" 565853 565870 566783 566788) (-355 "FFP.spad" 565250 565270 565569 565662) (-354 "FF.spad" 564698 564714 564931 565024) (-353 "FFNBX.spad" 563210 563230 564414 564507) (-352 "FFNBP.spad" 561723 561740 562926 563019) (-351 "FFNB.spad" 560188 560209 561404 561497) (-350 "FFINTBAS.spad" 557602 557621 560178 560183) (-349 "FFIELDC.spad" 555177 555185 557504 557597) (-348 "FFIELDC.spad" 552838 552848 555167 555172) (-347 "FFHOM.spad" 551586 551603 552828 552833) (-346 "FFF.spad" 549021 549032 551576 551581) (-345 "FFCGX.spad" 547868 547888 548737 548830) (-344 "FFCGP.spad" 546757 546777 547584 547677) (-343 "FFCG.spad" 545549 545570 546438 546531) (-342 "FFCAT.spad" 538576 538598 545388 545544) (-341 "FFCAT.spad" 531682 531706 538496 538501) (-340 "FFCAT2.spad" 531427 531467 531672 531677) (-339 "FEXPR.spad" 523136 523182 531183 531222) (-338 "FEVALAB.spad" 522842 522852 523126 523131) (-337 "FEVALAB.spad" 522333 522345 522619 522624) (-336 "FDIV.spad" 521775 521799 522323 522328) (-335 "FDIVCAT.spad" 519817 519841 521765 521770) (-334 "FDIVCAT.spad" 517857 517883 519807 519812) (-333 "FDIV2.spad" 517511 517551 517847 517852) (-332 "FCPAK1.spad" 516064 516072 517501 517506) (-331 "FCOMP.spad" 515443 515453 516054 516059) (-330 "FC.spad" 505358 505366 515433 515438) (-329 "FAXF.spad" 498293 498307 505260 505353) (-328 "FAXF.spad" 491280 491296 498249 498254) (-327 "FARRAY.spad" 489426 489436 490463 490490) (-326 "FAMR.spad" 487546 487558 489324 489421) (-325 "FAMR.spad" 485650 485664 487430 487435) (-324 "FAMONOID.spad" 485300 485310 485604 485609) (-323 "FAMONC.spad" 483522 483534 485290 485295) (-322 "FAGROUP.spad" 483128 483138 483418 483445) (-321 "FACUTIL.spad" 481324 481341 483118 483123) (-320 "FACTFUNC.spad" 480500 480510 481314 481319) (-319 "EXPUPXS.spad" 477333 477356 478632 478781) (-318 "EXPRTUBE.spad" 474561 474569 477323 477328) (-317 "EXPRODE.spad" 471433 471449 474551 474556) (-316 "EXPR.spad" 466708 466718 467422 467829) (-315 "EXPR2UPS.spad" 462800 462813 466698 466703) (-314 "EXPR2.spad" 462503 462515 462790 462795) (-313 "EXPEXPAN.spad" 459441 459466 460075 460168) (-312 "EXIT.spad" 459112 459120 459431 459436) (-311 "EXITAST.spad" 458848 458856 459102 459107) (-310 "EVALCYC.spad" 458306 458320 458838 458843) (-309 "EVALAB.spad" 457870 457880 458296 458301) (-308 "EVALAB.spad" 457432 457444 457860 457865) (-307 "EUCDOM.spad" 454974 454982 457358 457427) (-306 "EUCDOM.spad" 452578 452588 454964 454969) (-305 "ESTOOLS.spad" 444418 444426 452568 452573) (-304 "ESTOOLS2.spad" 444019 444033 444408 444413) (-303 "ESTOOLS1.spad" 443704 443715 444009 444014) (-302 "ES.spad" 436251 436259 443694 443699) (-301 "ES.spad" 428704 428714 436149 436154) (-300 "ESCONT.spad" 425477 425485 428694 428699) (-299 "ESCONT1.spad" 425226 425238 425467 425472) (-298 "ES2.spad" 424721 424737 425216 425221) (-297 "ES1.spad" 424287 424303 424711 424716) (-296 "ERROR.spad" 421608 421616 424277 424282) (-295 "EQTBL.spad" 420080 420102 420289 420316) (-294 "EQ.spad" 414954 414964 417753 417865) (-293 "EQ2.spad" 414670 414682 414944 414949) (-292 "EP.spad" 410984 410994 414660 414665) (-291 "ENV.spad" 409660 409668 410974 410979) (-290 "ENTIRER.spad" 409328 409336 409604 409655) (-289 "EMR.spad" 408529 408570 409254 409323) (-288 "ELTAGG.spad" 406769 406788 408519 408524) (-287 "ELTAGG.spad" 404973 404994 406725 406730) (-286 "ELTAB.spad" 404420 404438 404963 404968) (-285 "ELFUTS.spad" 403799 403818 404410 404415) (-284 "ELEMFUN.spad" 403488 403496 403789 403794) (-283 "ELEMFUN.spad" 403175 403185 403478 403483) (-282 "ELAGG.spad" 401118 401128 403155 403170) (-281 "ELAGG.spad" 398998 399010 401037 401042) (-280 "ELABEXPR.spad" 397921 397929 398988 398993) (-279 "EFUPXS.spad" 394697 394727 397877 397882) (-278 "EFULS.spad" 391533 391556 394653 394658) (-277 "EFSTRUC.spad" 389488 389504 391523 391528) (-276 "EF.spad" 384254 384270 389478 389483) (-275 "EAB.spad" 382530 382538 384244 384249) (-274 "E04UCFA.spad" 382066 382074 382520 382525) (-273 "E04NAFA.spad" 381643 381651 382056 382061) (-272 "E04MBFA.spad" 381223 381231 381633 381638) (-271 "E04JAFA.spad" 380759 380767 381213 381218) (-270 "E04GCFA.spad" 380295 380303 380749 380754) (-269 "E04FDFA.spad" 379831 379839 380285 380290) (-268 "E04DGFA.spad" 379367 379375 379821 379826) (-267 "E04AGNT.spad" 375209 375217 379357 379362) (-266 "DVARCAT.spad" 371894 371904 375199 375204) (-265 "DVARCAT.spad" 368577 368589 371884 371889) (-264 "DSMP.spad" 366008 366022 366313 366440) (-263 "DROPT.spad" 359953 359961 365998 366003) (-262 "DROPT1.spad" 359616 359626 359943 359948) (-261 "DROPT0.spad" 354443 354451 359606 359611) (-260 "DRAWPT.spad" 352598 352606 354433 354438) (-259 "DRAW.spad" 345198 345211 352588 352593) (-258 "DRAWHACK.spad" 344506 344516 345188 345193) (-257 "DRAWCX.spad" 341948 341956 344496 344501) (-256 "DRAWCURV.spad" 341485 341500 341938 341943) (-255 "DRAWCFUN.spad" 330657 330665 341475 341480) (-254 "DQAGG.spad" 328825 328835 330625 330652) (-253 "DPOLCAT.spad" 324166 324182 328693 328820) (-252 "DPOLCAT.spad" 319593 319611 324122 324127) (-251 "DPMO.spad" 311819 311835 311957 312258) (-250 "DPMM.spad" 304058 304076 304183 304484) (-249 "DOMCTOR.spad" 303950 303958 304048 304053) (-248 "DOMAIN.spad" 303081 303089 303940 303945) (-247 "DMP.spad" 300303 300318 300875 301002) (-246 "DLP.spad" 299651 299661 300293 300298) (-245 "DLIST.spad" 298230 298240 298834 298861) (-244 "DLAGG.spad" 296641 296651 298220 298225) (-243 "DIVRING.spad" 296183 296191 296585 296636) (-242 "DIVRING.spad" 295769 295779 296173 296178) (-241 "DISPLAY.spad" 293949 293957 295759 295764) (-240 "DIRPROD.spad" 283529 283545 284169 284300) (-239 "DIRPROD2.spad" 282337 282355 283519 283524) (-238 "DIRPCAT.spad" 281279 281295 282201 282332) (-237 "DIRPCAT.spad" 279950 279968 280874 280879) (-236 "DIOSP.spad" 278775 278783 279940 279945) (-235 "DIOPS.spad" 277759 277769 278755 278770) (-234 "DIOPS.spad" 276717 276729 277715 277720) (-233 "DIFRING.spad" 276009 276017 276697 276712) (-232 "DIFRING.spad" 275309 275319 275999 276004) (-231 "DIFEXT.spad" 274468 274478 275289 275304) (-230 "DIFEXT.spad" 273544 273556 274367 274372) (-229 "DIAGG.spad" 273174 273184 273524 273539) (-228 "DIAGG.spad" 272812 272824 273164 273169) (-227 "DHMATRIX.spad" 271116 271126 272269 272296) (-226 "DFSFUN.spad" 264524 264532 271106 271111) (-225 "DFLOAT.spad" 261245 261253 264414 264519) (-224 "DFINTTLS.spad" 259454 259470 261235 261240) (-223 "DERHAM.spad" 257364 257396 259434 259449) (-222 "DEQUEUE.spad" 256682 256692 256971 256998) (-221 "DEGRED.spad" 256297 256311 256672 256677) (-220 "DEFINTRF.spad" 253822 253832 256287 256292) (-219 "DEFINTEF.spad" 252318 252334 253812 253817) (-218 "DEFAST.spad" 251686 251694 252308 252313) (-217 "DECIMAL.spad" 249792 249800 250153 250246) (-216 "DDFACT.spad" 247591 247608 249782 249787) (-215 "DBLRESP.spad" 247189 247213 247581 247586) (-214 "DBASE.spad" 245843 245853 247179 247184) (-213 "DATAARY.spad" 245305 245318 245833 245838) (-212 "D03FAFA.spad" 245133 245141 245295 245300) (-211 "D03EEFA.spad" 244953 244961 245123 245128) (-210 "D03AGNT.spad" 244033 244041 244943 244948) (-209 "D02EJFA.spad" 243495 243503 244023 244028) (-208 "D02CJFA.spad" 242973 242981 243485 243490) (-207 "D02BHFA.spad" 242463 242471 242963 242968) (-206 "D02BBFA.spad" 241953 241961 242453 242458) (-205 "D02AGNT.spad" 236757 236765 241943 241948) (-204 "D01WGTS.spad" 235076 235084 236747 236752) (-203 "D01TRNS.spad" 235053 235061 235066 235071) (-202 "D01GBFA.spad" 234575 234583 235043 235048) (-201 "D01FCFA.spad" 234097 234105 234565 234570) (-200 "D01ASFA.spad" 233565 233573 234087 234092) (-199 "D01AQFA.spad" 233011 233019 233555 233560) (-198 "D01APFA.spad" 232435 232443 233001 233006) (-197 "D01ANFA.spad" 231929 231937 232425 232430) (-196 "D01AMFA.spad" 231439 231447 231919 231924) (-195 "D01ALFA.spad" 230979 230987 231429 231434) (-194 "D01AKFA.spad" 230505 230513 230969 230974) (-193 "D01AJFA.spad" 230028 230036 230495 230500) (-192 "D01AGNT.spad" 226087 226095 230018 230023) (-191 "CYCLOTOM.spad" 225593 225601 226077 226082) (-190 "CYCLES.spad" 222425 222433 225583 225588) (-189 "CVMP.spad" 221842 221852 222415 222420) (-188 "CTRIGMNP.spad" 220332 220348 221832 221837) (-187 "CTOR.spad" 220023 220031 220322 220327) (-186 "CTORKIND.spad" 219626 219634 220013 220018) (-185 "CTORCAT.spad" 218875 218883 219616 219621) (-184 "CTORCAT.spad" 218122 218132 218865 218870) (-183 "CTORCALL.spad" 217702 217710 218112 218117) (-182 "CSTTOOLS.spad" 216945 216958 217692 217697) (-181 "CRFP.spad" 210649 210662 216935 216940) (-180 "CRCEAST.spad" 210369 210377 210639 210644) (-179 "CRAPACK.spad" 209412 209422 210359 210364) (-178 "CPMATCH.spad" 208912 208927 209337 209342) (-177 "CPIMA.spad" 208617 208636 208902 208907) (-176 "COORDSYS.spad" 203510 203520 208607 208612) (-175 "CONTOUR.spad" 202921 202929 203500 203505) (-174 "CONTFRAC.spad" 198533 198543 202823 202916) (-173 "CONDUIT.spad" 198291 198299 198523 198528) (-172 "COMRING.spad" 197965 197973 198229 198286) (-171 "COMPPROP.spad" 197479 197487 197955 197960) (-170 "COMPLPAT.spad" 197246 197261 197469 197474) (-169 "COMPLEX.spad" 191270 191280 191514 191775) (-168 "COMPLEX2.spad" 190983 190995 191260 191265) (-167 "COMPFACT.spad" 190585 190599 190973 190978) (-166 "COMPCAT.spad" 188653 188663 190319 190580) (-165 "COMPCAT.spad" 186414 186426 188082 188087) (-164 "COMMUPC.spad" 186160 186178 186404 186409) (-163 "COMMONOP.spad" 185693 185701 186150 186155) (-162 "COMM.spad" 185502 185510 185683 185688) (-161 "COMMAAST.spad" 185265 185273 185492 185497) (-160 "COMBOPC.spad" 184170 184178 185255 185260) (-159 "COMBINAT.spad" 182915 182925 184160 184165) (-158 "COMBF.spad" 180283 180299 182905 182910) (-157 "COLOR.spad" 179120 179128 180273 180278) (-156 "COLONAST.spad" 178786 178794 179110 179115) (-155 "CMPLXRT.spad" 178495 178512 178776 178781) (-154 "CLLCTAST.spad" 178157 178165 178485 178490) (-153 "CLIP.spad" 174249 174257 178147 178152) (-152 "CLIF.spad" 172888 172904 174205 174244) (-151 "CLAGG.spad" 169373 169383 172878 172883) (-150 "CLAGG.spad" 165729 165741 169236 169241) (-149 "CINTSLPE.spad" 165054 165067 165719 165724) (-148 "CHVAR.spad" 163132 163154 165044 165049) (-147 "CHARZ.spad" 163047 163055 163112 163127) (-146 "CHARPOL.spad" 162555 162565 163037 163042) (-145 "CHARNZ.spad" 162308 162316 162535 162550) (-144 "CHAR.spad" 160176 160184 162298 162303) (-143 "CFCAT.spad" 159492 159500 160166 160171) (-142 "CDEN.spad" 158650 158664 159482 159487) (-141 "CCLASS.spad" 156799 156807 158061 158100) (-140 "CATEGORY.spad" 155889 155897 156789 156794) (-139 "CATCTOR.spad" 155780 155788 155879 155884) (-138 "CATAST.spad" 155398 155406 155770 155775) (-137 "CASEAST.spad" 155112 155120 155388 155393) (-136 "CARTEN.spad" 150215 150239 155102 155107) (-135 "CARTEN2.spad" 149601 149628 150205 150210) (-134 "CARD.spad" 146890 146898 149575 149596) (-133 "CAPSLAST.spad" 146664 146672 146880 146885) (-132 "CACHSET.spad" 146286 146294 146654 146659) (-131 "CABMON.spad" 145839 145847 146276 146281) (-130 "BYTEORD.spad" 145514 145522 145829 145834) (-129 "BYTE.spad" 144939 144947 145504 145509) (-128 "BYTEBUF.spad" 142796 142804 144108 144135) (-127 "BTREE.spad" 141865 141875 142403 142430) (-126 "BTOURN.spad" 140868 140878 141472 141499) (-125 "BTCAT.spad" 140256 140266 140836 140863) (-124 "BTCAT.spad" 139664 139676 140246 140251) (-123 "BTAGG.spad" 138786 138794 139632 139659) (-122 "BTAGG.spad" 137928 137938 138776 138781) (-121 "BSTREE.spad" 136663 136673 137535 137562) (-120 "BRILL.spad" 134858 134869 136653 136658) (-119 "BRAGG.spad" 133782 133792 134848 134853) (-118 "BRAGG.spad" 132670 132682 133738 133743) (-117 "BPADICRT.spad" 130651 130663 130906 130999) (-116 "BPADIC.spad" 130315 130327 130577 130646) (-115 "BOUNDZRO.spad" 129971 129988 130305 130310) (-114 "BOP.spad" 124996 125004 129961 129966) (-113 "BOP1.spad" 122382 122392 124952 124957) (-112 "BOOLEAN.spad" 121706 121714 122372 122377) (-111 "BMODULE.spad" 121418 121430 121674 121701) (-110 "BITS.spad" 120837 120845 121054 121081) (-109 "BINDING.spad" 120256 120264 120827 120832) (-108 "BINARY.spad" 118367 118375 118723 118816) (-107 "BGAGG.spad" 117564 117574 118347 118362) (-106 "BGAGG.spad" 116769 116781 117554 117559) (-105 "BFUNCT.spad" 116333 116341 116749 116764) (-104 "BEZOUT.spad" 115467 115494 116283 116288) (-103 "BBTREE.spad" 112286 112296 115074 115101) (-102 "BASTYPE.spad" 111958 111966 112276 112281) (-101 "BASTYPE.spad" 111628 111638 111948 111953) (-100 "BALFACT.spad" 111067 111080 111618 111623) (-99 "AUTOMOR.spad" 110514 110523 111047 111062) (-98 "ATTREG.spad" 107233 107240 110266 110509) (-97 "ATTRBUT.spad" 103256 103263 107213 107228) (-96 "ATTRAST.spad" 102973 102980 103246 103251) (-95 "ATRIG.spad" 102443 102450 102963 102968) (-94 "ATRIG.spad" 101911 101920 102433 102438) (-93 "ASTCAT.spad" 101815 101822 101901 101906) (-92 "ASTCAT.spad" 101717 101726 101805 101810) (-91 "ASTACK.spad" 101050 101059 101324 101351) (-90 "ASSOCEQ.spad" 99850 99861 101006 101011) (-89 "ASP9.spad" 98931 98944 99840 99845) (-88 "ASP8.spad" 97974 97987 98921 98926) (-87 "ASP80.spad" 97296 97309 97964 97969) (-86 "ASP7.spad" 96456 96469 97286 97291) (-85 "ASP78.spad" 95907 95920 96446 96451) (-84 "ASP77.spad" 95276 95289 95897 95902) (-83 "ASP74.spad" 94368 94381 95266 95271) (-82 "ASP73.spad" 93639 93652 94358 94363) (-81 "ASP6.spad" 92506 92519 93629 93634) (-80 "ASP55.spad" 91015 91028 92496 92501) (-79 "ASP50.spad" 88832 88845 91005 91010) (-78 "ASP4.spad" 88127 88140 88822 88827) (-77 "ASP49.spad" 87126 87139 88117 88122) (-76 "ASP42.spad" 85533 85572 87116 87121) (-75 "ASP41.spad" 84112 84151 85523 85528) (-74 "ASP35.spad" 83100 83113 84102 84107) (-73 "ASP34.spad" 82401 82414 83090 83095) (-72 "ASP33.spad" 81961 81974 82391 82396) (-71 "ASP31.spad" 81101 81114 81951 81956) (-70 "ASP30.spad" 79993 80006 81091 81096) (-69 "ASP29.spad" 79459 79472 79983 79988) (-68 "ASP28.spad" 70732 70745 79449 79454) (-67 "ASP27.spad" 69629 69642 70722 70727) (-66 "ASP24.spad" 68716 68729 69619 69624) (-65 "ASP20.spad" 68180 68193 68706 68711) (-64 "ASP1.spad" 67561 67574 68170 68175) (-63 "ASP19.spad" 62247 62260 67551 67556) (-62 "ASP12.spad" 61661 61674 62237 62242) (-61 "ASP10.spad" 60932 60945 61651 61656) (-60 "ARRAY2.spad" 60292 60301 60539 60566) (-59 "ARRAY1.spad" 59127 59136 59475 59502) (-58 "ARRAY12.spad" 57796 57807 59117 59122) (-57 "ARR2CAT.spad" 53458 53479 57764 57791) (-56 "ARR2CAT.spad" 49140 49163 53448 53453) (-55 "ARITY.spad" 48512 48519 49130 49135) (-54 "APPRULE.spad" 47756 47778 48502 48507) (-53 "APPLYORE.spad" 47371 47384 47746 47751) (-52 "ANY.spad" 45713 45720 47361 47366) (-51 "ANY1.spad" 44784 44793 45703 45708) (-50 "ANTISYM.spad" 43223 43239 44764 44779) (-49 "ANON.spad" 42916 42923 43213 43218) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 28845 28859 29646 29651) (-41 "ALGMANIP.spad" 26265 26280 28642 28647) (-40 "ALGFF.spad" 24580 24607 24797 24953) (-39 "ALGFACT.spad" 23701 23711 24570 24575) (-38 "ALGEBRA.spad" 23534 23543 23657 23696) (-37 "ALGEBRA.spad" 23399 23410 23524 23529) (-36 "ALAGG.spad" 22909 22930 23367 23394) (-35 "AHYP.spad" 22290 22297 22899 22904) (-34 "AGG.spad" 20599 20606 22280 22285) (-33 "AGG.spad" 18872 18881 20555 20560) (-32 "AF.spad" 17297 17312 18807 18812) (-31 "ADDAST.spad" 16975 16982 17287 17292) (-30 "ACPLOT.spad" 15546 15553 16965 16970) (-29 "ACFS.spad" 13297 13306 15448 15541) (-28 "ACFS.spad" 11134 11145 13287 13292) (-27 "ACF.spad" 7736 7743 11036 11129) (-26 "ACF.spad" 4424 4433 7726 7731) (-25 "ABELSG.spad" 3965 3972 4414 4419) (-24 "ABELSG.spad" 3504 3513 3955 3960) (-23 "ABELMON.spad" 3047 3054 3494 3499) (-22 "ABELMON.spad" 2588 2597 3037 3042) (-21 "ABELGRP.spad" 2160 2167 2578 2583) (-20 "ABELGRP.spad" 1730 1739 2150 2155) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2283410 2283415 2283420 2283425) (-2 NIL 2283390 2283395 2283400 2283405) (-1 NIL 2283370 2283375 2283380 2283385) (0 NIL 2283350 2283355 2283360 2283365) (-1287 "ZMOD.spad" 2283159 2283172 2283288 2283345) (-1286 "ZLINDEP.spad" 2282203 2282214 2283149 2283154) (-1285 "ZDSOLVE.spad" 2272052 2272074 2282193 2282198) (-1284 "YSTREAM.spad" 2271545 2271556 2272042 2272047) (-1283 "XRPOLY.spad" 2270765 2270785 2271401 2271470) (-1282 "XPR.spad" 2268556 2268569 2270483 2270582) (-1281 "XPOLY.spad" 2268111 2268122 2268412 2268481) (-1280 "XPOLYC.spad" 2267428 2267444 2268037 2268106) (-1279 "XPBWPOLY.spad" 2265865 2265885 2267208 2267277) (-1278 "XF.spad" 2264326 2264341 2265767 2265860) (-1277 "XF.spad" 2262767 2262784 2264210 2264215) (-1276 "XFALG.spad" 2259791 2259807 2262693 2262762) (-1275 "XEXPPKG.spad" 2259042 2259068 2259781 2259786) (-1274 "XDPOLY.spad" 2258656 2258672 2258898 2258967) (-1273 "XALG.spad" 2258316 2258327 2258612 2258651) (-1272 "WUTSET.spad" 2254155 2254172 2257962 2257989) (-1271 "WP.spad" 2253354 2253398 2254013 2254080) (-1270 "WHILEAST.spad" 2253152 2253161 2253344 2253349) (-1269 "WHEREAST.spad" 2252823 2252832 2253142 2253147) (-1268 "WFFINTBS.spad" 2250386 2250408 2252813 2252818) (-1267 "WEIER.spad" 2248600 2248611 2250376 2250381) (-1266 "VSPACE.spad" 2248273 2248284 2248568 2248595) (-1265 "VSPACE.spad" 2247966 2247979 2248263 2248268) (-1264 "VOID.spad" 2247643 2247652 2247956 2247961) (-1263 "VIEW.spad" 2245265 2245274 2247633 2247638) (-1262 "VIEWDEF.spad" 2240462 2240471 2245255 2245260) (-1261 "VIEW3D.spad" 2224297 2224306 2240452 2240457) (-1260 "VIEW2D.spad" 2212034 2212043 2224287 2224292) (-1259 "VECTOR.spad" 2210709 2210720 2210960 2210987) (-1258 "VECTOR2.spad" 2209336 2209349 2210699 2210704) (-1257 "VECTCAT.spad" 2207236 2207247 2209304 2209331) (-1256 "VECTCAT.spad" 2204944 2204957 2207014 2207019) (-1255 "VARIABLE.spad" 2204724 2204739 2204934 2204939) (-1254 "UTYPE.spad" 2204368 2204377 2204714 2204719) (-1253 "UTSODETL.spad" 2203661 2203685 2204324 2204329) (-1252 "UTSODE.spad" 2201849 2201869 2203651 2203656) (-1251 "UTS.spad" 2196638 2196666 2200316 2200413) (-1250 "UTSCAT.spad" 2194089 2194105 2196536 2196633) (-1249 "UTSCAT.spad" 2191184 2191202 2193633 2193638) (-1248 "UTS2.spad" 2190777 2190812 2191174 2191179) (-1247 "URAGG.spad" 2185409 2185420 2190767 2190772) (-1246 "URAGG.spad" 2180005 2180018 2185365 2185370) (-1245 "UPXSSING.spad" 2177648 2177674 2179086 2179219) (-1244 "UPXS.spad" 2174796 2174824 2175780 2175929) (-1243 "UPXSCONS.spad" 2172553 2172573 2172928 2173077) (-1242 "UPXSCCA.spad" 2171118 2171138 2172399 2172548) (-1241 "UPXSCCA.spad" 2169825 2169847 2171108 2171113) (-1240 "UPXSCAT.spad" 2168406 2168422 2169671 2169820) (-1239 "UPXS2.spad" 2167947 2168000 2168396 2168401) (-1238 "UPSQFREE.spad" 2166359 2166373 2167937 2167942) (-1237 "UPSCAT.spad" 2163952 2163976 2166257 2166354) (-1236 "UPSCAT.spad" 2161251 2161277 2163558 2163563) (-1235 "UPOLYC.spad" 2156229 2156240 2161093 2161246) (-1234 "UPOLYC.spad" 2151099 2151112 2155965 2155970) (-1233 "UPOLYC2.spad" 2150568 2150587 2151089 2151094) (-1232 "UP.spad" 2147725 2147740 2148118 2148271) (-1231 "UPMP.spad" 2146615 2146628 2147715 2147720) (-1230 "UPDIVP.spad" 2146178 2146192 2146605 2146610) (-1229 "UPDECOMP.spad" 2144415 2144429 2146168 2146173) (-1228 "UPCDEN.spad" 2143622 2143638 2144405 2144410) (-1227 "UP2.spad" 2142984 2143005 2143612 2143617) (-1226 "UNISEG.spad" 2142337 2142348 2142903 2142908) (-1225 "UNISEG2.spad" 2141830 2141843 2142293 2142298) (-1224 "UNIFACT.spad" 2140931 2140943 2141820 2141825) (-1223 "ULS.spad" 2131483 2131511 2132576 2133005) (-1222 "ULSCONS.spad" 2123877 2123897 2124249 2124398) (-1221 "ULSCCAT.spad" 2121606 2121626 2123723 2123872) (-1220 "ULSCCAT.spad" 2119443 2119465 2121562 2121567) (-1219 "ULSCAT.spad" 2117659 2117675 2119289 2119438) (-1218 "ULS2.spad" 2117171 2117224 2117649 2117654) (-1217 "UINT8.spad" 2117048 2117057 2117161 2117166) (-1216 "UINT64.spad" 2116924 2116933 2117038 2117043) (-1215 "UINT32.spad" 2116800 2116809 2116914 2116919) (-1214 "UINT16.spad" 2116676 2116685 2116790 2116795) (-1213 "UFD.spad" 2115741 2115750 2116602 2116671) (-1212 "UFD.spad" 2114868 2114879 2115731 2115736) (-1211 "UDVO.spad" 2113715 2113724 2114858 2114863) (-1210 "UDPO.spad" 2111142 2111153 2113671 2113676) (-1209 "TYPE.spad" 2111074 2111083 2111132 2111137) (-1208 "TYPEAST.spad" 2110993 2111002 2111064 2111069) (-1207 "TWOFACT.spad" 2109643 2109658 2110983 2110988) (-1206 "TUPLE.spad" 2109127 2109138 2109542 2109547) (-1205 "TUBETOOL.spad" 2105964 2105973 2109117 2109122) (-1204 "TUBE.spad" 2104605 2104622 2105954 2105959) (-1203 "TS.spad" 2103194 2103210 2104170 2104267) (-1202 "TSETCAT.spad" 2090321 2090338 2103162 2103189) (-1201 "TSETCAT.spad" 2077434 2077453 2090277 2090282) (-1200 "TRMANIP.spad" 2071800 2071817 2077140 2077145) (-1199 "TRIMAT.spad" 2070759 2070784 2071790 2071795) (-1198 "TRIGMNIP.spad" 2069276 2069293 2070749 2070754) (-1197 "TRIGCAT.spad" 2068788 2068797 2069266 2069271) (-1196 "TRIGCAT.spad" 2068298 2068309 2068778 2068783) (-1195 "TREE.spad" 2066869 2066880 2067905 2067932) (-1194 "TRANFUN.spad" 2066700 2066709 2066859 2066864) (-1193 "TRANFUN.spad" 2066529 2066540 2066690 2066695) (-1192 "TOPSP.spad" 2066203 2066212 2066519 2066524) (-1191 "TOOLSIGN.spad" 2065866 2065877 2066193 2066198) (-1190 "TEXTFILE.spad" 2064423 2064432 2065856 2065861) (-1189 "TEX.spad" 2061555 2061564 2064413 2064418) (-1188 "TEX1.spad" 2061111 2061122 2061545 2061550) (-1187 "TEMUTL.spad" 2060666 2060675 2061101 2061106) (-1186 "TBCMPPK.spad" 2058759 2058782 2060656 2060661) (-1185 "TBAGG.spad" 2057795 2057818 2058739 2058754) (-1184 "TBAGG.spad" 2056839 2056864 2057785 2057790) (-1183 "TANEXP.spad" 2056215 2056226 2056829 2056834) (-1182 "TABLE.spad" 2054626 2054649 2054896 2054923) (-1181 "TABLEAU.spad" 2054107 2054118 2054616 2054621) (-1180 "TABLBUMP.spad" 2050890 2050901 2054097 2054102) (-1179 "SYSTEM.spad" 2050118 2050127 2050880 2050885) (-1178 "SYSSOLP.spad" 2047591 2047602 2050108 2050113) (-1177 "SYSNNI.spad" 2046771 2046782 2047581 2047586) (-1176 "SYSINT.spad" 2046175 2046186 2046761 2046766) (-1175 "SYNTAX.spad" 2042369 2042378 2046165 2046170) (-1174 "SYMTAB.spad" 2040425 2040434 2042359 2042364) (-1173 "SYMS.spad" 2036410 2036419 2040415 2040420) (-1172 "SYMPOLY.spad" 2035417 2035428 2035499 2035626) (-1171 "SYMFUNC.spad" 2034892 2034903 2035407 2035412) (-1170 "SYMBOL.spad" 2032319 2032328 2034882 2034887) (-1169 "SWITCH.spad" 2029076 2029085 2032309 2032314) (-1168 "SUTS.spad" 2025975 2026003 2027543 2027640) (-1167 "SUPXS.spad" 2023110 2023138 2024107 2024256) (-1166 "SUP.spad" 2019879 2019890 2020660 2020813) (-1165 "SUPFRACF.spad" 2018984 2019002 2019869 2019874) (-1164 "SUP2.spad" 2018374 2018387 2018974 2018979) (-1163 "SUMRF.spad" 2017340 2017351 2018364 2018369) (-1162 "SUMFS.spad" 2016973 2016990 2017330 2017335) (-1161 "SULS.spad" 2007512 2007540 2008618 2009047) (-1160 "SUCHTAST.spad" 2007281 2007290 2007502 2007507) (-1159 "SUCH.spad" 2006961 2006976 2007271 2007276) (-1158 "SUBSPACE.spad" 1998968 1998983 2006951 2006956) (-1157 "SUBRESP.spad" 1998128 1998142 1998924 1998929) (-1156 "STTF.spad" 1994227 1994243 1998118 1998123) (-1155 "STTFNC.spad" 1990695 1990711 1994217 1994222) (-1154 "STTAYLOR.spad" 1983093 1983104 1990576 1990581) (-1153 "STRTBL.spad" 1981598 1981615 1981747 1981774) (-1152 "STRING.spad" 1981007 1981016 1981021 1981048) (-1151 "STRICAT.spad" 1980795 1980804 1980975 1981002) (-1150 "STREAM.spad" 1977653 1977664 1980320 1980335) (-1149 "STREAM3.spad" 1977198 1977213 1977643 1977648) (-1148 "STREAM2.spad" 1976266 1976279 1977188 1977193) (-1147 "STREAM1.spad" 1975970 1975981 1976256 1976261) (-1146 "STINPROD.spad" 1974876 1974892 1975960 1975965) (-1145 "STEP.spad" 1974077 1974086 1974866 1974871) (-1144 "STBL.spad" 1972603 1972631 1972770 1972785) (-1143 "STAGG.spad" 1971678 1971689 1972593 1972598) (-1142 "STAGG.spad" 1970751 1970764 1971668 1971673) (-1141 "STACK.spad" 1970102 1970113 1970358 1970385) (-1140 "SREGSET.spad" 1967806 1967823 1969748 1969775) (-1139 "SRDCMPK.spad" 1966351 1966371 1967796 1967801) (-1138 "SRAGG.spad" 1961448 1961457 1966319 1966346) (-1137 "SRAGG.spad" 1956565 1956576 1961438 1961443) (-1136 "SQMATRIX.spad" 1954181 1954199 1955097 1955184) (-1135 "SPLTREE.spad" 1948733 1948746 1953617 1953644) (-1134 "SPLNODE.spad" 1945321 1945334 1948723 1948728) (-1133 "SPFCAT.spad" 1944098 1944107 1945311 1945316) (-1132 "SPECOUT.spad" 1942648 1942657 1944088 1944093) (-1131 "SPADXPT.spad" 1934787 1934796 1942638 1942643) (-1130 "spad-parser.spad" 1934252 1934261 1934777 1934782) (-1129 "SPADAST.spad" 1933953 1933962 1934242 1934247) (-1128 "SPACEC.spad" 1917966 1917977 1933943 1933948) (-1127 "SPACE3.spad" 1917742 1917753 1917956 1917961) (-1126 "SORTPAK.spad" 1917287 1917300 1917698 1917703) (-1125 "SOLVETRA.spad" 1915044 1915055 1917277 1917282) (-1124 "SOLVESER.spad" 1913564 1913575 1915034 1915039) (-1123 "SOLVERAD.spad" 1909574 1909585 1913554 1913559) (-1122 "SOLVEFOR.spad" 1907994 1908012 1909564 1909569) (-1121 "SNTSCAT.spad" 1907594 1907611 1907962 1907989) (-1120 "SMTS.spad" 1905854 1905880 1907159 1907256) (-1119 "SMP.spad" 1903293 1903313 1903683 1903810) (-1118 "SMITH.spad" 1902136 1902161 1903283 1903288) (-1117 "SMATCAT.spad" 1900246 1900276 1902080 1902131) (-1116 "SMATCAT.spad" 1898288 1898320 1900124 1900129) (-1115 "SKAGG.spad" 1897249 1897260 1898256 1898283) (-1114 "SINT.spad" 1896075 1896084 1897115 1897244) (-1113 "SIMPAN.spad" 1895803 1895812 1896065 1896070) (-1112 "SIG.spad" 1895131 1895140 1895793 1895798) (-1111 "SIGNRF.spad" 1894239 1894250 1895121 1895126) (-1110 "SIGNEF.spad" 1893508 1893525 1894229 1894234) (-1109 "SIGAST.spad" 1892889 1892898 1893498 1893503) (-1108 "SHP.spad" 1890807 1890822 1892845 1892850) (-1107 "SHDP.spad" 1880518 1880545 1881027 1881158) (-1106 "SGROUP.spad" 1880126 1880135 1880508 1880513) (-1105 "SGROUP.spad" 1879732 1879743 1880116 1880121) (-1104 "SGCF.spad" 1872613 1872622 1879722 1879727) (-1103 "SFRTCAT.spad" 1871541 1871558 1872581 1872608) (-1102 "SFRGCD.spad" 1870604 1870624 1871531 1871536) (-1101 "SFQCMPK.spad" 1865241 1865261 1870594 1870599) (-1100 "SFORT.spad" 1864676 1864690 1865231 1865236) (-1099 "SEXOF.spad" 1864519 1864559 1864666 1864671) (-1098 "SEX.spad" 1864411 1864420 1864509 1864514) (-1097 "SEXCAT.spad" 1861962 1862002 1864401 1864406) (-1096 "SET.spad" 1860262 1860273 1861383 1861422) (-1095 "SETMN.spad" 1858696 1858713 1860252 1860257) (-1094 "SETCAT.spad" 1858181 1858190 1858686 1858691) (-1093 "SETCAT.spad" 1857664 1857675 1858171 1858176) (-1092 "SETAGG.spad" 1854185 1854196 1857644 1857659) (-1091 "SETAGG.spad" 1850714 1850727 1854175 1854180) (-1090 "SEQAST.spad" 1850417 1850426 1850704 1850709) (-1089 "SEGXCAT.spad" 1849539 1849552 1850407 1850412) (-1088 "SEG.spad" 1849352 1849363 1849458 1849463) (-1087 "SEGCAT.spad" 1848259 1848270 1849342 1849347) (-1086 "SEGBIND.spad" 1847331 1847342 1848214 1848219) (-1085 "SEGBIND2.spad" 1847027 1847040 1847321 1847326) (-1084 "SEGAST.spad" 1846741 1846750 1847017 1847022) (-1083 "SEG2.spad" 1846166 1846179 1846697 1846702) (-1082 "SDVAR.spad" 1845442 1845453 1846156 1846161) (-1081 "SDPOL.spad" 1842832 1842843 1843123 1843250) (-1080 "SCPKG.spad" 1840911 1840922 1842822 1842827) (-1079 "SCOPE.spad" 1840064 1840073 1840901 1840906) (-1078 "SCACHE.spad" 1838746 1838757 1840054 1840059) (-1077 "SASTCAT.spad" 1838655 1838664 1838736 1838741) (-1076 "SAOS.spad" 1838527 1838536 1838645 1838650) (-1075 "SAERFFC.spad" 1838240 1838260 1838517 1838522) (-1074 "SAE.spad" 1836415 1836431 1837026 1837161) (-1073 "SAEFACT.spad" 1836116 1836136 1836405 1836410) (-1072 "RURPK.spad" 1833757 1833773 1836106 1836111) (-1071 "RULESET.spad" 1833198 1833222 1833747 1833752) (-1070 "RULE.spad" 1831402 1831426 1833188 1833193) (-1069 "RULECOLD.spad" 1831254 1831267 1831392 1831397) (-1068 "RTVALUE.spad" 1830987 1830996 1831244 1831249) (-1067 "RSTRCAST.spad" 1830704 1830713 1830977 1830982) (-1066 "RSETGCD.spad" 1827082 1827102 1830694 1830699) (-1065 "RSETCAT.spad" 1816866 1816883 1827050 1827077) (-1064 "RSETCAT.spad" 1806670 1806689 1816856 1816861) (-1063 "RSDCMPK.spad" 1805122 1805142 1806660 1806665) (-1062 "RRCC.spad" 1803506 1803536 1805112 1805117) (-1061 "RRCC.spad" 1801888 1801920 1803496 1803501) (-1060 "RPTAST.spad" 1801590 1801599 1801878 1801883) (-1059 "RPOLCAT.spad" 1780950 1780965 1801458 1801585) (-1058 "RPOLCAT.spad" 1760024 1760041 1780534 1780539) (-1057 "ROUTINE.spad" 1755887 1755896 1758671 1758698) (-1056 "ROMAN.spad" 1755215 1755224 1755753 1755882) (-1055 "ROIRC.spad" 1754295 1754327 1755205 1755210) (-1054 "RNS.spad" 1753198 1753207 1754197 1754290) (-1053 "RNS.spad" 1752187 1752198 1753188 1753193) (-1052 "RNG.spad" 1751922 1751931 1752177 1752182) (-1051 "RMODULE.spad" 1751560 1751571 1751912 1751917) (-1050 "RMCAT2.spad" 1750968 1751025 1751550 1751555) (-1049 "RMATRIX.spad" 1749792 1749811 1750135 1750174) (-1048 "RMATCAT.spad" 1745325 1745356 1749748 1749787) (-1047 "RMATCAT.spad" 1740748 1740781 1745173 1745178) (-1046 "RINTERP.spad" 1740636 1740656 1740738 1740743) (-1045 "RING.spad" 1740106 1740115 1740616 1740631) (-1044 "RING.spad" 1739584 1739595 1740096 1740101) (-1043 "RIDIST.spad" 1738968 1738977 1739574 1739579) (-1042 "RGCHAIN.spad" 1737547 1737563 1738453 1738480) (-1041 "RGBCSPC.spad" 1737328 1737340 1737537 1737542) (-1040 "RGBCMDL.spad" 1736858 1736870 1737318 1737323) (-1039 "RF.spad" 1734472 1734483 1736848 1736853) (-1038 "RFFACTOR.spad" 1733934 1733945 1734462 1734467) (-1037 "RFFACT.spad" 1733669 1733681 1733924 1733929) (-1036 "RFDIST.spad" 1732657 1732666 1733659 1733664) (-1035 "RETSOL.spad" 1732074 1732087 1732647 1732652) (-1034 "RETRACT.spad" 1731502 1731513 1732064 1732069) (-1033 "RETRACT.spad" 1730928 1730941 1731492 1731497) (-1032 "RETAST.spad" 1730740 1730749 1730918 1730923) (-1031 "RESULT.spad" 1728800 1728809 1729387 1729414) (-1030 "RESRING.spad" 1728147 1728194 1728738 1728795) (-1029 "RESLATC.spad" 1727471 1727482 1728137 1728142) (-1028 "REPSQ.spad" 1727200 1727211 1727461 1727466) (-1027 "REP.spad" 1724752 1724761 1727190 1727195) (-1026 "REPDB.spad" 1724457 1724468 1724742 1724747) (-1025 "REP2.spad" 1714029 1714040 1724299 1724304) (-1024 "REP1.spad" 1708019 1708030 1713979 1713984) (-1023 "REGSET.spad" 1705816 1705833 1707665 1707692) (-1022 "REF.spad" 1705145 1705156 1705771 1705776) (-1021 "REDORDER.spad" 1704321 1704338 1705135 1705140) (-1020 "RECLOS.spad" 1703104 1703124 1703808 1703901) (-1019 "REALSOLV.spad" 1702236 1702245 1703094 1703099) (-1018 "REAL.spad" 1702108 1702117 1702226 1702231) (-1017 "REAL0Q.spad" 1699390 1699405 1702098 1702103) (-1016 "REAL0.spad" 1696218 1696233 1699380 1699385) (-1015 "RDUCEAST.spad" 1695939 1695948 1696208 1696213) (-1014 "RDIV.spad" 1695590 1695615 1695929 1695934) (-1013 "RDIST.spad" 1695153 1695164 1695580 1695585) (-1012 "RDETRS.spad" 1693949 1693967 1695143 1695148) (-1011 "RDETR.spad" 1692056 1692074 1693939 1693944) (-1010 "RDEEFS.spad" 1691129 1691146 1692046 1692051) (-1009 "RDEEF.spad" 1690125 1690142 1691119 1691124) (-1008 "RCFIELD.spad" 1687311 1687320 1690027 1690120) (-1007 "RCFIELD.spad" 1684583 1684594 1687301 1687306) (-1006 "RCAGG.spad" 1682495 1682506 1684573 1684578) (-1005 "RCAGG.spad" 1680334 1680347 1682414 1682419) (-1004 "RATRET.spad" 1679694 1679705 1680324 1680329) (-1003 "RATFACT.spad" 1679386 1679398 1679684 1679689) (-1002 "RANDSRC.spad" 1678705 1678714 1679376 1679381) (-1001 "RADUTIL.spad" 1678459 1678468 1678695 1678700) (-1000 "RADIX.spad" 1675360 1675374 1676926 1677019) (-999 "RADFF.spad" 1673774 1673810 1673892 1674048) (-998 "RADCAT.spad" 1673368 1673376 1673764 1673769) (-997 "RADCAT.spad" 1672960 1672970 1673358 1673363) (-996 "QUEUE.spad" 1672303 1672313 1672567 1672594) (-995 "QUAT.spad" 1670885 1670895 1671227 1671292) (-994 "QUATCT2.spad" 1670504 1670522 1670875 1670880) (-993 "QUATCAT.spad" 1668669 1668679 1670434 1670499) (-992 "QUATCAT.spad" 1666585 1666597 1668352 1668357) (-991 "QUAGG.spad" 1665411 1665421 1666553 1666580) (-990 "QQUTAST.spad" 1665180 1665188 1665401 1665406) (-989 "QFORM.spad" 1664643 1664657 1665170 1665175) (-988 "QFCAT.spad" 1663346 1663356 1664545 1664638) (-987 "QFCAT.spad" 1661640 1661652 1662841 1662846) (-986 "QFCAT2.spad" 1661331 1661347 1661630 1661635) (-985 "QEQUAT.spad" 1660888 1660896 1661321 1661326) (-984 "QCMPACK.spad" 1655635 1655654 1660878 1660883) (-983 "QALGSET.spad" 1651710 1651742 1655549 1655554) (-982 "QALGSET2.spad" 1649706 1649724 1651700 1651705) (-981 "PWFFINTB.spad" 1647016 1647037 1649696 1649701) (-980 "PUSHVAR.spad" 1646345 1646364 1647006 1647011) (-979 "PTRANFN.spad" 1642471 1642481 1646335 1646340) (-978 "PTPACK.spad" 1639559 1639569 1642461 1642466) (-977 "PTFUNC2.spad" 1639380 1639394 1639549 1639554) (-976 "PTCAT.spad" 1638629 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(-826 "OMSAGG.spad" 1377288 1377298 1377456 1377495) (-825 "OMPKG.spad" 1375900 1375908 1377278 1377283) (-824 "OM.spad" 1374865 1374873 1375890 1375895) (-823 "OMLO.spad" 1374290 1374302 1374751 1374790) (-822 "OMEXPR.spad" 1374124 1374134 1374280 1374285) (-821 "OMERR.spad" 1373667 1373675 1374114 1374119) (-820 "OMERRK.spad" 1372701 1372709 1373657 1373662) (-819 "OMENC.spad" 1372045 1372053 1372691 1372696) (-818 "OMDEV.spad" 1366334 1366342 1372035 1372040) (-817 "OMCONN.spad" 1365743 1365751 1366324 1366329) (-816 "OINTDOM.spad" 1365506 1365514 1365669 1365738) (-815 "OFMONOID.spad" 1361693 1361703 1365496 1365501) (-814 "ODVAR.spad" 1360954 1360964 1361683 1361688) (-813 "ODR.spad" 1360598 1360624 1360766 1360915) (-812 "ODPOL.spad" 1357944 1357954 1358284 1358411) (-811 "ODP.spad" 1347791 1347811 1348164 1348295) (-810 "ODETOOLS.spad" 1346374 1346393 1347781 1347786) (-809 "ODESYS.spad" 1344024 1344041 1346364 1346369) (-808 "ODERTRIC.spad" 1339965 1339982 1343981 1343986) 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"FORMULA.spad" 646045 646053 648571 648576) (-393 "FORMULA1.spad" 645524 645534 646035 646040) (-392 "FORDER.spad" 645215 645239 645514 645519) (-391 "FOP.spad" 644416 644424 645205 645210) (-390 "FNLA.spad" 643840 643862 644384 644411) (-389 "FNCAT.spad" 642427 642435 643830 643835) (-388 "FNAME.spad" 642319 642327 642417 642422) (-387 "FMTC.spad" 642117 642125 642245 642314) (-386 "FMONOID.spad" 639172 639182 642073 642078) (-385 "FM.spad" 638867 638879 639106 639133) (-384 "FMFUN.spad" 635897 635905 638857 638862) (-383 "FMC.spad" 634949 634957 635887 635892) (-382 "FMCAT.spad" 632603 632621 634917 634944) (-381 "FM1.spad" 631960 631972 632537 632564) (-380 "FLOATRP.spad" 629681 629695 631950 631955) (-379 "FLOAT.spad" 622969 622977 629547 629676) (-378 "FLOATCP.spad" 620386 620400 622959 622964) (-377 "FLINEXP.spad" 620098 620108 620366 620381) (-376 "FLINEXP.spad" 619764 619776 620034 620039) (-375 "FLASORT.spad" 619084 619096 619754 619759) (-374 "FLALG.spad" 616730 616749 619010 619079) (-373 "FLAGG.spad" 613748 613758 616710 616725) (-372 "FLAGG.spad" 610667 610679 613631 613636) (-371 "FLAGG2.spad" 609348 609364 610657 610662) (-370 "FINRALG.spad" 607377 607390 609304 609343) (-369 "FINRALG.spad" 605332 605347 607261 607266) (-368 "FINITE.spad" 604484 604492 605322 605327) (-367 "FINAALG.spad" 593465 593475 604426 604479) (-366 "FINAALG.spad" 582458 582470 593421 593426) (-365 "FILE.spad" 582041 582051 582448 582453) (-364 "FILECAT.spad" 580559 580576 582031 582036) (-363 "FIELD.spad" 579965 579973 580461 580554) (-362 "FIELD.spad" 579457 579467 579955 579960) (-361 "FGROUP.spad" 578066 578076 579437 579452) (-360 "FGLMICPK.spad" 576853 576868 578056 578061) (-359 "FFX.spad" 576228 576243 576569 576662) (-358 "FFSLPE.spad" 575717 575738 576218 576223) (-357 "FFPOLY.spad" 566969 566980 575707 575712) (-356 "FFPOLY2.spad" 566029 566046 566959 566964) (-355 "FFP.spad" 565426 565446 565745 565838) (-354 "FF.spad" 564874 564890 565107 565200) (-353 "FFNBX.spad" 563386 563406 564590 564683) (-352 "FFNBP.spad" 561899 561916 563102 563195) (-351 "FFNB.spad" 560364 560385 561580 561673) (-350 "FFINTBAS.spad" 557778 557797 560354 560359) (-349 "FFIELDC.spad" 555353 555361 557680 557773) (-348 "FFIELDC.spad" 553014 553024 555343 555348) (-347 "FFHOM.spad" 551762 551779 553004 553009) (-346 "FFF.spad" 549197 549208 551752 551757) (-345 "FFCGX.spad" 548044 548064 548913 549006) (-344 "FFCGP.spad" 546933 546953 547760 547853) (-343 "FFCG.spad" 545725 545746 546614 546707) (-342 "FFCAT.spad" 538752 538774 545564 545720) (-341 "FFCAT.spad" 531858 531882 538672 538677) (-340 "FFCAT2.spad" 531603 531643 531848 531853) (-339 "FEXPR.spad" 523312 523358 531359 531398) (-338 "FEVALAB.spad" 523018 523028 523302 523307) (-337 "FEVALAB.spad" 522509 522521 522795 522800) (-336 "FDIV.spad" 521951 521975 522499 522504) (-335 "FDIVCAT.spad" 519993 520017 521941 521946) (-334 "FDIVCAT.spad" 518033 518059 519983 519988) (-333 "FDIV2.spad" 517687 517727 518023 518028) (-332 "FCPAK1.spad" 516240 516248 517677 517682) (-331 "FCOMP.spad" 515619 515629 516230 516235) (-330 "FC.spad" 505534 505542 515609 515614) (-329 "FAXF.spad" 498469 498483 505436 505529) (-328 "FAXF.spad" 491456 491472 498425 498430) (-327 "FARRAY.spad" 489602 489612 490639 490666) (-326 "FAMR.spad" 487722 487734 489500 489597) (-325 "FAMR.spad" 485826 485840 487606 487611) (-324 "FAMONOID.spad" 485476 485486 485780 485785) (-323 "FAMONC.spad" 483698 483710 485466 485471) (-322 "FAGROUP.spad" 483304 483314 483594 483621) (-321 "FACUTIL.spad" 481500 481517 483294 483299) (-320 "FACTFUNC.spad" 480676 480686 481490 481495) (-319 "EXPUPXS.spad" 477509 477532 478808 478957) (-318 "EXPRTUBE.spad" 474737 474745 477499 477504) (-317 "EXPRODE.spad" 471609 471625 474727 474732) (-316 "EXPR.spad" 466884 466894 467598 468005) (-315 "EXPR2UPS.spad" 462976 462989 466874 466879) (-314 "EXPR2.spad" 462679 462691 462966 462971) (-313 "EXPEXPAN.spad" 459617 459642 460251 460344) (-312 "EXIT.spad" 459288 459296 459607 459612) (-311 "EXITAST.spad" 459024 459032 459278 459283) (-310 "EVALCYC.spad" 458482 458496 459014 459019) (-309 "EVALAB.spad" 458046 458056 458472 458477) (-308 "EVALAB.spad" 457608 457620 458036 458041) (-307 "EUCDOM.spad" 455150 455158 457534 457603) (-306 "EUCDOM.spad" 452754 452764 455140 455145) (-305 "ESTOOLS.spad" 444594 444602 452744 452749) (-304 "ESTOOLS2.spad" 444195 444209 444584 444589) (-303 "ESTOOLS1.spad" 443880 443891 444185 444190) (-302 "ES.spad" 436427 436435 443870 443875) (-301 "ES.spad" 428880 428890 436325 436330) (-300 "ESCONT.spad" 425653 425661 428870 428875) (-299 "ESCONT1.spad" 425402 425414 425643 425648) (-298 "ES2.spad" 424897 424913 425392 425397) (-297 "ES1.spad" 424463 424479 424887 424892) (-296 "ERROR.spad" 421784 421792 424453 424458) (-295 "EQTBL.spad" 420256 420278 420465 420492) (-294 "EQ.spad" 415130 415140 417929 418041) (-293 "EQ2.spad" 414846 414858 415120 415125) (-292 "EP.spad" 411160 411170 414836 414841) (-291 "ENV.spad" 409836 409844 411150 411155) (-290 "ENTIRER.spad" 409504 409512 409780 409831) (-289 "EMR.spad" 408705 408746 409430 409499) (-288 "ELTAGG.spad" 406945 406964 408695 408700) (-287 "ELTAGG.spad" 405149 405170 406901 406906) (-286 "ELTAB.spad" 404596 404614 405139 405144) (-285 "ELFUTS.spad" 403975 403994 404586 404591) (-284 "ELEMFUN.spad" 403664 403672 403965 403970) (-283 "ELEMFUN.spad" 403351 403361 403654 403659) (-282 "ELAGG.spad" 401294 401304 403331 403346) (-281 "ELAGG.spad" 399174 399186 401213 401218) (-280 "ELABEXPR.spad" 398097 398105 399164 399169) (-279 "EFUPXS.spad" 394873 394903 398053 398058) (-278 "EFULS.spad" 391709 391732 394829 394834) (-277 "EFSTRUC.spad" 389664 389680 391699 391704) (-276 "EF.spad" 384430 384446 389654 389659) (-275 "EAB.spad" 382706 382714 384420 384425) (-274 "E04UCFA.spad" 382242 382250 382696 382701) (-273 "E04NAFA.spad" 381819 381827 382232 382237) (-272 "E04MBFA.spad" 381399 381407 381809 381814) (-271 "E04JAFA.spad" 380935 380943 381389 381394) (-270 "E04GCFA.spad" 380471 380479 380925 380930) (-269 "E04FDFA.spad" 380007 380015 380461 380466) (-268 "E04DGFA.spad" 379543 379551 379997 380002) (-267 "E04AGNT.spad" 375385 375393 379533 379538) (-266 "DVARCAT.spad" 372070 372080 375375 375380) (-265 "DVARCAT.spad" 368753 368765 372060 372065) (-264 "DSMP.spad" 366184 366198 366489 366616) (-263 "DROPT.spad" 360129 360137 366174 366179) (-262 "DROPT1.spad" 359792 359802 360119 360124) (-261 "DROPT0.spad" 354619 354627 359782 359787) (-260 "DRAWPT.spad" 352774 352782 354609 354614) (-259 "DRAW.spad" 345374 345387 352764 352769) (-258 "DRAWHACK.spad" 344682 344692 345364 345369) (-257 "DRAWCX.spad" 342124 342132 344672 344677) (-256 "DRAWCURV.spad" 341661 341676 342114 342119) (-255 "DRAWCFUN.spad" 330833 330841 341651 341656) (-254 "DQAGG.spad" 329001 329011 330801 330828) (-253 "DPOLCAT.spad" 324342 324358 328869 328996) (-252 "DPOLCAT.spad" 319769 319787 324298 324303) (-251 "DPMO.spad" 311995 312011 312133 312434) (-250 "DPMM.spad" 304234 304252 304359 304660) (-249 "DOMCTOR.spad" 304126 304134 304224 304229) (-248 "DOMAIN.spad" 303257 303265 304116 304121) (-247 "DMP.spad" 300479 300494 301051 301178) (-246 "DLP.spad" 299827 299837 300469 300474) (-245 "DLIST.spad" 298406 298416 299010 299037) (-244 "DLAGG.spad" 296817 296827 298396 298401) (-243 "DIVRING.spad" 296359 296367 296761 296812) (-242 "DIVRING.spad" 295945 295955 296349 296354) (-241 "DISPLAY.spad" 294125 294133 295935 295940) (-240 "DIRPROD.spad" 283705 283721 284345 284476) (-239 "DIRPROD2.spad" 282513 282531 283695 283700) (-238 "DIRPCAT.spad" 281455 281471 282377 282508) (-237 "DIRPCAT.spad" 280126 280144 281050 281055) (-236 "DIOSP.spad" 278951 278959 280116 280121) (-235 "DIOPS.spad" 277935 277945 278931 278946) (-234 "DIOPS.spad" 276893 276905 277891 277896) (-233 "DIFRING.spad" 276185 276193 276873 276888) (-232 "DIFRING.spad" 275485 275495 276175 276180) (-231 "DIFEXT.spad" 274644 274654 275465 275480) (-230 "DIFEXT.spad" 273720 273732 274543 274548) (-229 "DIAGG.spad" 273350 273360 273700 273715) (-228 "DIAGG.spad" 272988 273000 273340 273345) (-227 "DHMATRIX.spad" 271292 271302 272445 272472) (-226 "DFSFUN.spad" 264700 264708 271282 271287) (-225 "DFLOAT.spad" 261421 261429 264590 264695) (-224 "DFINTTLS.spad" 259630 259646 261411 261416) (-223 "DERHAM.spad" 257540 257572 259610 259625) (-222 "DEQUEUE.spad" 256858 256868 257147 257174) (-221 "DEGRED.spad" 256473 256487 256848 256853) (-220 "DEFINTRF.spad" 253998 254008 256463 256468) (-219 "DEFINTEF.spad" 252494 252510 253988 253993) (-218 "DEFAST.spad" 251862 251870 252484 252489) (-217 "DECIMAL.spad" 249968 249976 250329 250422) (-216 "DDFACT.spad" 247767 247784 249958 249963) (-215 "DBLRESP.spad" 247365 247389 247757 247762) (-214 "DBASE.spad" 246019 246029 247355 247360) (-213 "DATAARY.spad" 245481 245494 246009 246014) (-212 "D03FAFA.spad" 245309 245317 245471 245476) (-211 "D03EEFA.spad" 245129 245137 245299 245304) (-210 "D03AGNT.spad" 244209 244217 245119 245124) (-209 "D02EJFA.spad" 243671 243679 244199 244204) (-208 "D02CJFA.spad" 243149 243157 243661 243666) (-207 "D02BHFA.spad" 242639 242647 243139 243144) (-206 "D02BBFA.spad" 242129 242137 242629 242634) (-205 "D02AGNT.spad" 236933 236941 242119 242124) (-204 "D01WGTS.spad" 235252 235260 236923 236928) (-203 "D01TRNS.spad" 235229 235237 235242 235247) (-202 "D01GBFA.spad" 234751 234759 235219 235224) (-201 "D01FCFA.spad" 234273 234281 234741 234746) (-200 "D01ASFA.spad" 233741 233749 234263 234268) (-199 "D01AQFA.spad" 233187 233195 233731 233736) (-198 "D01APFA.spad" 232611 232619 233177 233182) (-197 "D01ANFA.spad" 232105 232113 232601 232606) (-196 "D01AMFA.spad" 231615 231623 232095 232100) (-195 "D01ALFA.spad" 231155 231163 231605 231610) (-194 "D01AKFA.spad" 230681 230689 231145 231150) (-193 "D01AJFA.spad" 230204 230212 230671 230676) (-192 "D01AGNT.spad" 226263 226271 230194 230199) (-191 "CYCLOTOM.spad" 225769 225777 226253 226258) (-190 "CYCLES.spad" 222601 222609 225759 225764) (-189 "CVMP.spad" 222018 222028 222591 222596) (-188 "CTRIGMNP.spad" 220508 220524 222008 222013) (-187 "CTOR.spad" 220199 220207 220498 220503) (-186 "CTORKIND.spad" 219802 219810 220189 220194) (-185 "CTORCAT.spad" 219051 219059 219792 219797) (-184 "CTORCAT.spad" 218298 218308 219041 219046) (-183 "CTORCALL.spad" 217878 217886 218288 218293) (-182 "CSTTOOLS.spad" 217121 217134 217868 217873) (-181 "CRFP.spad" 210825 210838 217111 217116) (-180 "CRCEAST.spad" 210545 210553 210815 210820) (-179 "CRAPACK.spad" 209588 209598 210535 210540) (-178 "CPMATCH.spad" 209088 209103 209513 209518) (-177 "CPIMA.spad" 208793 208812 209078 209083) (-176 "COORDSYS.spad" 203686 203696 208783 208788) (-175 "CONTOUR.spad" 203097 203105 203676 203681) (-174 "CONTFRAC.spad" 198709 198719 202999 203092) (-173 "CONDUIT.spad" 198467 198475 198699 198704) (-172 "COMRING.spad" 198141 198149 198405 198462) (-171 "COMPPROP.spad" 197655 197663 198131 198136) (-170 "COMPLPAT.spad" 197422 197437 197645 197650) (-169 "COMPLEX.spad" 191446 191456 191690 191951) (-168 "COMPLEX2.spad" 191159 191171 191436 191441) (-167 "COMPFACT.spad" 190761 190775 191149 191154) (-166 "COMPCAT.spad" 188829 188839 190495 190756) (-165 "COMPCAT.spad" 186590 186602 188258 188263) (-164 "COMMUPC.spad" 186336 186354 186580 186585) (-163 "COMMONOP.spad" 185869 185877 186326 186331) (-162 "COMM.spad" 185678 185686 185859 185864) (-161 "COMMAAST.spad" 185441 185449 185668 185673) (-160 "COMBOPC.spad" 184346 184354 185431 185436) (-159 "COMBINAT.spad" 183091 183101 184336 184341) (-158 "COMBF.spad" 180459 180475 183081 183086) (-157 "COLOR.spad" 179296 179304 180449 180454) (-156 "COLONAST.spad" 178962 178970 179286 179291) (-155 "CMPLXRT.spad" 178671 178688 178952 178957) (-154 "CLLCTAST.spad" 178333 178341 178661 178666) (-153 "CLIP.spad" 174425 174433 178323 178328) (-152 "CLIF.spad" 173064 173080 174381 174420) (-151 "CLAGG.spad" 169549 169559 173054 173059) (-150 "CLAGG.spad" 165905 165917 169412 169417) (-149 "CINTSLPE.spad" 165230 165243 165895 165900) (-148 "CHVAR.spad" 163308 163330 165220 165225) (-147 "CHARZ.spad" 163223 163231 163288 163303) (-146 "CHARPOL.spad" 162731 162741 163213 163218) (-145 "CHARNZ.spad" 162484 162492 162711 162726) (-144 "CHAR.spad" 160352 160360 162474 162479) (-143 "CFCAT.spad" 159668 159676 160342 160347) (-142 "CDEN.spad" 158826 158840 159658 159663) (-141 "CCLASS.spad" 156975 156983 158237 158276) (-140 "CATEGORY.spad" 156065 156073 156965 156970) (-139 "CATCTOR.spad" 155956 155964 156055 156060) (-138 "CATAST.spad" 155574 155582 155946 155951) (-137 "CASEAST.spad" 155288 155296 155564 155569) (-136 "CARTEN.spad" 150391 150415 155278 155283) (-135 "CARTEN2.spad" 149777 149804 150381 150386) (-134 "CARD.spad" 147066 147074 149751 149772) (-133 "CAPSLAST.spad" 146840 146848 147056 147061) (-132 "CACHSET.spad" 146462 146470 146830 146835) (-131 "CABMON.spad" 146015 146023 146452 146457) (-130 "BYTEORD.spad" 145690 145698 146005 146010) (-129 "BYTE.spad" 145115 145123 145680 145685) (-128 "BYTEBUF.spad" 142972 142980 144284 144311) (-127 "BTREE.spad" 142041 142051 142579 142606) (-126 "BTOURN.spad" 141044 141054 141648 141675) (-125 "BTCAT.spad" 140432 140442 141012 141039) (-124 "BTCAT.spad" 139840 139852 140422 140427) (-123 "BTAGG.spad" 138962 138970 139808 139835) (-122 "BTAGG.spad" 138104 138114 138952 138957) (-121 "BSTREE.spad" 136839 136849 137711 137738) (-120 "BRILL.spad" 135034 135045 136829 136834) (-119 "BRAGG.spad" 133958 133968 135024 135029) (-118 "BRAGG.spad" 132846 132858 133914 133919) (-117 "BPADICRT.spad" 130827 130839 131082 131175) (-116 "BPADIC.spad" 130491 130503 130753 130822) (-115 "BOUNDZRO.spad" 130147 130164 130481 130486) (-114 "BOP.spad" 124996 125004 130137 130142) (-113 "BOP1.spad" 122382 122392 124952 124957) (-112 "BOOLEAN.spad" 121706 121714 122372 122377) (-111 "BMODULE.spad" 121418 121430 121674 121701) (-110 "BITS.spad" 120837 120845 121054 121081) (-109 "BINDING.spad" 120256 120264 120827 120832) (-108 "BINARY.spad" 118367 118375 118723 118816) (-107 "BGAGG.spad" 117564 117574 118347 118362) (-106 "BGAGG.spad" 116769 116781 117554 117559) (-105 "BFUNCT.spad" 116333 116341 116749 116764) (-104 "BEZOUT.spad" 115467 115494 116283 116288) (-103 "BBTREE.spad" 112286 112296 115074 115101) (-102 "BASTYPE.spad" 111958 111966 112276 112281) (-101 "BASTYPE.spad" 111628 111638 111948 111953) (-100 "BALFACT.spad" 111067 111080 111618 111623) (-99 "AUTOMOR.spad" 110514 110523 111047 111062) (-98 "ATTREG.spad" 107233 107240 110266 110509) (-97 "ATTRBUT.spad" 103256 103263 107213 107228) (-96 "ATTRAST.spad" 102973 102980 103246 103251) (-95 "ATRIG.spad" 102443 102450 102963 102968) (-94 "ATRIG.spad" 101911 101920 102433 102438) (-93 "ASTCAT.spad" 101815 101822 101901 101906) (-92 "ASTCAT.spad" 101717 101726 101805 101810) (-91 "ASTACK.spad" 101050 101059 101324 101351) (-90 "ASSOCEQ.spad" 99850 99861 101006 101011) (-89 "ASP9.spad" 98931 98944 99840 99845) (-88 "ASP8.spad" 97974 97987 98921 98926) (-87 "ASP80.spad" 97296 97309 97964 97969) (-86 "ASP7.spad" 96456 96469 97286 97291) (-85 "ASP78.spad" 95907 95920 96446 96451) (-84 "ASP77.spad" 95276 95289 95897 95902) (-83 "ASP74.spad" 94368 94381 95266 95271) (-82 "ASP73.spad" 93639 93652 94358 94363) (-81 "ASP6.spad" 92506 92519 93629 93634) (-80 "ASP55.spad" 91015 91028 92496 92501) (-79 "ASP50.spad" 88832 88845 91005 91010) (-78 "ASP4.spad" 88127 88140 88822 88827) (-77 "ASP49.spad" 87126 87139 88117 88122) (-76 "ASP42.spad" 85533 85572 87116 87121) (-75 "ASP41.spad" 84112 84151 85523 85528) (-74 "ASP35.spad" 83100 83113 84102 84107) (-73 "ASP34.spad" 82401 82414 83090 83095) (-72 "ASP33.spad" 81961 81974 82391 82396) (-71 "ASP31.spad" 81101 81114 81951 81956) (-70 "ASP30.spad" 79993 80006 81091 81096) (-69 "ASP29.spad" 79459 79472 79983 79988) (-68 "ASP28.spad" 70732 70745 79449 79454) (-67 "ASP27.spad" 69629 69642 70722 70727) (-66 "ASP24.spad" 68716 68729 69619 69624) (-65 "ASP20.spad" 68180 68193 68706 68711) (-64 "ASP1.spad" 67561 67574 68170 68175) (-63 "ASP19.spad" 62247 62260 67551 67556) (-62 "ASP12.spad" 61661 61674 62237 62242) (-61 "ASP10.spad" 60932 60945 61651 61656) (-60 "ARRAY2.spad" 60292 60301 60539 60566) (-59 "ARRAY1.spad" 59127 59136 59475 59502) (-58 "ARRAY12.spad" 57796 57807 59117 59122) (-57 "ARR2CAT.spad" 53458 53479 57764 57791) (-56 "ARR2CAT.spad" 49140 49163 53448 53453) (-55 "ARITY.spad" 48512 48519 49130 49135) (-54 "APPRULE.spad" 47756 47778 48502 48507) (-53 "APPLYORE.spad" 47371 47384 47746 47751) (-52 "ANY.spad" 45713 45720 47361 47366) (-51 "ANY1.spad" 44784 44793 45703 45708) (-50 "ANTISYM.spad" 43223 43239 44764 44779) (-49 "ANON.spad" 42916 42923 43213 43218) (-48 "AN.spad" 41217 41224 42732 42825) (-47 "AMR.spad" 39396 39407 41115 41212) (-46 "AMR.spad" 37412 37425 39133 39138) (-45 "ALIST.spad" 34824 34845 35174 35201) (-44 "ALGSC.spad" 33947 33973 34696 34749) (-43 "ALGPKG.spad" 29656 29667 33903 33908) (-42 "ALGMFACT.spad" 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"A1AGG.spad" 30 41 860 865))
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T)) (|has| |#1| (-556)) (|has| |#1| (-556)) @@ -256,21 +256,21 @@ (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) (((|#1| (-967)) . T)) (((#0=(-866 |#1|) $) |has| #0# (-286 #0# #0#))) @@ -314,7 +314,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -326,27 +326,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -475,10 +475,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -489,7 +489,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) ((((-858)) . T)) ((((-858)) . T)) @@ -732,22 +732,22 @@ (|has| |#1| (-1094)) (((|#2|) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) -(((|#4|) -2789 (|has| |#4| (-172)) (|has| |#4| (-363)))) -(((|#3|) -2789 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(((|#4|) -2797 (|has| |#4| (-172)) (|has| |#4| (-363)))) +(((|#3|) -2797 (|has| |#3| (-172)) (|has| |#3| (-363)))) ((((-858)) . T)) (((|#1|) . T)) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-905))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((($ $) . T) ((#0=(-1170) $) |has| |#1| (-233)) ((#0# |#1|) |has| |#1| (-233)) ((#1=(-814 (-1170)) |#1|) . T) ((#1# $) . 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T)) (|has| (-407 |#2|) (-147)) (|has| (-407 |#2|) (-145)) @@ -760,15 +760,15 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-858)) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-388) (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($ $) . T)) ((((-858)) . T)) ((($ $) . T)) @@ -837,12 +837,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-407 (-564))) . T) (((-564)) . T)) ((((-564) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2789 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2797 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-858)) . T)) ((((-1175)) . T)) (|has| |#1| (-816)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-846)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-905)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-858)) . 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T)) -(-2789 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -942,14 +942,14 @@ ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -960,7 +960,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-2059 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-2078 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -975,20 +975,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2789 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -(-2789 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2789 (|has| |#3| (-789)) (|has| |#3| (-844))) +(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1012,11 +1012,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-564)) -2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1045))) ((|#2|) -2789 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094)))) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-564)) -2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1045))) ((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094)))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1024,8 +1024,8 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) |has| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (-309 (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1036,10 +1036,10 @@ ((($ $) . T) ((#0=(-860 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1127,11 +1127,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-896 (-1170)))) -(-2789 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-2797 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-858)) . T)) ((((-858)) . T)) @@ -1139,8 +1139,8 @@ ((((-906 |#1|)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1149,16 +1149,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-866 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . 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T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1169,8 +1169,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -1185,14 +1185,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((($) . T) (((-407 (-564))) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) #0#) |has| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (-309 (-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))))) +(((#0=(-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) (|has| |#2| (-846)) ((($) . T)) (((|#2|) |has| |#2| (-1094))) -((((-858)) -2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +((((-858)) -2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) ((((-1152) (-52)) . T)) @@ -1201,10 +1201,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1231,21 +1231,21 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . 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T)) @@ -1253,39 +1253,39 @@ (|has| |#1| (-556)) ((((-1152) |#1|) . T)) (|has| |#1| (-1145)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-954 |#1|)) . T)) -(((#0=(-407 (-564)) #0#) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) +(((#0=(-407 (-564)) #0#) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-564))) (((-564)) |has| |#1| (-1034 (-564))) (((-1170)) |has| |#1| (-1034 (-1170))) ((|#1|) . T)) ((((-564) |#2|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-858)) -2789 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) +((((-858)) -2797 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(((|#2| |#2|) -2789 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(((|#2| |#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1152) (-1170) (-564) (-225) (-858)) . T)) @@ -1320,8 +1320,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -(((|#2|) -2789 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-889 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) @@ -1333,11 +1333,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1374,7 +1374,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1382,9 +1382,9 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1397,7 +1397,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1432,19 +1432,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) #0#) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-846)) (((|#2| (-767) (-1076)) . T)) (((|#1| |#2|) . T)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-787)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2789 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-2789 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-2797 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-2797 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1458,10 +1458,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1475,8 +1475,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3076 (-1152)) (|:| -2511 #0#))) . T)) +((((-858)) -2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3090 (-1152)) (|:| -2538 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1484,7 +1484,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-2789 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2797 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (|has| |#1| (-363)) ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1495,8 +1495,8 @@ (|has| |#1| (-844)) ((((-858)) . T)) (((|#2|) . T)) -((((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2789 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2789 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1505,7 +1505,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2059 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-2078 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1525,16 +1525,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-906 |#1|)) . T)) -(((|#1|) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2789 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1553,11 +1553,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-846)) (|has| |#1| (-846)) -(((|#3|) -2789 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-2789 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) +(((|#3|) -2797 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-2797 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -2789 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1566,7 +1566,7 @@ (|has| |#1| (-816)) (|has| |#1| (-816)) (((|#1|) . T)) -(-2789 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-844)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -1575,13 +1575,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-1170)) |has| |#1| (-896 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) #0#) |has| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (-309 (-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))))) +(((#0=(-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-858)) . T) (((-1175)) . T)) @@ -1600,11 +1600,11 @@ (((|#1| (-767) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2789 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2797 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1627,32 +1627,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1661,7 +1661,7 @@ ((((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1669,12 +1669,12 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) -(-2789 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1687,16 +1687,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-2789 (|has| |#2| (-816)) (|has| |#2| (-846))) +(-2797 (|has| |#2| (-816)) (|has| |#2| (-846))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-858)) . T)) ((((-564)) . T) (($) . T)) ((((-767)) . T)) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((($) . T) (((-564)) . T)) @@ -1704,30 +1704,30 @@ (|has| |#2| (-905)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-858)) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) (|has| |#1| (-905)) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) ((($) . T) ((|#2|) . T)) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-858)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1749,7 +1749,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1769,18 +1769,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-858)) . T)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) (((|#3|) . T)) -(-2789 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2797 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2789 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2797 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-767)) . T)) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -1788,7 +1788,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1796,7 +1796,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -2789 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-816)) @@ -1806,8 +1806,8 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| (-564) (-1076)) . T)) -(-2789 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +(-2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (|has| |#1| (-846)) @@ -1820,33 +1820,33 @@ (|has| |#1| (-1094)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -2789 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +((((-564)) -2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) -((((-685 (-339 (-2335) (-2335 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +((((-685 (-339 (-2355) (-2355 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -(((|#1| |#1|) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1| |#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) |has| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (-309 (-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-905))) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-858)) . T)) ((((-858)) . T)) @@ -1877,25 +1877,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1034 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2789 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2797 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-858)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1922,7 +1922,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -2789 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -2797 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1943,25 +1943,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-844)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1034 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-858)) -2789 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-858)) -2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-858)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-948 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-846)) @@ -1972,14 +1972,14 @@ (((|#3|) |has| |#3| (-1045))) ((((-1170)) |has| |#2| (-896 (-1170)))) ((((-858)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2000,11 +2000,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-846)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) |has| (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)) (-309 (-2 (|:| -3076 |#1|) (|:| -2511 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2022,11 +2022,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -2789 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2037,11 +2037,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-858)) . T)) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-905))) (((|#1|) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-767)) . T)) @@ -2052,13 +2052,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564)))) (($) . T)) ((((-564)) . T)) (|has| |#1| (-363)) -(-2789 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2789 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2797 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2797 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2073,23 +2073,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2789 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) ((((-858)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2789 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -2797 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-896 (-1170)))) -(((|#1|) . T) (($) -2789 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -2797 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-858)) . T)) (((|#1|) . T)) @@ -2097,8 +2097,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-866 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2789 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2789 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2797 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-858)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2114,17 +2114,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1034 (-407 (-564)))) (((-564)) |has| #0# (-1034 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-767)) . T)) (|has| |#1| (-846)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2789 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))) |has| (-2 (|:| -3076 (-1152)) (|:| -2511 (-52))) (-309 (-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))))) +((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-564)))) @@ -2148,29 +2148,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-858)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(((|#2|) . 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T)) -((($ $) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) ((($) . T)) ((((-407 (-948 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-858)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) |has| (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|)) (-309 (-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-846)) @@ -2179,16 +2179,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-2789 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2789 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2797 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2797 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-844)) (((|#1| |#2|) . T)) @@ -2212,9 +2212,9 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2236,13 +2236,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2789 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1|) . T)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2258,7 +2258,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2789 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2789 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2797 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1034 (-407 (-564)))) (((-564)) |has| |#2| (-1034 (-564))) ((|#2|) . T) (((-860 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) @@ -2271,12 +2271,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2296,14 +2296,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-2789 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-767)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-905)) -(-2789 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2797 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-858)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) @@ -2312,14 +2312,14 @@ ((((-858)) . T)) ((($) . T)) ((($) . T)) -(-2789 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-2789 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2789 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2797 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) @@ -2352,27 +2352,27 @@ (((|#1|) |has| |#1| (-172))) ((((-858)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -2789 (|has| |#2| (-6 (-4408 "*"))) (|has| |#2| (-172)))) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2|) -2797 (|has| |#2| (-6 (-4408 "*"))) (|has| |#2| (-172)))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#2| (-846)) (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-2789 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-2797 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-844)) @@ -2388,7 +2388,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2401,7 +2401,7 @@ ((((-858)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2413,16 +2413,16 @@ (((|#2|) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-2789 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2789 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2797 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2797 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1170) (-52)) . T)) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-905)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-905)) @@ -2439,12 +2439,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-816)) (((#0=(-906 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-844)) -((((-1195 |#1|)) . T) (((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) @@ -2455,11 +2455,11 @@ (((|#2|) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3076 (-1170)) (|:| -2511 #0#))) . T)) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3090 (-1170)) (|:| -2538 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-858)) . T)) @@ -2467,15 +2467,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-858)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -2789 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -2789 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2797 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2797 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2498,7 +2498,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2536,7 +2536,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2544,9 +2544,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-906 |#1|)) . T)) -((($) -2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2789 (|has| |#1| (-368)) (|has| |#1| (-846))) +(-2797 (|has| |#1| (-368)) (|has| |#1| (-846))) (((|#1|) . T)) ((((-767)) . T)) ((((-858)) . T)) @@ -2557,16 +2557,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-2059 |#1|) (-767))) . T)) +(((|#2| (-240 (-2078 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-1152)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) #0#) |has| (-2 (|:| -3076 (-1170)) (|:| -2511 (-52))) (-309 (-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))))) +(((#0=(-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) -(-2789 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) (((|#1|) . T)) @@ -2583,11 +2583,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-824))) ((((-858)) . T)) -((((-1170)) -2789 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) +((((-1170)) -2797 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) (|has| |#1| (-363)) @@ -2598,7 +2598,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2623,9 +2623,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2634,22 +2634,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-2789 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T)) (((|#2|) . T)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2657,7 +2657,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2789 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) ((($) . T)) @@ -2685,7 +2685,7 @@ ((((-858)) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2707,7 +2707,7 @@ ((((-564)) . T)) ((((-858)) . T)) ((((-564)) . T)) -(-2789 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2797 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2719,9 +2719,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2751,7 +2751,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-776 |#1| (-860 |#2|))) |has| (-776 |#1| (-860 |#2|)) (-309 (-776 |#1| (-860 |#2|))))) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2763,13 +2763,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 (-52)))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((((-858)) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2799,7 +2799,7 @@ (((|#1|) . T)) ((((-858)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2789 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2797 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2807,21 +2807,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -2789 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -2789 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-905)) (|has| |#1| (-905)) -((($) -2789 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) (((|#1|) . T)) -((((-2 (|:| -3076 (-1152)) (|:| -2511 |#1|))) . T)) +((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2836,10 +2836,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . T)) -(-2789 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1|) . T)) (((|#1|) . T)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-536)) . T)) ((((-858)) . T)) @@ -2856,12 +2856,12 @@ ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-1170)) |has| |#1| (-896 (-1170)))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) -((($) . T) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2789 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-556)))) ((($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2789 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2797 (|has| |#1| (-172)) (|has| |#1| (-556)))) (|has| |#1| (-556)) (((|#1|) |has| |#1| (-363))) ((((-564)) . T)) @@ -2880,8 +2880,8 @@ ((((-858)) . T)) (|has| |#2| (-816)) (|has| |#2| (-816)) -((((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2789 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -2907,12 +2907,12 @@ (((|#2| (-767)) . T)) ((((-1170)) . T)) ((((-866 |#1|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3256,17 +3256,17 @@ ((((-129)) . T)) ((((-858)) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1098)) . T)) ((((-858)) . 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T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3288,13 +3288,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-2789 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-767)) . T)) @@ -3309,16 +3309,16 @@ ((((-888 (-379))) . T) (((-888 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-858)) . T)) -(-2789 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2789 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2789 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2797 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045)))) -(-2789 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2797 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3344,7 +3344,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-2789 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2797 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3356,7 +3356,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) @@ -3367,14 +3367,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1175)) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2789 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2797 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#2|) . T)) -(-2789 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2797 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-858)) -2789 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-858)) -2797 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3386,19 +3386,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-2789 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2789 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2797 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2797 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T) (((-1175)) . 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T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3433,15 +3433,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-858)) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-564) |#1|) . 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T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-858)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3465,13 +3465,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2789 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2789 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -3076 (-1170)) (|:| -2511 (-52)))) . T)) +((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3485,8 +3485,8 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) -(-2789 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2789 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((($) . T)) (((|#2| (-531 (-860 |#1|))) . T)) ((((-1175)) . T)) @@ -3501,13 +3501,13 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-858)) -2789 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-767)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -3076 |#1|) (|:| -2511 |#2|))) . T)) +((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3516,14 +3516,14 @@ ((((-564)) . T) (($) . 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-131) T) ((-394 . -1094) T) ((-690 . -370) 143997) ((-866 . -1052) T) ((-223 . -618) 143974) ((-327 . -286) 143951) ((-474 . -111) 143772) ((-1243 . -1045) T) ((-1222 . -1045) T) ((-812 . -377) 143756) ((-169 . -722) T) ((-650 . -102) T) ((-1243 . -243) 143735) ((-1243 . -233) 143687) ((-1222 . -233) 143592) ((-1222 . -243) 143571) ((-999 . -402) NIL) ((-666 . -637) 143519) ((-316 . -38) 143429) ((-313 . -38) 143358) ((-69 . -611) 143340) ((-319 . -493) 143306) ((-1182 . -288) 143285) ((-1217 . -846) T) ((-1107 . -1106) 143195) ((-83 . -1209) T) ((-61 . -611) 143177) ((-479 . -288) 143156) ((-1274 . -1034) 143133) ((-1158 . -1094) T) ((-1107 . -23) 143003) ((-812 . -896) 142939) ((-1232 . -722) T) ((-1096 . -1209) T) ((-474 . -614) 142765) ((-1081 . -290) 142696) ((-962 . -1094) T) ((-889 . -102) T) ((-778 . -290) 142607) ((-327 . -19) 142591) ((-59 . -288) 142568) ((-776 . -290) 142499) ((-851 . -722) T) ((-117 . -844) NIL) ((-516 . -288) 142476) ((-327 . -602) 142453) ((-496 . -288) 142430) ((-454 . -290) 142361) ((-1031 . -309) 142212) ((-677 . -490) 142193) ((-571 . -722) T) ((-672 . -490) 142174) ((-677 . -611) 142124) ((-672 . -611) 142090) ((-658 . -611) 142072) ((-478 . -490) 142053) ((-478 . -611) 142019) ((-245 . -612) 141980) ((-245 . -490) 141957) ((-138 . -490) 141938) ((-137 . -490) 141919) ((-133 . -490) 141900) ((-245 . -611) 141792) ((-213 . -102) T) ((-138 . -611) 141758) ((-137 . -611) 141724) ((-133 . -611) 141690) ((-1141 . -34) T) ((-939 . -1209) T) ((-343 . -713) 141635) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141616) ((-474 . -1045) T) ((-633 . -417) 141581) ((-605 . -417) 141546) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141525) ((-474 . -233) 141477) ((-474 . -243) 141456) ((-1223 . -307) 141435) ((-1223 . -1018) NIL) ((-1074 . -131) T) ((-868 . -791) 141414) ((-144 . -102) T) ((-40 . -1094) T) ((-868 . -788) 141393) ((-641 . -1006) 141377) ((-580 . -1052) T) ((-564 . -1052) T) ((-495 . -1052) T) 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137495) ((-954 . -34) T) ((-355 . -233) 137474) ((-355 . -243) T) ((-352 . -233) 137453) ((-352 . -243) T) ((-344 . -233) 137432) ((-344 . -243) T) ((-247 . -326) 137389) ((-264 . -326) 137361) ((-264 . -233) 137340) ((-1150 . -151) 137324) ((-251 . -896) 137256) ((-250 . -896) 137188) ((-1076 . -846) T) ((-414 . -1106) T) ((-1049 . -23) T) ((-906 . -1045) T) ((-322 . -644) 137170) ((-1020 . -844) T) ((-1203 . -998) 137136) ((-1167 . -916) 137115) ((-1161 . -916) 137094) ((-1161 . -816) NIL) ((-906 . -243) T) ((-813 . -363) 137073) ((-385 . -23) T) ((-127 . -1094) 137051) ((-121 . -1094) 137029) ((-906 . -233) T) ((-128 . -34) T) ((-379 . -644) 136994) ((-866 . -713) 136981) ((-1042 . -151) 136946) ((-40 . -172) T) ((-690 . -411) 136928) ((-708 . -309) 136915) ((-832 . -644) 136875) ((-823 . -644) 136849) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136828) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136805) ((-313 . -231) 136766) ((-1166 . -882) NIL) ((-55 . -1094) T) ((-1119 . -882) 136625) ((-129 . -846) T) ((-1166 . -1034) 136505) ((-1119 . -1034) 136388) ((-183 . -611) 136370) ((-850 . -1034) 136266) ((-778 . -286) 136193) ((-813 . -1106) T) ((-1030 . -722) T) ((-600 . -647) 136177) ((-1042 . -972) 136106) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1145) 136084) ((-690 . -1052) T) ((-600 . -373) 136068) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136050) ((-1166 . -377) 136034) ((-1119 . -377) 136018) ((-1020 . -411) 135980) ((-141 . -229) 135962) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -611) 135944) ((-708 . -38) 135773) ((-1259 . -1257) 135757) ((-351 . -402) T) ((-1259 . -1094) 135707) ((-580 . -713) 135694) ((-564 . -713) 135681) ((-495 . -713) 135646) ((-316 . -627) 135625) ((-832 . -722) T) ((-823 . -722) T) 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-614) 134844) ((-487 . -556) T) ((-478 . -614) 134825) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134802) ((-138 . -614) 134783) ((-137 . -614) 134764) ((-133 . -614) 134745) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134727) ((-733 . -732) 134711) ((-336 . -611) 134693) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134677) ((-1056 . -882) 134659) ((-948 . -882) 134584) ((-649 . -1106) T) ((-621 . -713) 134571) ((-481 . -882) NIL) ((-1140 . -102) T) ((-1088 . -616) 134555) ((-1056 . -1034) 134537) ((-97 . -611) 134519) ((-477 . -147) T) ((-948 . -1034) 134399) ((-117 . -713) 134344) ((-649 . -23) T) ((-481 . -1034) 134220) ((-1081 . -612) NIL) ((-1081 . -611) 134202) ((-778 . -612) NIL) ((-778 . -611) 134163) ((-776 . -612) 133797) ((-776 . -611) 133711) ((-1107 . -637) 133617) ((-461 . -611) 133599) ((-454 . -611) 133581) ((-454 . -612) 133442) ((-1031 . -229) 133388) ((-868 . -905) 133367) ((-126 . -34) T) ((-813 . -131) T) ((-645 . -611) 133349) ((-578 . -102) T) ((-355 . -1278) 133333) ((-352 . -1278) 133317) ((-344 . -1278) 133301) ((-127 . -514) 133234) ((-121 . -514) 133167) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133105) ((-222 . -102) 133083) ((-690 . -1094) T) ((-695 . -172) T) ((-868 . -644) 133035) ((-65 . -384) T) ((-275 . -611) 133017) ((-65 . -395) T) ((-948 . -377) 133001) ((-866 . -290) T) ((-50 . -611) 132983) ((-995 . -38) 132931) ((-581 . -611) 132913) ((-481 . -377) 132897) ((-581 . -612) 132879) ((-518 . -611) 132861) ((-906 . -1278) 132848) ((-867 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132814) ((-487 . -363) T) ((-355 . -368) 132793) ((-352 . -368) 132772) ((-344 . -368) 132751) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132735) ((-867 . -880) 132712) ((-867 . -882) NIL) ((-960 . -846) 132611) ((-811 . -846) 132562) ((-1216 . -102) T) ((-650 . -652) 132546) ((-1195 . -34) T) ((-171 . -611) 132528) ((-1107 . -21) 132438) ((-1107 . -25) 132289) ((-867 . -1034) 132266) ((-948 . -896) 132247) ((-1232 . -47) 132224) ((-906 . -368) T) ((-59 . -647) 132208) ((-516 . -647) 132192) ((-481 . -896) 132169) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132153) ((-59 . -373) 132137) ((-621 . -172) T) ((-516 . -373) 132121) ((-496 . -373) 132105) ((-823 . -704) 132089) ((-1166 . -307) 132068) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132006) ((-169 . -1209) T) ((-633 . -740) 131990) ((-605 . -740) 131974) ((-1271 . -131) T) ((-1244 . -916) 131953) ((-1223 . -916) 131932) ((-1223 . -816) NIL) ((-690 . -713) 131882) ((-1222 . -905) 131835) ((-1020 . -1094) T) ((-867 . -377) 131812) ((-867 . -338) 131789) ((-901 . -1106) T) ((-169 . -880) 131773) ((-169 . -882) 131698) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131594) ((-319 . -846) T) ((-1259 . -514) 131527) ((-1243 . -644) 131424) ((-1222 . -644) 131294) ((-868 . -790) 131273) ((-868 . -787) 131252) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -611) 131234) ((-174 . -452) T) ((-222 . -309) 131172) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131151) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1034) 131135) ((-495 . -290) T) ((-136 . -470) 131090) ((-48 . -1094) T) ((-708 . -231) 131074) ((-867 . -896) NIL) ((-1232 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131058) ((-169 . -338) 131042) ((-1232 . -1034) 130922) ((-851 . -1034) 130818) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130726) ((-658 . -788) 130705) ((-658 . -791) 130684) ((-571 . -1034) 130666) ((-294 . -1266) 130636) ((-862 . -102) T) ((-959 . -556) 130615) ((-1203 . -1051) 130498) ((-482 . -637) 130404) ((-900 . -1094) T) ((-1020 . -713) 130341) ((-707 . -1051) 130306) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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. -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 129021) ((-394 . -611) 129003) ((-474 . -722) T) ((-1114 . -844) T) ((-888 . -1034) 128971) ((-108 . -846) T) ((-654 . -1051) 128955) ((-487 . -131) T) ((-1245 . -1052) T) ((-217 . -131) T) ((-1150 . -102) 128933) ((-99 . -1094) T) ((-245 . -662) 128917) ((-245 . -647) 128901) ((-654 . -111) 128880) ((-585 . -614) 128864) ((-316 . -411) 128848) ((-245 . -373) 128832) ((-1153 . -235) 128779) ((-995 . -231) 128763) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128745) ((-1081 . -1051) 128588) ((-264 . -905) 128567) ((-247 . -905) 128546) ((-778 . -1051) 128369) ((-776 . -1051) 128212) ((-606 . -1209) T) ((-1158 . -611) 128194) ((-1081 . -111) 128023) ((-1042 . -102) T) ((-475 . -1209) T) ((-461 . -1051) 127994) ((-454 . -1051) 127837) ((-660 . -644) 127821) ((-867 . -307) T) ((-778 . -111) 127630) ((-776 . -111) 127459) ((-355 . -644) 127411) ((-352 . -644) 127363) ((-344 . -644) 127315) ((-264 . -644) 127240) ((-247 . -644) 127165) ((-1152 . -846) T) ((-1082 . -1034) 127149) ((-461 . -111) 127110) ((-454 . -111) 126939) ((-1070 . -1034) 126916) ((-996 . -34) T) ((-962 . -611) 126898) ((-954 . -1209) T) ((-126 . -1006) 126882) ((-959 . -1106) T) ((-867 . -1018) NIL) ((-731 . -1106) T) ((-711 . -1106) T) ((-654 . -614) 126800) ((-1259 . -489) 126784) ((-1136 . -38) 126744) ((-959 . -23) T) ((-861 . -1094) T) ((-839 . -102) T) ((-813 . -21) T) ((-813 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-110 . -657) T) ((-906 . -644) 126709) ((-581 . -1051) 126674) ((-518 . -1051) 126619) ((-227 . -57) 126577) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-690 . -290) T) ((-862 . -38) 126547) ((-581 . -111) 126503) ((-518 . -111) 126432) ((-1081 . -614) 126168) ((-418 . -1106) T) ((-316 . -1052) 126058) ((-313 . -1052) T) ((-128 . -1209) T) ((-778 . -614) 125806) ((-776 . -614) 125572) ((-654 . -1045) T) ((-1287 . -1094) T) ((-454 . -614) 125357) ((-169 . -307) 125288) ((-418 . -23) T) ((-40 . -611) 125270) ((-40 . -612) 125254) ((-108 . -988) 125236) ((-116 . -865) 125220) ((-645 . -614) 125204) ((-48 . -514) 125170) ((-1195 . -1006) 125154) ((-1175 . -611) 125121) ((-1182 . -34) T) ((-950 . -611) 125087) ((-917 . -611) 125069) ((-1107 . -846) 125020) ((-767 . -611) 125002) ((-668 . -611) 124984) ((-1150 . -309) 124922) ((-479 . -34) T) ((-1086 . -1209) T) ((-477 . -452) T) ((-1135 . -34) T) ((-1081 . -1045) T) ((-50 . -614) 124891) ((-778 . -1045) T) ((-776 . -1045) T) ((-643 . -235) 124875) ((-630 . -235) 124821) ((-581 . -614) 124771) ((-518 . -614) 124701) ((-1232 . -307) 124680) ((-1081 . -326) 124641) ((-454 . -1045) T) ((-1172 . -21) T) ((-1081 . -233) 124620) ((-778 . -326) 124597) ((-778 . -233) T) ((-776 . -326) 124569) ((-727 . -1213) 124548) ((-327 . -647) 124532) ((-1172 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124511) ((-327 . -373) 124495) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1145) NIL) ((-727 . -556) 124426) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124334) ((-897 . -1094) 124312) ((-50 . -1045) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 124291) ((-1167 . -1213) 124270) ((-581 . -1045) T) ((-518 . -1045) T) ((-1161 . -1213) 124249) ((-361 . -1034) 124233) ((-322 . -1034) 124217) ((-1020 . -290) T) ((-379 . -882) 124199) ((-1167 . -556) 124150) ((-1161 . -556) 124101) ((-999 . -38) 124046) ((-795 . -1106) T) ((-906 . -722) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 124025) ((-354 . -290) T) ((-643 . -691) 124009) ((-379 . -1034) 123969) ((-1114 . -1052) T) ((-103 . -125) 123953) ((-795 . -23) T) ((-1281 . -1276) 123929) ((-1259 . -286) 123906) ((-407 . -309) 123871) 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-611) 123303) ((-121 . -611) 123235) ((-1287 . -172) T) ((-1167 . -363) 123214) ((-1161 . -363) 123193) ((-316 . -1094) T) ((-418 . -131) T) ((-313 . -1094) T) ((-407 . -38) 123145) ((-1127 . -102) T) ((-1245 . -713) 123037) ((-650 . -1052) T) ((-1129 . -1254) T) ((-319 . -145) 123016) ((-319 . -147) 122995) ((-139 . -1094) T) ((-136 . -1094) T) ((-114 . -1094) T) ((-854 . -102) T) ((-580 . -611) 122977) ((-564 . -612) 122876) ((-564 . -611) 122858) ((-495 . -611) 122840) ((-495 . -612) 122785) ((-485 . -23) T) ((-482 . -846) 122736) ((-487 . -637) 122718) ((-961 . -611) 122700) ((-217 . -637) 122682) ((-225 . -404) T) ((-658 . -644) 122666) ((-55 . -611) 122648) ((-1166 . -916) 122627) ((-727 . -1106) T) ((-351 . -102) T) ((-1208 . -1077) T) ((-1114 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122572) ((-1152 . -1151) T) ((-1141 . -107) 122556) ((-1168 . -1106) T) ((-1167 . -1106) T) ((-515 . -1034) 122540) ((-1161 . -1106) T) ((-1120 . -1106) T) ((-343 . -111) 122469) ((-1000 . -1213) T) ((-126 . -1209) T) ((-910 . -1213) T) ((-690 . -286) NIL) ((-1260 . -611) 122451) ((-1168 . -23) T) ((-1167 . -23) T) ((-1161 . -23) T) ((-1000 . -556) T) ((-1136 . -231) 122435) ((-910 . -556) T) ((-1120 . -23) T) ((-248 . -611) 122417) ((-1069 . -1094) T) ((-795 . -131) T) ((-706 . -611) 122399) ((-316 . -713) 122309) ((-313 . -713) 122238) ((-695 . -611) 122220) ((-695 . -612) 122165) ((-407 . -400) 122149) ((-438 . -1094) T) ((-487 . -25) T) ((-487 . -21) T) ((-1114 . -1094) T) ((-217 . -25) T) ((-217 . -21) T) ((-708 . -411) 122133) ((-710 . -1034) 122102) ((-1259 . -611) 122014) ((-1259 . -612) 121975) ((-1245 . -172) T) ((-245 . -34) T) ((-343 . -614) 121905) ((-394 . -614) 121887) ((-922 . -970) T) ((-1195 . -1209) T) ((-658 . -787) 121866) ((-658 . -790) 121845) ((-398 . -395) T) ((-523 . -102) 121823) ((-1031 . -1094) T) ((-222 . -991) 121807) ((-504 . -102) T) ((-621 . -611) 121789) ((-45 . -846) NIL) ((-621 . -612) 121766) ((-1031 . -608) 121741) 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117307) ((-388 . -490) 117288) ((-1031 . -514) 117132) ((-388 . -611) 117098) ((-812 . -556) 117029) ((-585 . -644) 117004) ((-264 . -47) 116976) ((-247 . -47) 116933) ((-531 . -509) 116910) ((-580 . -614) 116882) ((-564 . -614) 116854) ((-495 . -614) 116787) ((-1068 . -1209) T) ((-996 . -1209) T) ((-695 . -1051) 116752) ((-1251 . -23) T) ((-1251 . -1106) T) ((-1244 . -1106) T) ((-1223 . -1106) T) ((-999 . -370) 116724) ((-112 . -368) T) ((-474 . -896) 116630) ((-1244 . -23) T) ((-900 . -611) 116612) ((-55 . -614) 116594) ((-91 . -107) 116578) ((-1203 . -722) T) ((-901 . -846) 116529) ((-697 . -1145) T) ((-695 . -111) 116485) ((-1223 . -23) T) ((-595 . -1106) T) ((-594 . -1106) T) ((-708 . -713) 116314) ((-707 . -722) T) ((-1114 . -290) T) ((-1000 . -131) T) ((-487 . -846) T) ((-967 . -131) T) ((-910 . -131) T) ((-795 . -25) T) ((-217 . -846) T) ((-795 . -21) T) ((-580 . -1045) T) ((-564 . -1045) T) ((-495 . -1045) T) ((-595 . -23) T) ((-343 . -1278) 116291) ((-319 . -452) 116270) 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115278) ((-264 . -1034) 115122) ((-247 . -1034) 114998) ((-117 . -111) 114927) ((-59 . -1209) T) ((-519 . -1209) T) ((-516 . -1209) T) ((-497 . -1209) T) ((-496 . -1209) T) ((-437 . -611) 114909) ((-434 . -611) 114891) ((-3 . -102) T) ((-1023 . -1202) 114860) ((-829 . -102) T) ((-685 . -57) 114818) ((-695 . -1045) T) ((-50 . -644) 114792) ((-289 . -452) T) ((-476 . -1202) 114761) ((0 . -102) T) ((-581 . -644) 114726) ((-518 . -644) 114671) ((-49 . -102) T) ((-906 . -1034) 114658) ((-695 . -243) T) ((-1074 . -409) 114637) ((-727 . -637) 114585) ((-995 . -1094) T) ((-708 . -172) 114476) ((-621 . -614) 114371) ((-487 . -988) 114353) ((-264 . -377) 114337) ((-247 . -377) 114321) ((-399 . -1094) T) ((-1022 . -102) 114299) ((-339 . -38) 114283) ((-217 . -988) 114265) ((-117 . -614) 114195) ((-174 . -38) 114127) ((-1243 . -307) 114106) ((-1222 . -307) 114085) ((-654 . -722) T) ((-99 . -611) 114067) ((-1161 . -637) 114019) ((-485 . -25) T) ((-485 . -21) T) ((-1222 . -1018) 113971) ((-621 . -1045) T) ((-379 . -404) T) ((-390 . -102) T) ((-1099 . -616) 113886) ((-264 . -896) 113832) ((-247 . -896) 113809) ((-117 . -1045) T) ((-812 . -1106) T) ((-1081 . -722) T) ((-621 . -233) 113788) ((-619 . -102) T) ((-778 . -722) T) ((-776 . -722) T) ((-413 . -1106) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1214 . -846) T) ((-454 . -722) T) ((-812 . -23) T) ((-727 . -25) T) ((-727 . -21) T) ((-1071 . -286) 113767) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -763) 113749) ((-690 . -1051) 113699) ((-1251 . -131) T) ((-1244 . -131) T) ((-1223 . -131) T) ((-1168 . -25) T) ((-1136 . -411) 113683) ((-633 . -367) 113615) ((-605 . -367) 113547) ((-1150 . -1143) 113531) ((-103 . -1094) 113509) ((-1168 . -21) T) ((-1167 . -21) T) ((-861 . -611) 113491) ((-995 . -713) 113439) ((-223 . -644) 113406) ((-690 . -111) 113340) ((-50 . -722) T) ((-1167 . -25) T) ((-351 . -349) T) ((-1161 . -21) T) ((-1074 . -452) 113291) ((-1161 . -25) T) ((-708 . -514) 113238) ((-581 . -722) T) 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((-812 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1106) 110962) ((-250 . -1106) 110872) ((-1020 . -1045) T) ((-999 . -1052) T) ((-48 . -614) 110805) ((-343 . -644) 110750) ((-619 . -38) 110734) ((-1272 . -611) 110696) ((-1272 . -612) 110657) ((-1071 . -611) 110639) ((-1020 . -243) T) ((-354 . -1045) T) ((-811 . -1266) 110609) ((-251 . -23) T) ((-250 . -23) T) ((-983 . -611) 110591) ((-733 . -612) 110552) ((-733 . -611) 110534) ((-795 . -846) 110513) ((-1153 . -151) 110460) ((-995 . -514) 110372) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 110353) ((-1000 . -25) T) ((-141 . -611) 110335) ((-141 . -612) 110294) ((-906 . -307) T) ((-1000 . -21) T) ((-967 . -25) T) ((-910 . -21) T) ((-910 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-839 . -411) 110278) ((-48 . -1045) T) ((-1281 . -1273) 110262) ((-1279 . -1273) 110246) ((-1031 . -602) 110221) ((-316 . -612) 110082) ((-316 . -611) 110064) ((-313 . -612) NIL) 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-145) NIL) ((-1114 . -612) 109167) ((-438 . -611) 109149) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 109131) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 109083) ((-479 . -107) 109033) ((-989 . -23) T) ((-1283 . -38) 109003) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1056 . -1213) T) ((-311 . -102) T) ((-850 . -1106) T) ((-948 . -1213) 108982) ((-481 . -1213) 108961) ((-727 . -846) 108940) ((-1056 . -556) T) ((-948 . -556) 108871) ((-1166 . -23) T) ((-1119 . -23) T) ((-850 . -23) T) ((-481 . -556) 108802) ((-1136 . -713) 108734) ((-1140 . -514) 108667) ((-1031 . -612) NIL) ((-1031 . -611) 108649) ((-96 . -1077) T) ((-862 . -713) 108619) ((-1203 . -47) 108588) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-999 . -1094) T) ((-62 . -611) 108570) ((-1161 . -846) NIL) ((-1020 . -788) T) ((-1020 . -791) T) ((-1287 . -1051) 108557) ((-1287 . -111) 108542) ((-866 . -644) 108529) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) ((-1023 . -151) 108513) ((-868 . -816) 108492) ((-868 . -916) T) ((-708 . -286) 108419) ((-595 . -21) T) ((-595 . -25) T) ((-594 . -21) T) ((-40 . -722) T) ((-222 . -514) 108352) ((-594 . -25) T) ((-476 . -151) 108336) ((-463 . -151) 108320) ((-917 . -790) T) ((-917 . -722) T) ((-767 . -789) T) ((-767 . -790) T) ((-506 . -1094) T) ((-502 . -1094) T) ((-767 . -722) T) ((-225 . -363) T) ((-1150 . -1094) 108298) ((-867 . -1213) T) ((-650 . -611) 108280) ((-867 . -556) T) ((-690 . -368) NIL) ((-1287 . -614) 108262) ((-1282 . -1094) T) ((-359 . -1266) 108246) ((-666 . -102) T) ((-353 . -1266) 108230) ((-345 . -1266) 108214) ((-548 . -102) T) ((-520 . -846) 108193) ((-813 . -452) 108172) ((-1042 . -1094) T) ((-1042 . -1065) 108101) ((-1023 . -972) 108070) ((-815 . -1106) T) ((-999 . -713) 108015) ((-386 . -1106) T) ((-476 . -972) 107984) ((-463 . -972) 107953) ((-110 . -151) 107935) ((-73 . -611) 107917) ((-889 . -611) 107899) ((-1074 . -720) 107878) ((-1287 . -1045) T) 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105407) ((-1081 . -882) NIL) ((-867 . -1106) T) ((-117 . -905) NIL) ((-1281 . -1280) 105383) ((-1279 . -1280) 105362) ((-778 . -882) NIL) ((-776 . -882) 105221) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105199) ((-1100 . -395) T) ((-621 . -644) 105186) ((-454 . -882) NIL) ((-671 . -102) 105164) ((-1081 . -1034) 104991) ((-867 . -23) T) ((-778 . -1034) 104850) ((-776 . -1034) 104707) ((-117 . -644) 104652) ((-454 . -1034) 104528) ((-316 . -614) 104092) ((-313 . -614) 103975) ((-645 . -1034) 103959) ((-625 . -102) T) ((-222 . -489) 103943) ((-1259 . -34) T) ((-136 . -614) 103927) ((-633 . -713) 103911) ((-605 . -713) 103895) ((-666 . -38) 103855) ((-319 . -102) T) ((-85 . -611) 103837) ((-50 . -1034) 103821) ((-1114 . -1051) 103808) ((-1081 . -377) 103792) ((-778 . -377) 103776) ((-695 . -722) T) ((-695 . -790) T) ((-695 . -787) T) ((-581 . -1034) 103763) ((-518 . -1034) 103740) ((-60 . -57) 103702) ((-324 . -131) T) ((-316 . -1045) 103592) ((-313 . -1045) T) ((-169 . -1106) T) 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-231) 99766) ((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99715) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99505) ((-829 . -411) 99489) ((-1114 . -791) T) ((-1114 . -788) T) ((-697 . -1094) T) ((-578 . -611) 99471) ((-379 . -363) T) ((-169 . -493) 99449) ((-222 . -611) 99381) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -722) T) ((-1042 . -489) 99346) ((-141 . -425) 99328) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99307) ((-708 . -614) 99063) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1106) T) ((-1216 . -611) 99045) ((-1175 . -1034) 98981) ((-1168 . -35) 98947) ((-1168 . -95) 98913) ((-1168 . -1197) 98879) ((-1168 . -1194) 98845) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98824) ((-1167 . -1194) 98790) ((-1167 . -1197) 98756) ((-1030 . -23) T) ((-1167 . -95) 98722) ((-571 . -493) T) ((-1167 . -35) 98688) ((-1161 . -1194) 98654) ((-1161 . -1197) 98620) ((-1161 . -95) 98586) ((-361 . -1106) T) ((-359 . -1145) 98565) ((-353 . -1145) 98544) ((-345 . -1145) 98523) ((-1161 . -35) 98489) ((-1120 . -35) 98455) ((-1120 . -95) 98421) ((-108 . -1145) T) ((-1120 . -1197) 98387) ((-829 . -1052) 98366) ((-643 . -309) 98304) ((-630 . -309) 98155) ((-1120 . -1194) 98121) ((-708 . -1045) T) ((-1056 . -637) 98103) ((-1074 . -38) 97971) ((-948 . -637) 97919) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1106) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97898) ((-708 . -326) 97875) ((-481 . -637) 97823) ((-40 . -1034) 97711) ((-708 . -233) T) ((-697 . -713) 97698) ((-339 . -1094) T) ((-174 . -1094) T) ((-331 . -846) T) ((-418 . -452) 97648) ((-379 . -23) T) ((-359 . -38) 97613) ((-353 . -38) 97578) ((-345 . -38) 97543) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1106) T) ((-108 . -38) 97493) ((-823 . -1106) T) ((-770 . -1094) T) ((-116 . -713) 97480) ((-668 . -1034) 97464) ((-610 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1150 . -286) 97441) ((-1107 . -309) 97379) ((-1096 . -235) 97363) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97340) ((-96 . -102) T) ((-649 . -848) 97324) ((-1129 . -1077) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97293) ((-948 . -25) T) ((-948 . -21) T) ((-619 . -1052) T) ((-1114 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 97231) ((-885 . -611) 97213) ((-881 . -611) 97195) ((-251 . -846) 97146) ((-250 . -846) 97097) ((-523 . -514) 97030) ((-867 . -637) 97007) ((-476 . -309) 96945) ((-463 . -309) 96883) ((-351 . -290) T) ((-1150 . -1247) 96867) ((-1136 . -611) 96829) ((-1136 . -612) 96790) ((-1134 . -102) T) ((-995 . -1051) 96686) ((-40 . -896) 96638) ((-1150 . -602) 96615) ((-1287 . -644) 96602) ((-862 . -490) 96579) ((-1057 . -151) 96525) ((-868 . -1213) T) ((-995 . -111) 96407) ((-339 . -713) 96391) ((-862 . -611) 96353) ((-174 . -713) 96285) ((-407 . -286) 96243) ((-868 . -556) T) ((-108 . -400) 96225) ((-84 . -384) T) ((-84 . -395) T) ((-697 . -172) T) ((-615 . -611) 96207) ((-99 . -722) T) ((-482 . -102) 95997) ((-99 . -473) T) ((-116 . -172) T) ((-1107 . -38) 95967) ((-169 . -637) 95915) ((-1049 . -102) T) ((-995 . -614) 95805) ((-867 . -25) T) ((-811 . -238) 95784) ((-867 . -21) T) ((-814 . -102) T) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 95762) ((-127 . -1209) T) ((-121 . -1209) T) ((-1030 . -131) T) ((-666 . -367) 95746) ((-995 . -1045) T) ((-1232 . -637) 95694) ((-1098 . -611) 95676) ((-999 . -611) 95658) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1094) T) ((-999 . -612) 95642) ((-995 . -243) 95621) ((-995 . -233) 95600) ((-1287 . -722) T) ((-1251 . -145) 95579) ((-829 . -1094) T) ((-1251 . -147) 95558) ((-1244 . -147) 95537) ((-1244 . -145) 95516) ((-1243 . -1213) 95495) ((-1223 . -145) 95402) ((-1223 . -147) 95309) ((-1222 . -1213) 95288) ((-379 . -131) T) ((-564 . -882) 95270) ((0 . -1094) T) ((-174 . -172) T) ((-169 . -21) T) ((-169 . -25) T) ((-49 . -1094) T) ((-1245 . -644) 95175) ((-1243 . -556) 95126) ((-710 . -1106) T) ((-1222 . -556) 95077) ((-564 . -1034) 95059) ((-594 . -147) 95038) ((-594 . -145) 95017) ((-495 . -1034) 94960) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -611) 94926) ((-502 . -611) 94908) ((-1283 . -1052) T) ((-379 . -1054) T) ((-1022 . -1094) 94886) ((-55 . -1034) 94868) ((-897 . -34) T) ((-482 . -309) 94806) ((-591 . -102) T) ((-1150 . -612) 94767) ((-1150 . -611) 94699) ((-1166 . -846) 94678) ((-45 . -102) T) ((-1119 . -846) 94657) ((-813 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-851 . -25) T) ((-44 . -367) 94641) ((-851 . -21) T) ((-727 . -452) 94592) ((-1282 . -611) 94574) ((-1049 . -309) 94512) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -882) 94494) ((-1259 . -1209) T) ((-227 . -309) 94432) ((-144 . -368) T) ((-1042 . -612) 94374) ((-1042 . -611) 94317) ((-313 . -905) NIL) ((-1217 . -840) T) ((-695 . -1034) 94262) ((-707 . -916) T) ((-474 . -1213) 94241) ((-1167 . -452) 94220) ((-1161 . -452) 94199) ((-330 . -102) T) ((-868 . -1106) T) ((-316 . -644) 94020) ((-313 . -644) 93949) ((-474 . -556) 93900) ((-339 . -514) 93866) ((-550 . -151) 93816) ((-40 . -307) T) ((-839 . -611) 93798) ((-697 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93768) ((-512 . -102) T) ((-407 . -612) 93575) ((-407 . -611) 93557) ((-263 . -611) 93539) ((-116 . -290) T) ((-1245 . -722) T) ((-1243 . -363) 93518) ((-1222 . -363) 93497) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93479) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93463) ((-733 . -34) T) ((-482 . -38) 93433) ((-141 . -34) T) ((-117 . -880) 93410) ((-117 . -882) NIL) ((-621 . -1034) 93293) ((-641 . -846) 93272) ((-1271 . -102) T) ((-295 . -102) T) ((-708 . -368) 93251) 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-23) T) ((-714 . -1106) T) ((-710 . -131) T) ((-649 . -102) T) ((-477 . -713) 92004) ((-45 . -282) 91954) ((-105 . -1094) T) ((-68 . -611) 91936) ((-966 . -102) T) ((-860 . -102) T) ((-621 . -896) 91895) ((-1283 . -1094) T) ((-381 . -1094) T) ((-1208 . -1094) T) ((-1107 . -231) 91864) ((-82 . -1209) T) ((-1056 . -846) T) ((-948 . -846) 91843) ((-117 . -896) NIL) ((-778 . -916) 91822) ((-709 . -846) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91801) ((-247 . -1213) 91780) ((-533 . -856) T) ((-481 . -846) 91759) ((-1152 . -824) T) ((-1136 . -1051) 91743) ((-390 . -757) T) ((-690 . -1209) T) ((-687 . -1034) 91727) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91658) ((-247 . -556) 91589) ((-525 . -1077) T) ((-1136 . -111) 91568) ((-453 . -740) 91538) ((-862 . -1051) 91508) ((-813 . -38) 91450) ((-690 . -880) 91432) ((-690 . -882) 91414) ((-295 . -309) 91218) ((-906 . -1213) T) ((-666 . -411) 91202) ((-862 . -111) 91167) ((-690 . -1034) 91112) ((-1000 . -452) T) ((-906 . -556) T) ((-533 . -611) 91094) ((-581 . -916) T) ((-474 . -1106) T) ((-518 . -916) T) ((-1150 . -288) 91071) ((-910 . -452) T) ((-65 . -611) 91053) ((-630 . -229) 90999) ((-474 . -23) T) ((-1114 . -790) T) ((-868 . -131) T) ((-1114 . -787) T) ((-1274 . -1276) 90978) ((-1114 . -722) T) ((-650 . -644) 90952) ((-294 . -611) 90693) ((-1136 . -614) 90611) ((-1031 . -34) T) ((-811 . -844) 90590) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -713) 90560) ((-690 . -377) 90542) ((-690 . -338) 90524) ((-477 . -172) T) ((-381 . -713) 90494) ((-862 . -614) 90429) ((-867 . -846) NIL) ((-564 . -1018) T) ((-495 . -1018) T) ((-1127 . -611) 90411) ((-1107 . -238) 90390) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90372) ((-1136 . -1045) T) ((-1172 . -38) 90269) ((-854 . -611) 90251) ((-564 . -545) T) ((-666 . -1052) T) ((-727 . -945) 90204) ((-1136 . -233) 90183) ((-1076 . -1094) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 90128) ((-901 . -102) T) ((-862 . -1045) T) ((-690 . -896) NIL) ((-355 . -329) 90112) ((-355 . -363) T) ((-352 . -329) 90096) ((-352 . -363) T) ((-344 . -329) 90080) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90050) ((-546 . -846) T) ((-523 . -683) 90000) ((-217 . -102) T) ((-1020 . -1034) 89880) ((-999 . -111) 89809) ((-1168 . -969) 89778) ((-1167 . -969) 89740) ((-520 . -151) 89724) ((-1074 . -370) 89703) ((-351 . -611) 89685) ((-322 . -21) T) ((-354 . -1034) 89662) ((-322 . -25) T) ((-1161 . -969) 89631) ((-1120 . -969) 89598) ((-76 . -611) 89580) ((-695 . -307) T) ((-169 . -846) 89559) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89546) ((-86 . -611) 89528) ((-695 . -1018) T) ((-673 . -846) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-897 . -1006) 89512) ((-832 . -21) T) ((-48 . -1034) 89455) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1281 . -1052) T) ((-549 . -102) T) ((-1279 . -1052) T) 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. -131) T) ((-217 . -309) NIL) ((-407 . -111) 88435) ((-811 . -1052) 88365) ((-733 . -1092) 88349) ((-1243 . -493) 88315) ((-1222 . -493) 88281) ((-548 . -840) T) ((-141 . -1092) 88263) ((-477 . -290) T) ((-1282 . -1045) T) ((-1214 . -102) T) ((-1057 . -102) T) ((-839 . -614) 88131) ((-500 . -514) NIL) ((-482 . -238) 88110) ((-407 . -614) 88008) ((-1166 . -145) 87987) ((-1166 . -147) 87966) ((-1119 . -147) 87945) ((-1119 . -145) 87924) ((-633 . -1051) 87908) ((-605 . -1051) 87892) ((-1168 . -1250) 87876) ((-666 . -1094) T) ((-666 . -1048) 87816) ((-1168 . -1237) 87793) ((-548 . -1094) T) ((-487 . -1145) T) ((-1167 . -1242) 87754) ((-1167 . -1237) 87724) ((-1167 . -1240) 87708) ((-217 . -1145) T) ((-343 . -916) T) ((-814 . -266) 87692) ((-633 . -111) 87671) ((-605 . -111) 87650) ((-1161 . -1221) 87611) ((-839 . -1045) 87590) ((-1161 . -1237) 87567) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1161 . -1219) 87551) ((-407 . -1045) T) ((-319 . -1052) T) ((-690 . -307) T) ((-108 . -844) T) ((-708 . -722) T) ((-407 . -243) T) ((-407 . -233) 87530) ((-487 . -38) 87480) ((-217 . -38) 87430) ((-474 . -493) 87396) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87378) ((-697 . -612) 87293) ((-710 . -21) T) ((-710 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87275) ((-116 . -611) 87257) ((-157 . -25) T) ((-1281 . -1094) T) ((-868 . -637) 87205) ((-1279 . -1094) T) ((-959 . -102) T) ((-731 . -102) T) ((-711 . -102) T) ((-453 . -102) T) ((-812 . -452) 87156) ((-44 . -1094) T) ((-1082 . -846) T) ((-660 . -131) T) ((-1057 . -309) 87007) ((-666 . -713) 86991) ((-289 . -1052) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86941) ((-954 . -846) 86920) ((-995 . -644) 86858) ((-240 . -1266) 86828) ((-1020 . -307) T) ((-294 . -1051) 86749) ((-906 . -131) T) ((-40 . -916) T) ((-487 . -400) 86731) ((-354 . -307) T) ((-217 . -400) 86713) ((-1074 . -411) 86697) ((-294 . -111) 86613) ((-1177 . -846) T) ((-1176 . -846) T) ((-868 . -25) T) ((-868 . -21) T) ((-339 . -611) 86595) ((-1245 . -47) 86539) ((-225 . -147) T) ((-174 . -611) 86521) ((-1107 . -844) 86500) ((-770 . -611) 86482) ((-128 . -846) T) ((-606 . -235) 86429) ((-475 . -235) 86379) ((-1281 . -713) 86349) ((-48 . -307) T) ((-1279 . -713) 86319) ((-65 . -614) 86248) ((-960 . -1094) T) ((-811 . -1094) 86038) ((-312 . -102) T) ((-897 . -1209) T) ((-48 . -1018) T) ((-1222 . -637) 85946) ((-685 . -102) 85924) ((-44 . -713) 85908) ((-550 . -102) T) ((-294 . -614) 85839) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -757) T) ((-1206 . -1094) 85817) ((-351 . -1051) 85762) ((-671 . -1094) 85740) ((-1056 . -147) T) ((-948 . -147) 85719) ((-948 . -145) 85698) ((-795 . -102) T) ((-152 . -713) 85682) ((-481 . -147) 85661) ((-481 . -145) 85640) ((-351 . -111) 85569) ((-1074 . -1052) T) ((-322 . -846) 85548) ((-1251 . -969) 85517) 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83434) ((-225 . -35) T) ((-49 . -611) 83416) ((-477 . -1052) T) ((-487 . -231) 83398) ((-484 . -964) 83382) ((-482 . -844) 83361) ((-217 . -231) 83343) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-811 . -172) 83322) ((-727 . -102) T) ((-1022 . -611) 83289) ((-500 . -286) 83264) ((-316 . -377) 83233) ((-313 . -377) 83194) ((-313 . -338) 83155) ((-1079 . -611) 83137) ((-812 . -945) 83084) ((-658 . -131) T) ((-1232 . -145) 83063) ((-1232 . -147) 83042) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -713) 83029) ((-1153 . -608) 83005) ((-592 . -309) NIL) ((-484 . -1094) 82983) ((-390 . -611) 82965) ((-510 . -846) T) ((-1144 . -229) 82915) ((-1251 . -1250) 82899) ((-1251 . -1237) 82876) ((-1244 . -1242) 82837) ((-1244 . -1237) 82807) ((-1244 . -1240) 82791) ((-1223 . -1221) 82752) ((-1223 . -1237) 82729) ((-619 . -611) 82711) ((-1223 . -1219) 82695) ((-695 . -916) T) ((-1168 . -284) 82661) ((-1167 . -284) 82627) ((-1161 . -284) 82593) ((-1074 . -1094) T) ((-1055 . -1094) T) ((-48 . -302) T) ((-316 . -896) 82559) ((-313 . -896) NIL) ((-1055 . -1062) 82538) ((-1114 . -882) 82520) ((-795 . -38) 82504) ((-264 . -637) 82452) ((-247 . -637) 82400) ((-697 . -1051) 82387) ((-594 . -1237) 82364) ((-1120 . -284) 82330) ((-319 . -172) 82261) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82243) ((-1114 . -1034) 82225) ((-1096 . -151) 82209) ((-108 . -1094) T) ((-116 . -1051) 82196) ((-707 . -363) T) ((-500 . -602) 82171) ((-697 . -111) 82156) ((-436 . -102) T) ((-45 . -1143) 82106) ((-116 . -111) 82091) ((-633 . -716) T) ((-605 . -716) T) ((-811 . -514) 82024) ((-1031 . -1209) T) ((-939 . -151) 82008) ((-1217 . -611) 81990) ((-1166 . -452) 81921) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81871) ((-1136 . -644) 81845) ((-1119 . -452) 81796) ((-1081 . -1213) 81775) ((-778 . -1213) 81754) ((-776 . -1213) 81733) ((-62 . -1209) T) ((-477 . -611) 81685) ((-477 . -612) 81607) ((-1081 . -556) 81538) ((-990 . -1094) T) ((-778 . -556) 81449) ((-776 . -556) 81380) ((-482 . -411) 81349) ((-621 . -916) 81328) ((-454 . -1213) 81307) ((-727 . -309) 81294) ((-697 . -614) 81266) ((-398 . -611) 81248) ((-671 . -514) 81181) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81112) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 81094) ((-116 . -614) 81066) ((-1261 . -611) 81048) ((-1215 . -846) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80933) ((-1120 . -309) 80920) ((-1074 . -713) 80788) ((-862 . -644) 80748) ((-939 . -976) 80732) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80683) ((-707 . -1106) T) ((-707 . -23) T) ((-697 . -1045) T) ((-643 . -1094) 80661) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80636) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -713) 80588) ((-339 . -1051) 80572) ((-353 . -713) 80524) ((-345 . -713) 80476) ((-174 . -1051) 80408) ((-174 . -111) 80319) ((-108 . -713) 80269) ((-339 . -111) 80248) ((-274 . -1094) T) ((-273 . -1094) T) ((-272 . -1094) T) ((-271 . -1094) T) ((-270 . -1094) T) ((-269 . -1094) T) ((-268 . -1094) T) ((-212 . -1094) T) ((-211 . -1094) T) ((-169 . -1197) 80226) ((-169 . -1194) 80204) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1045) T) ((-207 . -1094) T) ((-206 . -1094) T) ((-203 . -1094) T) ((-202 . -1094) T) ((-201 . -1094) T) ((-200 . -1094) T) ((-199 . -1094) T) ((-198 . -1094) T) ((-197 . -1094) T) ((-196 . -1094) T) ((-195 . -1094) T) ((-194 . -1094) T) ((-193 . -1094) T) ((-240 . -102) 79994) ((-169 . -35) 79972) ((-169 . -95) 79950) ((-650 . -1034) 79846) ((-482 . -1052) 79776) ((-1107 . -1094) 79566) ((-1136 . -34) T) ((-666 . -489) 79550) ((-73 . -1209) T) 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-290) 78142) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -846) 78041) ((-108 . -172) T) ((-868 . -988) 78025) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 78012) ((-518 . -329) 77989) ((-518 . -363) T) ((-316 . -307) 77968) ((-313 . -307) T) ((-600 . -846) 77947) ((-1107 . -713) 77889) ((-520 . -282) 77873) ((-654 . -23) T) ((-418 . -231) 77857) ((-313 . -1018) NIL) ((-336 . -23) T) ((-103 . -1006) 77841) ((-45 . -36) 77820) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77758) ((-1081 . -1106) T) ((-1282 . -644) 77732) ((-778 . -1106) T) ((-776 . -1106) T) ((-454 . -1106) T) ((-1056 . -452) T) ((-948 . -452) 77683) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-813 . -1052) T) ((-778 . -23) T) ((-776 . -23) T) ((-481 . -452) 77634) ((-1153 . -514) 77417) ((-381 . -382) 77396) ((-1172 . -411) 77380) ((-461 . -23) T) ((-454 . -23) T) ((-96 . -1094) T) ((-484 . -514) 77313) ((-289 . -290) T) ((-1076 . -611) 77295) ((-1076 . -612) 77276) ((-407 . -905) 77255) ((-50 . -1106) T) ((-1020 . -916) T) ((-999 . -722) T) ((-708 . -882) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-839 . -644) 77228) ((-1203 . -131) T) ((-1161 . -400) 77180) ((-1000 . -309) NIL) ((-811 . -489) 77164) ((-354 . -916) T) ((-1150 . -34) T) ((-407 . -644) 77116) ((-50 . -23) T) ((-707 . -131) T) ((-708 . -1034) 76996) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 76967) ((-1134 . -1094) T) ((-1274 . -1273) 76951) ((-697 . -791) T) ((-697 . -788) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76933) ((-1222 . -988) 76903) ((-48 . -916) T) ((-671 . -489) 76887) ((-251 . -1266) 76857) ((-250 . -1266) 76827) ((-1170 . -846) T) ((-1107 . -172) 76806) ((-1114 . -1018) T) ((-1042 . -34) T) ((-832 . -147) 76785) ((-832 . -145) 76764) ((-733 . -107) 76748) ((-610 . -132) T) ((-482 . -1094) 76538) ((-1172 . -1052) T) ((-867 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76508) ((-141 . -107) 76490) ((-708 . -377) 76474) 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. -151) 67858) ((-418 . -1052) T) ((-487 . -713) 67808) ((-482 . -489) 67792) ((-327 . -846) 67771) ((-339 . -644) 67745) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67695) ((-169 . -720) 67666) ((-174 . -644) 67598) ((-581 . -21) T) ((-581 . -25) T) ((-518 . -25) T) ((-518 . -21) T) ((-475 . -151) 67548) ((-1074 . -611) 67530) ((-1055 . -611) 67512) ((-989 . -102) T) ((-858 . -102) T) ((-795 . -411) 67476) ((-40 . -131) T) ((-695 . -363) T) ((-697 . -722) T) ((-697 . -790) T) ((-697 . -787) T) ((-212 . -891) T) ((-580 . -1106) T) ((-564 . -1106) T) ((-495 . -1106) T) ((-359 . -611) 67458) ((-353 . -611) 67440) ((-345 . -611) 67422) ((-66 . -396) T) ((-66 . -395) T) ((-108 . -612) 67352) ((-108 . -611) 67294) ((-211 . -891) T) ((-954 . -151) 67278) ((-767 . -131) T) ((-666 . -614) 67196) ((-134 . -722) T) ((-116 . -722) T) ((-1243 . -35) 67162) ((-1049 . -489) 67146) ((-580 . -23) T) ((-564 . -23) T) ((-495 . -23) T) ((-1222 . -95) 67112) ((-1222 . -35) 67078) ((-1166 . -102) T) 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65262) ((-201 . -611) 65244) ((-200 . -611) 65226) ((-199 . -611) 65208) ((-198 . -611) 65190) ((-197 . -611) 65172) ((-536 . -1097) 65124) ((-196 . -611) 65106) ((-195 . -611) 65088) ((-45 . -489) 65025) ((-194 . -611) 65007) ((-193 . -611) 64989) ((-152 . -614) 64958) ((-1109 . -102) T) ((-811 . -111) 64848) ((-641 . -102) 64798) ((-482 . -286) 64775) ((-1107 . -611) 64506) ((-1095 . -1094) T) ((-1042 . -1209) T) ((-1282 . -1034) 64490) ((-621 . -1106) T) ((-1166 . -309) 64477) ((-1129 . -1094) T) ((-1119 . -309) 64464) ((-1090 . -1077) T) ((-1084 . -1077) T) ((-1067 . -1077) T) ((-1060 . -1077) T) ((-1032 . -1077) T) ((-1015 . -1077) T) ((-117 . -1106) T) ((-815 . -102) T) ((-624 . -1077) T) ((-621 . -23) T) ((-1144 . -514) 64256) ((-483 . -1077) T) ((-386 . -102) T) ((-324 . -102) T) ((-218 . -1077) T) ((-959 . -1094) T) ((-152 . -1045) T) ((-727 . -411) 64240) ((-117 . -23) T) ((-999 . -896) 64192) ((-731 . -1094) T) ((-711 . -1094) T) ((-453 . -1094) T) ((-407 . -1209) T) ((-316 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. -612) 23648) ((-939 . -611) 23560) ((-641 . -489) 23544) ((-45 . -1006) 23494) ((-615 . -963) T) ((-491 . -102) T) ((-331 . -611) 23476) ((-1107 . -1034) 23303) ((-592 . -647) 23285) ((-130 . -1094) T) ((-128 . -1094) T) ((-592 . -373) 23267) ((-343 . -1266) 23244) ((-439 . -611) 23226) ((-1023 . -1209) T) ((-867 . -290) T) ((-1232 . -514) 23173) ((-476 . -1209) T) ((-463 . -1209) T) ((-585 . -102) T) ((-1166 . -286) 23100) ((-621 . -452) 23079) ((-996 . -991) 23063) ((-1274 . -382) 23035) ((-517 . -1094) T) ((-117 . -452) T) ((-1189 . -102) T) ((-1086 . -1094) 23013) ((-1030 . -1094) T) ((-1109 . -93) T) ((-889 . -846) T) ((-351 . -1213) T) ((-1251 . -1051) 22896) ((-1107 . -377) 22865) ((-1244 . -1051) 22700) ((-1223 . -1051) 22490) ((-1251 . -111) 22359) ((-1244 . -111) 22180) ((-1223 . -111) 21949) ((-1203 . -309) 21936) ((-351 . -556) T) ((-365 . -611) 21918) ((-289 . -307) T) ((-595 . -1051) 21891) ((-594 . -1051) 21774) ((-361 . -1094) T) ((-322 . -1094) T) ((-251 . -611) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 80b76aa9..cc1ef3bc 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3451299465) +(30 . 3451368715) (4409 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,662 +477,658 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |setchildren!| |consnewpol| |symmetricDifference| - |imports| |associatorDependence| |Lazard2| |viewDeltaYDefault| - |isMult| |rectangularMatrix| |mainKernel| |constantToUnaryFunction| - |smith| |iFTable| |changeWeightLevel| |integral| - |lastSubResultantElseSplit| 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|lowerPolynomial| |euclideanNormalForm| |atoms| |decreasePrecision| - |factorOfDegree| |map!| |magnitude| |bumptab1| |nonQsign| |typeLists| - |c02agf| |chainSubResultants| |c06ecf| |doublyTransitive?| - |pointColor| |qsetelt!| |series| |squareFreeLexTriangular| |li| - |rightTrim| |monomRDEsys| |submod| |freeOf?| |createThreeSpace| - |asechIfCan| |leftTrim| |blankSeparate| |sturmSequence| |powern| - |maxint| |outputBinaryFile| |cCosh| |rotatez| |wordInGenerators| - |rightUnit| |quickSort| |modulus| |oneDimensionalArray| |eyeDistance| - |increase| |prime| |monomial?| |f07aef| |bsolve| |minus!| - |setScreenResolution| |cot2trig| |OMbindTCP| |bfKeys| |makeFR| |min| - |leaves| |sizePascalTriangle| |pushNewContour| |kind| |iiasec| - |internalSubQuasiComponent?| |findBinding| |mesh?| |e02agf| |acsch| - |coleman| |op| |scan| |critM| |bitTruth| |leftDivide| - |useSingleFactorBound| |unrankImproperPartitions1| |block| |s18dcf| - |primitivePart!| |leftUnit| |frst| |fixPredicate| |zeroSquareMatrix| - |hMonic| |partialNumerators| |leftRecip| |squareMatrix| |moduleSum| - |rowEch| |f02abf| |polynomialZeros| |normalizeAtInfinity| |palgextint| - |stirling1| |isConnected?| |hi| |initTable!| |pattern| |f04mbf| |vark| - |shuffle| |stiffnessAndStabilityFactor| |fixedPoints| - |nextsousResultant2| |e02aef| |irreducibleFactors| |laguerre| |f02fjf| - |limitPlus| |associator| |printStats!| |any| |LowTriBddDenomInv| - |pade| |hermite| |e01baf| |iicot| |separate| - |wordsForStrongGenerators| |pquo| |showClipRegion| |union| - |extractClosed| |f2df| |symbolIfCan| |computeInt| |satisfy?| - |drawComplex| |integralMatrixAtInfinity| |currentSubProgram| |numeric| - |lazyResidueClass| |topPredicate| |poisson| |message| |rdregime| - |isExpt| |d03eef| |column| |getMultiplicationMatrix| |linSolve| - |roman| |arguments| |zeroDimPrimary?| |f01rdf| |radical| |e02akf| - |children| |sh| |makeCrit| |ip4Address| |algebraicVariables| |infix?| - |row| |zoom| |unaryFunction| |close| |patternVariable| |findCycle| - |singularAtInfinity?| |changeThreshhold| |mask| |wholeRagits| - |minColIndex| |perfectSqrt| |linearlyDependentOverZ?| |coefChoose| - |nextsubResultant2| |condition| |cothIfCan| |reseed| |imagE| - |chebyshevU| |BasicMethod| |ParCondList| |balancedBinaryTree| - |nextItem| |e01bgf| |OMputEndError| |nextNormalPoly| |display| - |wholePart| |expandPower| |rootOf| |unvectorise| |OMreadStr| |solve| - |exprToUPS| |measure| |f02axf| |node?| |monicRightFactorIfCan| - |alphanumeric| |leftRemainder| |sdf2lst| |lflimitedint| - |functionIsContinuousAtEndPoints| |createMultiplicationMatrix| - |generateIrredPoly| |normFactors| |cons| |quadratic?| |belong?| - |rotatey| |intersect| |viewDefaults| |headAst| |sequences| |bytes| - |infix| |curry| |modifyPoint| |derivative| |groebgen| |eigenvalues| - |permutationGroup| |symmetricTensors| |screenResolution| |pointPlot| - |Si| |real?| |firstUncouplingMatrix| |argumentList!| |leftZero| - |e02baf| |stronglyReduced?| |brillhartIrreducible?| - |jordanAdmissible?| |scripted?| |intensity| |elRow1!| |normalized?| - |bezoutMatrix| |lastSubResultant| |simpson| |permanent| |stirling2| - |less?| |input| |OMputBVar| |iroot| |tablePow| |ef2edf| - |clearFortranOutputStack| |iisqrt2| |e04jaf| |closed?| |getMatch| - |library| |roughBasicSet| |f04atf| |createRandomElement| |makeUnit| - |restorePrecision| |iipow| |f04asf| |makeSeries| |dmpToP| - |LiePolyIfCan| |mainForm| |spherical| |expIfCan| - |SturmHabichtMultiple| |resetAttributeButtons| |paraboloidal| - |hexDigit?| |seriesToOutputForm| |OMgetApp| |source| |mainExpression| - |groebner| |OMcloseConn| |acschIfCan| |bag| |bipolarCylindrical| - |setFormula!| |selectPolynomials| |singleFactorBound| |SturmHabicht| - |leftAlternative?| |setPoly| |indiceSubResultant| |pseudoDivide| - |aCubic| |mathieu12| |parametersOf| |elementary| - |semiResultantEuclidean2| |pdf2ef| |goodnessOfFit| |nary?| - |cosSinInfo| |getProperty| |integralBasisAtInfinity| |cardinality| - |f02adf| |set| |polar| |direction| |zag| |uniform01| |cAcosh| - |startTable!| |insertTop!| |setColumn!| |critMonD1| |length| |more?| - |pile| |printTypes| |bottom!| |setClosed| |var2Steps| |composites| - |finiteBasis| |setLength!| |critBonD| |scripts| |multiplyExponents| - |every?| |e04fdf| |selectAndPolynomials| |integers| |target| - |coordinate| |unexpand| |optional?| |compile| |writeInt8!| - |computeCycleEntry| |d01anf| |asinhIfCan| |getPickedPoints| - |createPrimitivePoly| |rst| |newTypeLists| |fprindINFO| |retract| - |messagePrint| |aromberg| |lfunc| |maxIndex| |ddFact| - |constantCoefficientRicDE| |idealiserMatrix| |lazyPrem| - |minimalPolynomial| |argumentListOf| |internal?| |cycleLength| - |unparse| |d03edf| |separant| |assign| |normal01| - |primPartElseUnitCanonical!| |certainlySubVariety?| - |algebraicCoefficients?| |pushuconst| |setStatus!| |ratDenom| - |axesColorDefault| |permutationRepresentation| |triangSolve| |leaf?| - |tubeRadiusDefault| |setleaves!| |qroot| |leadingTerm| |addMatch| - |zCoord| |subCase?| |sylvesterMatrix| |iiasinh| |orthonormalBasis| - |cycleTail| |capacity| |finiteBound| |ravel| |changeBase| |fortran| - |replaceKthElement| |df2mf| |f02bbf| |one?| |extensionDegree| |inc| - |integralMatrix| |internalDecompose| |perfectNthPower?| |members| - |divisor| |reshape| |unmakeSUP| |cosIfCan| |tube| - |commutativeEquality| |zeroSetSplit| |space| |testModulus| |setelt!| - |f01maf| |top| |associatedSystem| |internalIntegrate| |optimize| - |leadingSupport| |npcoef| |build| |standardBasisOfCyclicSubmodule| - |intermediateResultsIF| |randnum| |numberOfPrimitivePoly| |sin2csc| - |nil?| |e02bdf| |eigenvector| |finite?| |subtractIfCan| |appendPoint| - |unitNormal| |plus| |equation| |getDatabase| |signatureAst| - |hasPredicate?| |list| |f01qcf| |mkAnswer| |ricDsolve| |OMsetEncoding| - |parse| |preprocess| |printingInfo?| |singularitiesOf| - |quotedOperators| |stopTableGcd!| |denominator| |car| - |univariatePolynomials| |stosePrepareSubResAlgo| |trivialIdeal?| - |largest| |cAtan| |isTimes| |schwerpunkt| |df2ef| |infieldint| - |OMopenString| |cdr| |nextLatticePermutation| |bfEntry| |d02ejf| - |implies| |routines| |nonSingularModel| |setDifference| - |complexElementary| |hasTopPredicate?| |getMeasure| |true| |comp| - |d01bbf| |rewriteIdealWithRemainder| |repeating?| |iisec| - |increasePrecision| |graeffe| |times| |minIndex| |setIntersection| - |float?| |infLex?| |initial| |ocf2ocdf| |copies| |iomode| |operators| - |endSubProgram| |gcdcofactprim| |contains?| - |semiDegreeSubResultantEuclidean| |setUnion| |sts2stst| - |genericRightTraceForm| |setClipValue| |safeFloor| |duplicates| - |f07fdf| |times!| |opeval| |high| |d02raf| |apply| |rightRank| - |outputGeneral| |mkcomm| |leadingIndex| |checkRur| - |numberOfFractionalTerms| |rowEchLocal| |stoseSquareFreePart| - |readUInt32!| |green| |approximants| |infiniteProduct| |iisin| - |identification| |primeFactor| |leadingExponent| |unknownEndian| - |monom| |inverseIntegralMatrixAtInfinity| |maxPoints| |wholeRadix| - |size| |exp1| |s17ahf| |script| |intChoose| |split!| |decompose| - |factorSFBRlcUnit| |rule| |OMgetObject| |readLineIfCan!| |in?| - |factor1| |getCode| |firstNumer| |sinh2csch| |cyclicEqual?| - |OMgetInteger| |point?| |externalList| |kmax| |compose| |ranges| - |viewThetaDefault| |integralRepresents| |qinterval| - |halfExtendedResultant2| |squareFreePolynomial| |movedPoints| - |reverseLex| |addPoint| |common| |rightRegularRepresentation| - |sumOfKthPowerDivisors| |rombergo| |mapmult| |first| |delete| - |nextPrimitiveNormalPoly| |index| |tex| |lprop| |d02gaf| - |evaluateInverse| |s14baf| |closeComponent| |fglmIfCan| |tanh2trigh| - |writeUInt8!| |rest| |evenlambert| |rootPower| |tanNa| - |showTypeInOutput| |vspace| |totalDifferential| |mapMatrixIfCan| - |cCsch| |substitute| |selectsecond| |norm| |stoseLastSubResultant| - |hyperelliptic| |coshIfCan| |ksec| |pointSizeDefault| |e01bhf| - |e02daf| |removeDuplicates| |hermiteH| |collect| |tanAn| |fmecg| - |taylorQuoByVar| |ptFunc| |relativeApprox| |ref| |pair| |diagonal?| - |gcdPrimitive| |slash| |child?| |updateStatus!| |tubePointsDefault| - |pleskenSplit| |d01amf| |reduceBasisAtInfinity| |imagk| |compdegd| - |OMmakeConn| |binaryTree| |pomopo!| |viewPhiDefault| - |exprHasAlgebraicWeight| |value| |distribute| |lambert| EQ - |fortranCharacter| |screenResolution3D| |#| |qfactor| |s17dhf| - |listYoungTableaus| |lineColorDefault| |tanh2coth| |push| |exprex| - |trapezoidal| |totalGroebner| |extractSplittingLeaf| - |var2StepsDefault| |monomials| |midpoint| |degree| |iidprod| - |getConstant| |algDsolve| |debug3D| |changeMeasure| |logical?| - |linearDependence| |expandTrigProducts| |userOrdered?| - |symmetricProduct| |extractTop!| |calcRanges| |atanIfCan| - |removeRoughlyRedundantFactorsInContents| |laurentIfCan| - |LyndonWordsList1| |cscIfCan| |OMreceive| |setProperty| - |initiallyReduce| |subHeight| |red| |reopen!| - |semiResultantReduitEuclidean| |rightOne| |epilogue| - |SturmHabichtSequence| |s15adf| |stripCommentsAndBlanks| |supersub| - |startTableGcd!| |cAcot| |monomRDE| |fintegrate| |equality| - |mapBivariate| |alternating| |errorKind| |integralBasis| |multisect| - |connect| |moebius| |s17aff| |characteristicPolynomial| |exQuo| - |numberOfChildren| |twist| |mdeg| |rroot| |viewWriteAvailable| - |torsionIfCan| |makeprod| |arbitrary| |Aleph| |log10| |properties| - |zeroDimensional?| |primlimintfrac| |numberOfComputedEntries| - |countable?| |lowerCase!| |commonDenominator| |generalizedEigenvector| - |critT| |continue| |lintgcd| |univariateSolve| |bitand| - |lazyPseudoRemainder| |translate| |makeVariable| |antiAssociative?| - |constantOpIfCan| |rename| |innerint| |stFunc1| |subMatrix| |tree| - |lquo| |bitior| |HenselLift| |e02bbf| |removeSuperfluousCases| - |e02gaf| |imagJ| |iilog| |multiEuclidean| |closedCurve?| - |setMaxPoints3D| |possiblyNewVariety?| |iteratedInitials| |push!| - |quasiMonicPolynomials| |interpolate| |mapExponents| |OMconnInDevice| - |rarrow| |complexRoots| |symbol?| |sayLength| |rootDirectory| - |extendedIntegrate| |cyclicSubmodule| |rightZero| |constantRight| - |OMgetAttr| |primeFrobenius| |semiIndiceSubResultantEuclidean| - |setsubMatrix!| |acothIfCan| |loopPoints| |ScanArabic| - |OMunhandledSymbol| |external?| |incrementKthElement| |signAround| - |e01saf| |deepestTail| |prepareSubResAlgo| |startTableInvSet!| - |radicalRoots| |sn| |problemPoints| |untab| |polyRDE| - |selectMultiDimensionalRoutines| |att2Result| |outputFixed| |ipow| - |getOperands| |flagFactor| |saturate| |SturmHabichtCoefficients| - |isEquiv| |fixedPointExquo| |bindings| |makeFloatFunction| - |OMencodingUnknown| |factorSquareFree| |OMputInteger| - |extractProperty| |printCode| |interpret| |isList| |viewSizeDefault| - F2FG |stack| |over| |setAdaptive| |lfextlimint| |choosemon| |edf2ef| - |nextNormalPrimitivePoly| |search| |clip| |resetBadValues| - |cyclePartition| |skewSFunction| |numberOfComponents| |comment| - |edf2df| |noncommutativeJordanAlgebra?| |completeEval| |key?| - |removeSuperfluousQuasiComponents| |octon| |createNormalPoly| |pr2dmp| - |clipParametric| |representationType| |tower| |universe| |swap!| - |integral?| |fractRadix| |pdct| |getlo| |OMencodingXML| |paren| |blue| - |reduceLODE| |constant| |mapCoef| |critpOrder| |basisOfLeftNucloid| - |infinityNorm| |isOpen?| |doubleDisc| |rightUnits| - |stoseInvertibleSet| |unary?| |readInt32!| Y |c06gsf| |dim| - |viewport2D| |critB| |subNodeOf?| |normalElement| - |resultantReduitEuclidean| |anticoord| |viewport3D| |leftNorm| - |initializeGroupForWordProblem| |host| |f02ajf| |readInt16!| - |splitNodeOf!| |partialFraction| |optAttributes| |clearDenominator| - |nsqfree| F |binarySearchTree| |OMsend| |getBadValues| |content| - |multinomial| |rewriteSetWithReduction| |factorsOfDegree| - |createNormalPrimitivePoly| |parabolicCylindrical| |fortranTypeOf| - |genericPosition| |lazyIrreducibleFactors| |separateDegrees| |neglist| - |complexNumeric| |ellipticCylindrical| |coerceListOfPairs| - |selectfirst| |palgintegrate| |cRationalPower| |divergence| |shift| - |yCoord| ~= |determinant| |digit| |any?| |limitedint| |null| - |enterInCache| |queue| |size?| |colorFunction| |coerceP| |isAnd| - |coerce| |getVariableOrder| |kernels| |linearAssociatedOrder| |c05nbf| - |atrapezoidal| |argument| |not| |iiabs| |rightMinimalPolynomial| - |inR?| |updatF| |inputBinaryFile| |construct| |quartic| - |createLowComplexityTable| |iterationVar| |univcase| |univariate| - |chiSquare1| |and| |root| |scanOneDimSubspaces| |interval| |refine| - |reduction| |empty| |double?| |makeGraphImage| |numericalIntegration| - |physicalLength!| |or| |mainMonomials| |trim| |explicitlyEmpty?| - |toseInvertibleSet| |setAttributeButtonStep| |f07fef| |eof?| - |partitions| |round| |buildSyntax| |xor| |categoryFrame| - |antiCommutator| |xCoord| |removeCosSq| |rootNormalize| |s13adf| - |distdfact| |showSummary| |polyRicDE| |tanhIfCan| |factor| |null?| - |case| |antisymmetric?| |is?| |rootKerSimp| |solid| |solveInField| - |acotIfCan| |useEisensteinCriterion| |secIfCan| |hue| |sqrt| - |oddintegers| |Zero| |coHeight| |OMputEndAtp| |iicos| |df2st| - |subPolSet?| |sec2cos| |obj| |measure2Result| |rationalApproximation| - |showAttributes| |definingPolynomial| |real| |sinIfCan| |One| |cPower| - |character?| |degreeSubResultantEuclidean| |omError| |karatsuba| - |charthRoot| |autoReduced?| |number?| |makeSin| |cache| - |completeHermite| |imag| |rightGcd| |currentCategoryFrame| |graphs| - |evenInfiniteProduct| |name| |OMputObject| |nativeModuleExtension| - |monicCompleteDecompose| |nextPrimitivePoly| |tanIfCan| |normalDeriv| - |directProduct| |f01ref| |vconcat| |btwFact| |cyclicEntries| - |systemSizeIF| |body| |prevPrime| |zerosOf| |monicLeftDivide| - |OMputEndAttr| |lazyVariations| |createNormalElement| - |resultantEuclidean| |sort!| |components| |reverse!| - |topFortranOutputStack| |numFunEvals| |rational?| |reducedForm| - |exprToXXP| |OMgetAtp| |fixedDivisor| |brace| |semicolonSeparate| - |makeViewport2D| |wronskianMatrix| |varselect| |complexSolve| - |contractSolve| |divisors| |clearTheIFTable| |fortranLiteralLine| - |destruct| |showAllElements| |mightHaveRoots| |sincos| - |setTopPredicate| |rootSplit| |OMgetEndError| |presub| |extendedint| - |LazardQuotient| |integralAtInfinity?| |limit| |checkForZero| - |mainCoefficients| |completeHensel| |eulerPhi| |leftFactor| - |dimensions| |computeCycleLength| - |solveLinearPolynomialEquationByFractions| |mathieu22| |complement| - |makeTerm| |newLine| |returnType!| |palgLODE0| |gcdprim| - |generalizedContinuumHypothesisAssumed| |hcrf| |palglimint0| - |viewWriteDefault| |readInt8!| |reverse| |palgextint0| - |semiSubResultantGcdEuclidean1| |removeRedundantFactorsInPols| - |exponential| |exponential1| |port| |outputAsScript| - |extendedEuclidean| |se2rfi| |scopes| |coord| |c06ekf| |pole?| - |monomial| |genericLeftDiscriminant| |moreAlgebraic?| |morphism| - |entry| |prepareDecompose| |OMgetString| |hasoln| |leftRank| - |derivationCoordinates| |digit?| |laguerreL| |multivariate| - |primitivePart| |accuracyIF| |adaptive?| |subst| |bubbleSort!| |t| - |exquo| |getOrder| |leftTrace| |listBranches| |position!| - |indicialEquation| |error| |partition| |variables| |dot| - |leftCharacteristicPolynomial| |normInvertible?| |rischDE| - |basisOfCentroid| |div| |OMgetVariable| |sech2cosh| - |getSyntaxFormsFromFile| |maxdeg| |assert| |expintegrate| |factorset| - |toroidal| |curryRight| |index?| |delta| |quo| |enumerate| - |deepestInitial| |birth| |doubleResultant| |hasSolution?| - |mapUnivariate| |numberOfCycles| |curveColorPalette| |imagK| - |explicitlyFinite?| |unit| |cyclotomicDecomposition| |monicDivide| - |s18aff| |scalarMatrix| |sup| |rational| |c02aff| |startStats!| - |generalLambert| |groebner?| |rem| |basisOfCommutingElements| - |subresultantVector| |predicates| |stoseInvertible?reg| |cn| - |OMputSymbol| |quasiRegular| |safeCeiling| |superHeight| |cTanh| - |solveLinearPolynomialEquationByRecursion| |traceMatrix| - |complexExpand| |binding| |tab| |biRank| |localUnquote| |jacobi| - |taylor| |d01gbf| |resultant| |removeDuplicates!| |objects| - |remainder| |interactiveEnv| |cCsc| |tracePowMod| |module| - |sortConstraints| |swapRows!| |f07adf| |laurent| |localAbs| - |errorInfo| |figureUnits| |base| |fortranInteger| |constantKernel| - |d03faf| |complete| |minRowIndex| |SFunction| |commutator| |puiseux| - |readable?| |acosIfCan| |cCot| |max| |chiSquare| |frobenius| - |maxPoints3D| |squareFreePrim| |quotientByP| |d01asf| |torsion?| - |Gamma| |collectQuasiMonic| |meshPar2Var| |s21bdf| |s18acf| - |closedCurve| |rangeIsFinite| |ode2| |principalAncestors| |inv| - |characteristicSerie| |legendre| |selectSumOfSquaresRoutines| - |hexDigit| |OMputEndObject| |leftRegularRepresentation| - |doubleFloatFormat| |fTable| |OMputEndBind| |ground?| - |selectIntegrationRoutines| |prologue| |charpol| |removeConstantTerm| - |rspace| |complexNormalize| |getCurve| |squareFree| |harmonic| - |countRealRoots| |acosh| |weakBiRank| |ground| |fortranLinkerArgs| - |patternMatchTimes| |trigs| |quotient| |setImagSteps| - |numberOfIrreduciblePoly| |totalDegree| |callForm?| |coerceS| |atanh| - |basisOfCenter| |leadingMonomial| |conjugate| |commutative?| - |mapSolve| |rationalPoint?| |zeroDimPrime?| |quadraticNorm| - |rightExtendedGcd| |getZechTable| |tableau| |acoth| - |showFortranOutputStack| |leadingCoefficient| |shiftRight| |extension| - |recip| |readByte!| |someBasis| |listRepresentation| |identity| - |semiResultantEuclidean1| |asech| |presuper| |primitiveMonomials| - |gderiv| |d01fcf| |s13aaf| |mix| |numberOfComposites| |divideIfCan!| - |psolve| |normalDenom| |outlineRender| |iiasin| |imagi| BY |reductum| - |printStatement| |e04dgf| |cosh2sech| |OMputAtp| |s19abf| |postfix| - |f01brf| |isOp| |multiple| |po| |tensorProduct| |laplacian| - |cyclicParents| |airyAi| |asecIfCan| |say| |difference| |branchIfCan| - |generic?| |transcendent?| |applyQuote| - |solveLinearPolynomialEquation| |linearDependenceOverZ| |previous| - |continuedFraction| |iicsch| |forLoop| |numericalOptimization| - |nthRoot| |product| |char| |replace| |operation| - |lastSubResultantEuclidean| |internalLastSubResultant| |gramschmidt| - |prod| |nullity| |crest| |reducedSystem| |recur| |setOfMinN| - |flexible?| |internalZeroSetSplit| |modularFactor| |plusInfinity| - |partialQuotients| |ord| |d02kef| |diag| |radicalSolve| |ruleset| - |deepCopy| |factorAndSplit| |exprToGenUPS| |cSinh| |minusInfinity| - |showIntensityFunctions| |relationsIdeal| |PollardSmallFactor| - |comparison| |duplicates?| |OMgetSymbol| |showTheIFTable| - |genericLeftMinimalPolynomial| |basisOfMiddleNucleus| |makingStats?| - NOT |setPosition| |primlimitedint| |extractIfCan| |generators| - |negative?| |f02aff| |back| |positive?| |nextIrreduciblePoly| - |OMconnOutDevice| OR |leftScalarTimes!| |medialSet| |suchThat| |float| - |exponents| |createLowComplexityNormalBasis| |realZeros| - |genericLeftNorm| |getGoodPrime| |powerSum| |ramified?| - |halfExtendedSubResultantGcd1| AND |alternative?| |polCase| - |collectUnder| |matrixDimensions| |generalTwoFactor| - |basisOfRightNucleus| |lieAlgebra?| |e04mbf| |f04faf| |e04gcf| - |digamma| |print| |roughUnitIdeal?| |type| |OMUnknownSymbol?| - |totolex| |simpsono| |clearTable!| |adjoint| |setfirst!| - |beauzamyBound| |invertibleSet| |resolve| |cycles| |dihedral| - |lowerCase| |rootPoly| |writeLine!| |Ci| |upDateBranches| - |invmultisect| |numerators| |integer?| |invertibleElseSplit?| - |gcdPolynomial| |rdHack1| |low| |cschIfCan| |radPoly| - |symmetricRemainder| |keys| |reciprocalPolynomial| |unitVector| - |selectNonFiniteRoutines| |henselFact| |setref| |rur| - |LazardQuotient2| |fortranDouble| |addPoint2| |dequeue!| |e01daf| - |nthr| |quoByVar| |e01sef| |atanhIfCan| |quadratic| |light| - |lazyGintegrate| |OMgetError| |viewPosDefault| |setRealSteps| |iiacot| - |fortranComplex| |recoverAfterFail| GE |lex| |minimize| |interReduce| - |leftGcd| |aQuartic| |removeSinSq| |multiEuclideanTree| - |algSplitSimple| GT |qPot| |c05pbf| |power| |seriesSolve| - |ramifiedAtInfinity?| |definingInequation| |testDim| |addmod| - |setMinPoints3D| * LE |palgRDE0| |normalizedAssociate| |sinhcosh| - |generate| |fortranLogical| |fractionFreeGauss!| |OMgetEndObject| - |invertible?| |sub| |algebraicSort| LT |OMgetType| |ran| |mesh| - |primintegrate| |resetNew| |chineseRemainder| |ScanRoman| |oddlambert| - |drawCurves| |incrementBy| |d01alf| |cyclic?| |listexp| |predicate| - |has?| |stop| |pack!| |strongGenerators| |geometric| |expintfldpoly| - |irreducibleRepresentation| = |ratDsolve| |composite| |roughSubIdeal?| - |expand| |minset| |s17adf| |isobaric?| |reducedQPowers| - |monomialIntegrate| |LagrangeInterpolation| |getStream| |acoshIfCan| - |Beta| |filterWhile| |repeatUntilLoop| |mulmod| |prinpolINFO| - |zeroDim?| |getOperator| |extend| < |iicsc| |iflist2Result| - |totalfract| |filterUntil| |showTheFTable| |clearTheSymbolTable| - |maximumExponent| |csubst| |palgint0| |just| > |getProperties| - |leftOne| |setEpilogue!| |select| |usingTable?| |polyPart| - |functionIsFracPolynomial?| |pair?| |genericRightDiscriminant| - |ParCond| <= |center| |varList| |toseSquareFreePart| - |LyndonCoordinates| |OMputString| |whitePoint| |orbit| |denomLODE| - |sparsityIF| |innerSolve| |top!| |sumOfDivisors| >= |escape| |redmat| - |cotIfCan| |fill!| |subSet| |useNagFunctions| |status| - |pointColorPalette| |solveid| |internalAugment| |merge| |littleEndian| - |lyndonIfCan| |sturmVariationsOf| |property| |bernoulli| |binomial| - |f02agf| |iiperm| |corrPoly| |convergents| |cylindrical| |copyInto!| - |leftUnits| |parameters| |primaryDecomp| |modularGcd| |putGraph| - |fortranCarriageReturn| |rangePascalTriangle| |lexGroebner| - |lSpaceBasis| |stopTable!| + |inverseLaplace| |represents| - |setScreenResolution3D| |cAcos| |antisymmetricTensors| |decrease| - |splitDenominator| |abelianGroup| |maxColIndex| - |explogs2trigs| - |makeRecord| |dominantTerm| |indicialEquations| |units| - |particularSolution| |palgRDE| |createGenericMatrix| |LyndonBasis| - |hspace| |retractIfCan| |simplifyLog| / |rightTraceMatrix| |f04jgf| - |rightFactorCandidate| |processTemplate| |OMreadFile| |isTerm| |atom?| - |triangular?| |rotate| |rightScalarTimes!| |aQuadratic| |simplify| - |coerceL| |bright| |univariatePolynomialsGcds| |inputOutputBinaryFile| - |cycleSplit!| |expenseOfEvaluation| |Frobenius| UP2UTS - |powerAssociative?| |exists?| |xn| |cAcoth| |kernel| |fracPart| - |s14aaf| |exportedOperators| |rightTrace| |iibinom| |leftTraceMatrix| - |bandedHessian| |writeBytes!| |ptree| |pushdterm| |draw| - |safetyMargin| |bandedJacobian| |d01akf| |isPower| |aLinear| |key| - |bipolar| |function| |clearCache| |code| |isPlus| |monicModulo| - |curve?| |binaryTournament| |sign| |nonLinearPart| |currentScope| - |rootProduct| |d02gbf| |irreducibleFactor| |createZechTable| - |graphCurves| |startPolynomial| |conical| |eulerE| - |combineFeatureCompatibility| |setStatus| |filename| |bombieriNorm| - |eval| |addBadValue| |readBytes!| |hessian| |cAtanh| |rank| - |OMgetEndBVar| |createPrimitiveElement| |cAcsc| - |tableForDiscreteLogarithm| |c06eaf| |isQuotient| |B1solve| - |OMputAttr| |member?| |mr| |OMencodingSGML| |dualSignature| - |makeObject| |exponentialOrder| |genericLeftTraceForm| - |principalIdeal| |padicFraction| |map| |df2fi| |fortranDoubleComplex| - |augment| |s21baf| |f04mcf| |goto| |f02aaf| |dAndcExp| |listLoops| - |currentEnv| |gcdcofact| |leadingCoefficientRicDE| |definingEquations| - |normalise| |binary| |coef| GF2FG |extractPoint| |monicRightDivide| - |pastel| |semiDiscriminantEuclidean| |lexico| |diophantineSystem| - |iiacsch| |associative?| |compiledFunction| |isOr| - |useSingleFactorBound?| |e01sbf| |divide| |GospersMethod| |colorDef| - |lazyPremWithDefault| |copy!| |noLinearFactor?| |showTheSymbolTable| - |HermiteIntegrate| |maxrow| |height| |radicalEigenvectors| - |euclideanGroebner| |innerSolve1| |exprHasLogarithmicWeights| - |ratPoly| |dimensionsOf| |elem?| |probablyZeroDim?| |s17acf| |convert| - |bivariatePolynomials| |multiset| |remove!| |splitSquarefree| |lists| - |printHeader| |characteristic| UTS2UP |genericRightNorm| - |withPredicates| |fractRagits| |moebiusMu| |rightExactQuotient| |hclf| - |subscriptedVariables| |alphabetic| |slex| |rootRadius| |llprop| - |bothWays| |inGroundField?| |e01sff| |title| |mainDefiningPolynomial| - |zeroVector| |nor| |nthFractionalTerm| |leftPower| |polygon?| |lcm| - |OMconnectTCP| |perfectSquare?| |s18adf| |setprevious!| |Nul| |failed| - |algebraicOf| |complexIntegrate| |maxrank| |OMgetFloat| |expr| - |subresultantSequence| |genericRightTrace| |swapColumns!| |argscript| - |OMputVariable| |Vectorise| |lagrange| |conjugates| - |semiLastSubResultantEuclidean| |e| |append| |cLog| |rightMult| - |e02ajf| |lift| |tanintegrate| |indiceSubResultantEuclidean| - |sumOfSquares| |expandLog| |indicialEquationAtInfinity| |readLine!| - |gcd| |removeSinhSq| |dark| |setrest!| |reduce| |lyndon?| |transform| - |e02dcf| |divideExponents| |tubeRadius| |triangulate| |false| |unit?| - |infieldIntegrate| |countRealRootsMultiple| |initiallyReduced?| - |gethi| |sylvesterSequence| |positiveRemainder| |isNot| |d02bbf| - |variable| |domainOf| |dimensionOfIrreducibleRepresentation| |nothing| - |cyclicCopy| |primitive?| |declare| |setLabelValue| |zero?| - |iterators| |mpsode| |insertionSort!| |scale| |mapGen| |clipBoolean| - |solveRetract| |e01bef| |viewZoomDefault| |outputFloating| |rightLcm| - |s18def| |child| |datalist| |bit?| |summation| |diagonal| |empty?| - |lifting1| |tail| |cAsinh| |complexForm| |generalPosition| - |infRittWu?| |d01apf| |balancedFactorisation| |imagI| |pdf2df| - |generalizedContinuumHypothesisAssumed?| |rightRankPolynomial| - |approxNthRoot| |polygon| |surface| |rules| |redPo| |roughBase?| - |outputForm| |lighting| |reify| |conjug| |rightQuotient| |printInfo!| - |outputList| |rootsOf| |plus!| |showTheRoutinesTable| |collectUpper| - |LyndonWordsList| |divisorCascade| |unknown| |getIdentifier| - |socf2socdf| |decimal| |width| |returnTypeOf| |cyclic| - |removeSquaresIfCan| |airyBi| |lambda| |iExquo| |orbits| |baseRDE| - |iisinh| |conditionsForIdempotents| |firstDenom| |solveLinearlyOverQ| - |iicoth| |homogeneous?| |realEigenvalues| |stoseInvertible?sqfreg| - |bivariate?| |deleteRoutine!| |discreteLog| |radicalSimplify| - |simplifyExp| |increment| |symmetricGroup| |basis| |f01qdf| - |shallowExpand| |algint| |init| |idealSimplify| |byte| |fi2df| RF2UTS - |BumInSepFFE| |wordInStrongGenerators| |jacobiIdentity?| |isImplies| - |solid?| |factorList| |inf| |moduloP| |mainCharacterization| |part?| - |hitherPlane| |setTex!| |d02cjf| |var1StepsDefault| |curve| - |innerEigenvectors| |intPatternMatch| |An| |besselJ| - |localIntegralBasis| |lfextendedint| |twoFactor| |changeNameToObjf| - |LiePoly| |palglimint| |singRicDE| |selectOptimizationRoutines| |int| - |defineProperty| |e02ahf| |normalForm| |cot2tan| |optional| - |youngGroup| LODO2FUN |minimumDegree| |dequeue| |extendedResultant| - |mapDown!| |symmetric?| |variationOfParameters| |discriminant| |find| - |bat1| |polygamma| |leftMult| |toseInvertible?| |shade| |fractionPart| - |whileLoop| |imagj| |subResultantChain| |uncouplingMatrices| - |purelyAlgebraicLeadingMonomial?| |var1Steps| |pmComplexintegrate| - |eigenvectors| |expt| |pascalTriangle| |bitCoef| |endOfFile?| - |outputAsTex| |digits| |nullSpace| |odd?| |vertConcat| |unitNormalize| - |subTriSet?| |goodPoint| |s17akf| |realEigenvectors| - |primitiveElement| |factorSquareFreeByRecursion| |eigenMatrix| - |rationalPower| |setright!| |f02awf| |pushFortranOutputStack| |pol| - |iitanh| |subResultantGcdEuclidean| |exactQuotient| - |shanksDiscLogAlgorithm| |stoseInternalLastSubResultant| |returns| - |stFunc2| |OMputError| |numberOfVariables| |log| |cTan| |schema| - |rowEchelon| |setErrorBound| |variable?| |normalizedDivide| - |Hausdorff| |genus| |multMonom| |double| |test| |linearMatrix| - |anfactor| |squareFreePart| SEGMENT |newReduc| - |factorsOfCyclicGroupSize| |lieAdmissible?| |factorByRecursion| - |groebSolve| |mainVariable?| |inverseIntegralMatrix| |basisOfNucleus| - |pToHdmp| |elseBranch| |degreePartition| |patternMatch| |coefficient| - |setlast!| |tanSum| |partialDenominators| |merge!| |bumprow| - |makeMulti| |pToDmp| |asinIfCan| |factorials| |fixedPoint| |edf2fi| - |sizeMultiplication| |dimension| |numberOfFactors| |eq| |iiasech| - |heapSort| |/\\| |hconcat| |indices| |d02bhf| |pointLists| - |setProperty!| |axes| |insertBottom!| |singular?| |iter| - |physicalLength| |mindeg| |\\/| |prefix| |ideal| |setFieldInfo| - |mapUnivariateIfCan| |printInfo| |bits| |matrixGcd| |e02zaf| - |numberOfHues| |c06ebf| |meatAxe| |makeYoungTableau| |lllp| |c06gcf| - |OMgetEndApp| |isAbsolutelyIrreducible?| |byteBuffer| |flatten| - |pushdown| |laurentRep| |positiveSolve| |highCommonTerms| |zeroMatrix| - |declare!| |f04axf| |operator| |possiblyInfinite?| |getExplanations| - |distance| |localReal?| |ffactor| |s17dlf| |nil| |mainPrimitivePart| - |middle| |concat| |parts| |horizConcat| |separateFactors| |mantissa| - |changeVar| |newSubProgram| |cExp| |bezoutResultant| |irreducible?| - |companionBlocks| |divideIfCan| |subResultantGcd| |diff| |sizeLess?| - |karatsubaDivide| |controlPanel| |ode| |reducedContinuedFraction| - |OMwrite| |iCompose| |hdmpToDmp| |leftExactQuotient| - |tryFunctionalDecomposition?| |hex| |inverseColeman| |mergeFactors| - |badNum| |meshPar1Var| |addPointLast| |intcompBasis| |approximate| - |node| |close!| |sechIfCan| |noKaratsuba| |qualifier| |complex| |exp| - |iisqrt3| |tan2trig| |popFortranOutputStack| |nthRootIfCan| |s15aef| - |supRittWu?| |numberOfDivisors| |cup| |linearPolynomials| - |mainSquareFreePart| |OMlistCDs| |c06fuf| |repeating| |lazy?| - |leastMonomial| |clearTheFTable| |scaleRoots| |diagonals| |s19adf| - |dflist| |rootSimp| |f04adf| |ScanFloatIgnoreSpaces| |OMserve| - |segment| |erf| |abs| |alphabetic?| |createIrreduciblePoly| - |halfExtendedSubResultantGcd2| |musserTrials| |read!| |rk4f| |s19aaf| - |rk4a| |removeRoughlyRedundantFactorsInPols| |entry?| |elColumn2!| - |cap| |outerProduct| |mainValue| |parabolic| |taylorIfCan| - |OMgetEndBind| |deref| |symbolTableOf| |cfirst| |complementaryBasis| - |s20acf| |updatD| |unitCanonical| |notelem| |truncate| |hdmpToP| - |pointColorDefault| |reducedDiscriminant| |remove| |dilog| - |realElementary| |minGbasis| |OMputFloat| |eisensteinIrreducible?| - |iprint| |hypergeometric0F1| |matrixConcat3D| |lowerCase?| - |shrinkable| |sin| |ridHack1| |knownInfBasis| |plot| - |explicitEntries?| |c06gqf| |drawComplexVectorField| |invertIfCan| - |meshFun2Var| |quoted?| |last| |cos| |cyclicGroup| |eq?| |e02adf| - |head| |createMultiplicationTable| |failed?| |rightFactorIfCan| FG2F - |superscript| |assoc| |tan| |OMlistSymbols| |arity| |pseudoRemainder| - |purelyAlgebraic?| |tRange| |second| |OMread| |makeop| |iisech| - |fortranReal| |cot| |addMatchRestricted| |trueEqual| |e02ddf| - |lfinfieldint| |overlabel| |third| |alternatingGroup| |coefficients| - |sqfrFactor| |selectODEIVPRoutines| |quasiMonic?| |sec| |signature| - |mapUp!| |optpair| |euler| |regularRepresentation| - |numberOfOperations| |mvar| |mapExpon| |quasiAlgebraicSet| - |principal?| |list?| |linearAssociatedExp| |csc| |degreeSubResultant| - |ldf2lst| |cycle| |totalLex| |OMUnknownCD?| |removeCoshSq| - |decomposeFunc| |RemainderList| |rightRecip| |badValues| |asin| - |normalizeIfCan| |numericIfCan| |padicallyExpand| |oblateSpheroidal| - |lhs| |category| |OMputBind| |iiacos| |order| |pureLex| |integrate| - |acos| |inverse| |doubleComplex?| |adaptive| |thetaCoord| |rhs| - |domain| |structuralConstants| |fortranCompilerName| |ODESolve| - |pushup| |uniform| |atan| |linkToFortran| |void| |rk4| |besselY| - |stopTableInvSet!| |package| |root?| |radix| |radicalEigenvector| - |swap| |cycleEntry| |lexTriangular| |systemCommand| |acot| |show| - |nextColeman| |s17agf| |setelt| |nullary?| |connectTo| |iiacosh| - |useEisensteinCriterion?| |f01mcf| |setMaxPoints| |asec| - |brillhartTrials| |coth2tanh| |karatsubaOnce| |e04ucf| |bat| |minrank| - |delay| |rCoord| |besselI| |nextSubsetGray| |acsc| |quadraticForm| - |trace| |csc2sin| |copy| |numFunEvals3D| |powers| |toScale| - |enterPointData| |imaginary| |s21bcf| |sinh| |setAdaptive3D| |normal| - |selectFiniteRoutines| |concat!| |power!| |clipWithRanges| |besselK| - |rationalPoints| |cAsec| |transpose| |update| |formula| |cosh| - |phiCoord| |check| |upperCase!| |jacobian| |minPoints| - |setButtonValue| |write!| |repSq| |lazyPseudoDivide| |tanh| - |primextendedint| |OMReadError?| |mainVariables| |autoCoerce| |mkPrim| - |permutation| |radicalEigenvalues| |reorder| |sort| |logIfCan| - |exactQuotient!| |coth| |create3Space| |jordanAlgebra?| |mathieu24| - |listOfLists| |constantOperator| |listConjugateBases| |UnVectorise| - |monicDecomposeIfCan| |points| |cond| |sech| |crushedSet| |s13acf| - |numberOfImproperPartitions| |symmetricSquare| |whatInfinity| |style| - |factorPolynomial| |nilFactor| |nullary| |nrows| |csch| |mappingAst| - |unrankImproperPartitions0| |FormatArabic| |hash| |f04maf| |edf2efi| - |myDegree| |euclideanSize| |rightNorm| |subscript| |position| |ncols| - |asinh| |complexZeros| |drawToScale| |count| |internalInfRittWu?| - |s17ajf| |invmod| |s17aef| |mindegTerm| |match?| |dmp2rfi| |random| - |insert!| |symFunc| |simplifyPower| |coordinates| |rightPower| - |exponent| |traverse| |drawStyle| |lazyEvaluate| |padecf| |pow| - |extractBottom!| |weierstrass| |nextSublist| |parents| - |setVariableOrder| |f04qaf| |mainVariable| |setProperties!| |pop!| - |iiatanh| |stoseInvertible?| |substring?| |removeZeroes| |symbolTable| - |stFuncN| |insertMatch| |s01eaf| |rightRemainder| |logGamma| |makeEq| - |component| |rk4qc| |realSolve| |solve1| |call| |prinb| - |zeroSetSplitIntoTriangularSystems| |compBound| |cCoth| |iiacsc| |lo| - |bringDown| |suffix?| |debug| |pseudoQuotient| |internalSubPolSet?| - |c05adf| |setRow!| |subset?| |rischNormalize| - |genericRightMinimalPolynomial| |incr| |zeroOf| |randomR| - |stiffnessAndStabilityOfODEIF| D |associatedEquations| |splitLinear| - |squareTop| |exptMod| |polyred| - |rewriteSetByReducingWithParticularGenerators| |functionIsOscillatory| - |prefix?| |coth2trigh| |objectOf| |iiexp| |option?| |e02bef| - |removeRedundantFactors| |headReduced?| |sPol| |const| - |trailingCoefficient| |internalIntegrate0| |minimumExponent| |leader| - |bivariateSLPEBR| |move| |outputSpacing| |log2| |fortranLiteral| - |rootBound| |arg1| |setCondition!| |changeName| |fullDisplay| - |boundOfCauchy| |Is| |arg2| |completeSmith| |compound?| |s19acf| - |bumptab| |clipSurface| |complexLimit| |constantLeft| |rubiksGroup| - |prolateSpheroidal| |firstSubsetGray| |setPredicates| |trapezoidalo| - |plotPolar| |iiacoth| |sncndn| |monomialIntPoly| |super| |cross| - |hostPlatform| |redpps| |tValues| |conditions| |discriminantEuclidean| - |minPol| |leftFactorIfCan| |dictionary| |typeList| |palginfieldint| - |minPoints3D| |sequence| |completeEchelonBasis| |match| - |radicalOfLeftTraceForm| |e01bff| |ode1| |elRow2!| |splitConstant| - |qqq| |string?| |zero| |subNode?| |parent| |result| |elliptic| - |plenaryPower| |s17def| |basicSet| |adaptive3D?| |ignore?| |cartesian| - |transcendentalDecompose| |nthFlag| |s17dgf| |e02bcf| |chebyshevT| - |cyclotomic| |fullPartialFraction| |powmod| |s14abf| |And| - |writeByte!| |algebraicDecompose| |OMclose| |reset| |quatern| - |generalInfiniteProduct| |KrullNumber| |quasiComponent| |leftLcm| - |nextPrime| |initials| |Or| |associates?| |quote| |putColorInfo| - |relerror| |dihedralGroup| |doubleRank| |Lazard| |cAsech| |OMopenFile| - |quasiRegular?| |Not| |nthCoef| |s17dcf| |chvar| |write| - |resultantReduit| |enqueue!| |deleteProperty!| |makeSketch| - |arrayStack| |limitedIntegrate| |modifyPointData| |save| |nthFactor| - |binaryFunction| |makeSUP| |complexNumericIfCan| |aspFilename| - |basisOfLeftAnnihilator| |critMTonD1| |f02aef| |dmpToHdmp| - |stoseIntegralLastSubResultant| |OMputEndApp| |prefixRagits| - |weighted| |leftRankPolynomial| |randomLC| |genericLeftTrace| - |distFact| |outputArgs| |upperCase?| |rewriteIdealWithHeadRemainder| - |nthExpon| |prinshINFO| |integralLastSubResultant| |e02dff| |cSin| - |taylorRep| |contract| |nodes| |inconsistent?| |ReduceOrder| - |viewpoint| |OMgetBind| |deriv| |acscIfCan| |simpleBounds?| - |subResultantsChain| |lazyPquo| |upperCase| |readUInt16!| |id| - |basisOfLeftNucleus| |identitySquareMatrix| |graphStates| |writable?| - |cos2sec| |cycleElt| |overlap| |computePowers| |generator| |primes| - |stoseInvertibleSetreg| |factorGroebnerBasis| |branchPointAtInfinity?| - |shallowCopy| |rotatex| |setLegalFortranSourceExtensions| |inrootof| - |pushucoef| |overbar| |UpTriBddDenomInv| |bezoutDiscriminant| |table| - |directory| |identityMatrix| |integralDerivationMatrix| |sumSquares| - |constantIfCan| |setValue!| |deepExpand| |insert| - |coercePreimagesImages| |bounds| |supDimElseRittWu?| |c06fqf| |new| - |dec| |elements| |normal?| |viewDeltaXDefault| |vedf2vef| |OMputApp| - |cAsin| |nextPartition| |univariatePolynomial| |iiatan| - |RittWuCompare| |infinite?| |lazyIntegrate| |absolutelyIrreducible?| - |d01aqf| |numberOfMonomials| |s21bbf| |reflect| |readIfCan!| - |csch2sinh| |options| |setProperties| |findConstructor| |weight| - |integralCoordinates| |bernoulliB| |bracket| |rotate!| |level| - |romberg| |denominators| |selectPDERoutines| |sin?| |shiftRoots| - |retractable?| |sample| |gbasis| |setvalue!| |legendreP| - |OMsupportsSymbol?| |iitan| |complexEigenvalues| - |rewriteIdealWithQuasiMonicGenerators| |graphImage| - |subQuasiComponent?| |diagonalProduct| |multiple?| |getButtonValue| - |normalize| |outputMeasure| |resize| ~ |pointData| |rationalIfCan| - |contours| |string| |leastPower| |extendIfCan| |cycleRagits| - |listOfMonoms| |getGraph| |solveLinear| |extractIndex| |droot| - |backOldPos| |matrix| |mathieu23| |numer| |complex?| |commaSeparate| - |cubic| |prem| |reduceByQuasiMonic| |range| |element?| |open| - |reindex| |perspective| |e04naf| |denom| |ScanFloatIgnoreSpacesIfCan| - |reduced?| |groebnerIdeal| |logpart| |hasHi| |shufflein| |equiv| - |factorSquareFreePolynomial| |scalarTypeOf| - |semiSubResultantGcdEuclidean2| |setnext!| |unitsColorDefault| - |monic?| |lfintegrate| |primintfldpoly| |cSec| |tan2cot| |thenBranch| - |removeZero| |squareFreeFactors| |loadNativeModule| |pi| |prindINFO| - |componentUpperBound| |nlde| |rowEchelonLocal| |f01bsf| |prime?| - |stronglyReduce| |yellow| |antiCommutative?| |clikeUniv| - |primextintfrac| |infinity| |f02xef| |left| |categories| |revert| - |linearlyDependent?| |interpretString| |mkIntegral| - |removeIrreducibleRedundantFactors| |operations| |insertRoot!| - |yCoordinates| |OMgetEndAtp| |coerceImages| |areEquivalent?| |right| - |OMParseError?| |exteriorDifferential| |maxRowIndex| |applyRules| - |getRef| |credPol| |bitLength| |e04ycf| |lepol| |packageCall| - |charClass| |computeBasis| |permutations| |dioSolve| |directSum| - |characteristicSet| |flexibleArray| |addiag| |explimitedint| - |OMgetBVar| |compactFraction| |fibonacci| |setEmpty!| |redPol| - |sinhIfCan| |rightCharacteristicPolynomial| |delete!| |vectorise| - |elliptic?| |froot| |sum| |sqfree| |square?| - |stoseInvertibleSetsqfreg| |f02wef| |rischDEsys| |rightDiscriminant| - |OMencodingBinary| |diagonalMatrix| |leastAffineMultiple| - |OMsupportsCD?| |iidsum| |f2st| |sorted?| |subspace| |checkPrecision| - |transcendenceDegree| |multiplyCoefficients| |cAcsch| |regime| - |basisOfRightAnnihilator| |split| |getMultiplicationTable| - |leftExtendedGcd| |showScalarValues| |validExponential| |OMputEndBVar| - |outputAsFortran| |lyndon| |binomThmExpt| |janko2| |factorial| - |polarCoordinates| |setleft!| |iicosh| |showRegion| |idealiser| - |ListOfTerms| |front| |approxSqrt| |mirror| |factors| |hostByteOrder| - |entries| |rootOfIrreduciblePoly| |expint| |tanQ| |select!| - |constDsolve| |lp| |evaluate| |color| |createPrimitiveNormalPoly| - |iiGamma| |univariate?| |integerBound| |setMinPoints| - |numberOfNormalPoly| |leftMinimalPolynomial| |headReduce| - |modularGcdPrimitive| |rationalFunction| |nand| |complexEigenvectors| - |dom| |resultantEuclideannaif| |c06frf| |primPartElseUnitCanonical| - |specialTrigs| |branchPoint?| |symmetricPower| |headRemainder| |elt| - |rename!| |tab1| |purelyTranscendental?| |symbol| |rightDivide| - |linear?| |minordet| |denomRicDE| |modTree| |algebraic?| |parseString| - |d01gaf| |expression| |graphState| |leftQuotient| |lllip| |nodeOf?| - |iifact| |cyclotomicFactorization| |dfRange| |leadingIdeal| - |mainMonomial| |stopMusserTrials| |integer| |f02akf| |mat| |expPot| - |ceiling| |resultantnaif| |inHallBasis?| - |removeRedundantFactorsInContents| |linGenPos| |wrregime| |nil| - |infinite| |arbitraryExponent| |approximate| |complex| + |Record| |Union| |maxIndex| |number?| |meatAxe| |gbasis| + |outputBinaryFile| |rightOne| |zeroVector| |myDegree| + |linearDependenceOverZ| |ddFact| |makeSin| 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|paraboloidal| |c05nbf| + |f02awf| |sparsityIF| |deriv| |genericLeftTraceForm| |ksec| |f01mcf| + |selectIntegrationRoutines| |alphanumeric?| |hexDigit?| |pol| + |atrapezoidal| |innerSolve| |acscIfCan| |principalIdeal| + |pointSizeDefault| |setMaxPoints| |prologue| |showAll?| |iitanh| + |seriesToOutputForm| |argument| |set| |length| |top!| |simpleBounds?| + |e01bhf| |padicFraction| |brillhartTrials| |charpol| |region| |iiabs| + |OMgetApp| |scripts| |subResultantGcdEuclidean| |sumOfDivisors| + |subResultantsChain| |df2fi| |e02daf| |removeConstantTerm| |coth2tanh| + |trace2PowMod| |mainExpression| |rightMinimalPolynomial| + |exactQuotient| |escape| |lazyPquo| |fortranDoubleComplex| |hermiteH| + |target| |rspace| |karatsubaOnce| |tubePoints| |groebner| + |shanksDiscLogAlgorithm| |inR?| |redmat| |upperCase| |e04ucf| + |collect| |augment| |retract| |complexNormalize| |linears| |compile| + |OMcloseConn| |updatF| |stoseInternalLastSubResultant| |readUInt16!| + |cotIfCan| |s21baf| |tanAn| |bat| |getCurve| |htrigs| |acschIfCan| + |returns| |inputBinaryFile| |basisOfLeftNucleus| |fill!| |f04mcf| + |fmecg| |minrank| |squareFree| |Ei| |bag| |quartic| |stFunc2| + |identitySquareMatrix| |subSet| |goto| |taylorQuoByVar| |harmonic| + |delay| |perfectNthRoot| |bipolarCylindrical| |fortran| + |createLowComplexityTable| |OMputError| |useNagFunctions| + |graphStates| |ptFunc| |f02aaf| |rCoord| |countRealRoots| |ravel| + |mathieu11| |setFormula!| |iterationVar| |numberOfVariables| + |pointColorPalette| |writable?| |inc| |dAndcExp| |relativeApprox| + |weakBiRank| |besselI| |laplace| |reshape| |selectPolynomials| |cTan| + |univcase| |solveid| |cos2sec| |nextSubsetGray| |ref| |listLoops| + |fortranLinkerArgs| |top| |even?| |filename| |singleFactorBound| + |optimize| |schema| |chiSquare1| |cycleElt| |internalAugment| + |gcdcofact| |diagonal?| |patternMatchTimes| |quadraticForm| + |exprHasWeightCosWXorSinWX| |SturmHabicht| |root| |rowEchelon| + |overlap| |merge| |plus| |leadingCoefficientRicDE| |gcdPrimitive| + |list| |trigs| |csc2sin| |rightAlternative?| |setErrorBound| + |leftAlternative?| |scanOneDimSubspaces| |parse| |littleEndian| + |computePowers| |digit?| |quotient| |slash| |definingEquations| + |numFunEvals3D| |car| |setPoly| |variable?| |interval| |lyndonIfCan| + |primes| |setImagSteps| |child?| |normalise| |powers| |cdr| + |indiceSubResultant| |normalizedDivide| |refine| |sturmVariationsOf| + |stoseInvertibleSetreg| |toScale| |binary| |updateStatus!| + |numberOfIrreduciblePoly| |setDifference| |true| |reduction| + |pseudoDivide| |comp| |Hausdorff| |factorGroebnerBasis| |bernoulli| + GF2FG |times| |setIntersection| |tubePointsDefault| |totalDegree| + |enterPointData| |aCubic| |genus| |empty| |branchPointAtInfinity?| + |binomial| |imaginary| |pleskenSplit| |extractPoint| |callForm?| + |setUnion| |initial| |double?| |mathieu12| |multMonom| |f02agf| + |setchildren!| |shallowCopy| |coerceS| |d01amf| |monicRightDivide| + |s21bcf| |apply| |iiperm| |parametersOf| |linearMatrix| + |makeGraphImage| |rotatex| |consnewpol| |reduceBasisAtInfinity| + |pastel| |basisOfCenter| |setAdaptive3D| |elementary| + |setLegalFortranSourceExtensions| |script| |anfactor| + |numericalIntegration| |corrPoly| |symmetricDifference| |imagk| + |monom| |semiDiscriminantEuclidean| |conjugate| |size| + |selectFiniteRoutines| |inrootof| |convergents| + |semiResultantEuclidean2| |physicalLength!| |squareFreePart| |imports| + |trigs2explogs| |rule| |compdegd| |lexico| |commutative?| |concat!| + |max| |cylindrical| |pdf2ef| |associatorDependence| |newReduc| + |mainMonomials| |lookup| |pushucoef| |OMmakeConn| |diophantineSystem| + |power!| |mapSolve| |factorsOfCyclicGroupSize| |tex| |goodnessOfFit| + |copyInto!| |trim| |Lazard2| |overbar| |binaryTree| |common| + |clipWithRanges| |iiacsch| |rationalPoint?| |first| |delete| |nary?| + |lieAdmissible?| |leftUnits| |explicitlyEmpty?| |index| + |viewDeltaYDefault| |UpTriBddDenomInv| |pomopo!| |associative?| + |zeroDimPrime?| |besselK| |rest| |bezoutDiscriminant| |cosSinInfo| + |factorByRecursion| |toseInvertibleSet| |isMult| |primaryDecomp| + |false| |acosh| |rationalPoints| |compiledFunction| |viewPhiDefault| + |quadraticNorm| |substitute| |setAttributeButtonStep| |getProperty| + |groebSolve| |modularGcd| |identityMatrix| |rectangularMatrix| |atanh| + |removeDuplicates| |exprHasAlgebraicWeight| |isOr| |cAsec| + |rightExtendedGcd| |mainKernel| |integralBasisAtInfinity| |f07fef| + |mainVariable?| |pair| |integralDerivationMatrix| |putGraph| |acoth| + |distribute| |useSingleFactorBound?| |getZechTable| |transpose| + |inverseIntegralMatrix| |eof?| EQ |fortranCarriageReturn| |sumSquares| + |asech| |e01sbf| |lambert| |value| |phiCoord| |tableau| |e01bgf| + |basisOfNucleus| |partitions| |rangePascalTriangle| |constantIfCan| + |#| |fortranCharacter| |divide| |showFortranOutputStack| |check| + |OMputEndError| |inRadical?| |pToHdmp| |round| |lexGroebner| + |setValue!| |multiple| |GospersMethod| |screenResolution3D| + |upperCase!| |shiftRight| |nextNormalPoly| |lSpaceBasis| |elseBranch| + |buildSyntax| |deepExpand| |ratpart| |applyQuote| |extension| + |jacobian| |wholePart| |categoryFrame| |degreePartition| + |coercePreimagesImages| |stopTable!| |explogs2trigs| |duplicates| + |minPoints| |recip| |expandPower| |antiCommutator| |patternMatch| + |inverseLaplace| |bounds| |f07fdf| |dominantTerm| |showArrayValues| + |setButtonValue| |readByte!| |rootOf| |xCoord| |coefficient| + |represents| |supDimElseRittWu?| |inspect| |ruleset| |times!| + |indicialEquations| |write!| |someBasis| |unvectorise| + |constantToUnaryFunction| |c06fqf| |setScreenResolution3D| |opeval| + |particularSolution| |repSq| |listRepresentation| |OMreadStr| |fi2df| + |octon| |cAcos| |smith| |elements| |palgRDE| |high| |identity| + |lazyPseudoDivide| |log10| |solve| |createNormalPoly| RF2UTS |normal?| + |antisymmetricTensors| |suchThat| |d02raf| |createGenericMatrix| + |continue| |primextendedint| |semiResultantEuclidean1| |bitand| + |properties| |exprToUPS| |pr2dmp| |BumInSepFFE| |decrease| + |viewDeltaXDefault| |rightRank| |LyndonBasis| |bitior| |measure| + |translate| |clipParametric| |wordInStrongGenerators| |vedf2vef| + |splitDenominator| |outputGeneral| |hspace| |arity| |scalarMatrix| + |f02axf| |representationType| |jacobiIdentity?| |OMputApp| + |abelianGroup| |mkcomm| |simplifyLog| |sup| |pseudoRemainder| |node?| + |universe| |isImplies| |cAsin| |toseLastSubResultant| |maxColIndex| + |rightTraceMatrix| |leadingIndex| |rational| |purelyAlgebraic?| + |monicRightFactorIfCan| |solid?| |swap!| |makeCos| |checkRur| |f04jgf| + |c02aff| |tRange| |alphanumeric| |integral?| |factorList| |palgRDE0| + |s17dgf| |rightFactorCandidate| |numberOfFractionalTerms| |OMread| + |startStats!| |leftRemainder| |inf| |fractRadix| |e02bcf| + |normalizedAssociate| |processTemplate| |rowEchLocal| |makeop| + |generalLambert| |sdf2lst| |moduloP| |pdct| |chebyshevT| |sinhcosh| + |OMreadFile| |stoseSquareFreePart| |iisech| |groebner?| |getlo| + |lflimitedint| |mainCharacterization| |stack| |fortranLogical| + |cyclotomic| |readUInt32!| |isTerm| |basisOfCommutingElements| + |fortranReal| |iicosh| |search| |functionIsContinuousAtEndPoints| + |interpret| |OMencodingXML| |part?| |fullPartialFraction| + |fractionFreeGauss!| |green| |atom?| |addMatchRestricted| + |subresultantVector| |showRegion| |createMultiplicationMatrix| |paren| + |hitherPlane| |powmod| |OMgetEndObject| |approximants| |tower| + |triangular?| |trueEqual| |predicates| |idealiser| |generateIrredPoly| + |s14abf| |blue| |setTex!| |invertible?| |constant| |infiniteProduct| + |rotate| |e02ddf| |stoseInvertible?reg| |ListOfTerms| |stop| + |normFactors| |d02cjf| |reduceLODE| |writeByte!| |sub| Y |iisin| + |rightScalarTimes!| |dim| |lfinfieldint| |OMputSymbol| |front| + |quadratic?| |mapCoef| |var1StepsDefault| |algebraicSort| + |algebraicDecompose| |identification| |aQuadratic| |overlabel| + |quasiRegular| |approxSqrt| |critpOrder| |belong?| |curve| F |OMclose| + |OMgetType| |primeFactor| |simplify| |safeCeiling| |alternatingGroup| + |mirror| |rotatey| |basisOfLeftNucloid| |innerEigenvectors| |ran| + |quatern| |leadingExponent| |coerceL| |complexNumeric| |superHeight| + |coefficients| |factors| |infinityNorm| |intPatternMatch| |intersect| + |shift| ~= |mesh| |generalInfiniteProduct| |unknownEndian| + |sqfrFactor| |univariatePolynomialsGcds| |cTanh| |null| + |hostByteOrder| |primintegrate| |viewDefaults| |An| |isOpen?| |coerce| + |KrullNumber| |kernels| |inverseIntegralMatrixAtInfinity| + |inputOutputBinaryFile| |solveLinearPolynomialEquationByRecursion| + |center| |selectODEIVPRoutines| |not| |entries| |headAst| |construct| + |status| |doubleDisc| |besselJ| |resetNew| |quasiComponent| + |traceMatrix| |maxPoints| |univariate| |cycleSplit!| |quasiMonic?| + |and| |rootOfIrreduciblePoly| |sequences| |rightUnits| + |localIntegralBasis| |chineseRemainder| |leftLcm| |mapUp!| |node| + |expenseOfEvaluation| |wholeRadix| |complexExpand| |or| |expint| + |bytes| |lfextendedint| |stoseInvertibleSet| |ScanRoman| |nextPrime| + |binding| |exp1| |Frobenius| |optpair| |xor| |tanQ| |infix| |unary?| + |twoFactor| |initials| |oddlambert| |showSummary| |s17ahf| |euler| + |factor| UP2UTS |tab| |case| |select!| |curry| |changeNameToObjf| + |readInt32!| |associates?| |drawCurves| |biRank| |powerAssociative?| + |intChoose| |sqrt| |regularRepresentation| |Zero| |constDsolve| + |numerator| |obj| |modifyPoint| |LiePoly| |c06gsf| |d01alf| |quote| + |localUnquote| |iFTable| |exists?| |showAttributes| |real| |split!| + |numberOfOperations| |One| |evaluate| |pmintegrate| |derivative| + |palglimint| |viewport2D| |putColorInfo| |cyclic?| |changeWeightLevel| + |xn| |cache| |decompose| |imag| |jacobi| |mvar| |color| |name| + |groebgen| |critB| |singRicDE| |relerror| |listexp| |directProduct| + |cAcoth| |factorSFBRlcUnit| |mapExpon| |d01gbf| + |createPrimitiveNormalPoly| |body| |eigenvalues| + |selectOptimizationRoutines| |subNodeOf?| |has?| |dihedralGroup| + |fracPart| |OMgetObject| |quasiAlgebraicSet| |resultant| |iiGamma| + |permutationGroup| |normalElement| |defineProperty| |doubleRank| + |pack!| |s14aaf| |brace| |readLineIfCan!| |principal?| + |removeDuplicates!| |univariate?| |symmetricTensors| |e02ahf| + |resultantReduitEuclidean| |strongGenerators| |Lazard| + |exportedOperators| |in?| |destruct| |remainder| |list?| + |integerBound| |screenResolution| |anticoord| |normalForm| |cAsech| + |geometric| |s20adf| |rightTrace| |factor1| |interactiveEnv| + |linearAssociatedExp| |setMinPoints| |pointPlot| |cot2tan| + |viewport3D| |expintfldpoly| |OMopenFile| |bigEndian| |iibinom| + |getCode| |cCsc| |degreeSubResultant| |numberOfNormalPoly| |Si| + |leftNorm| |youngGroup| |irreducibleRepresentation| |quasiRegular?| + |reverse| |equation| |leftTraceMatrix| |firstNumer| |tracePowMod| + |ldf2lst| |leftMinimalPolynomial| |port| |real?| + |initializeGroupForWordProblem| LODO2FUN |nthCoef| |ratDsolve| + |bandedHessian| |monomial| |sinh2csch| |module| |cycle| |subst| + |headReduce| |entry| |firstUncouplingMatrix| |host| |minimumDegree| + |s17dcf| |composite| |writeBytes!| |multivariate| |cyclicEqual?| + |sortConstraints| |totalLex| |modularGcdPrimitive| |t| |exquo| + |argumentList!| |dequeue| |f02ajf| |chvar| |roughSubIdeal?| |error| + |pushdterm| |OMgetInteger| |variables| |swapRows!| |OMUnknownCD?| + |rationalFunction| |delta| |leftZero| |div| |readInt16!| + |extendedResultant| |minset| |resultantReduit| |assert| |safetyMargin| + |point?| |f07adf| |removeCoshSq| |nand| |e02baf| |quo| |mapDown!| + |splitNodeOf!| |s17adf| |enqueue!| |bandedJacobian| |externalList| + |localAbs| |decomposeFunc| |complexEigenvectors| |stronglyReduced?| + |partialFraction| |symmetric?| |deleteProperty!| |isobaric?| |kmax| + |d01akf| |errorInfo| |RemainderList| |resultantEuclideannaif| + |brillhartIrreducible?| |rem| |optAttributes| |variationOfParameters| + |makeSketch| |reducedQPowers| |cn| |figureUnits| |isPower| |compose| + |rightRecip| |e02def| |c06frf| |objects| |jordanAdmissible?| + |clearDenominator| |discriminant| |arrayStack| |monomialIntegrate| + |fortranInteger| |ranges| |aLinear| |taylor| |badValues| + |semiResultantEuclideannaif| |base| |primPartElseUnitCanonical| + |scripted?| |find| |nsqfree| |limitedIntegrate| + |LagrangeInterpolation| |bipolar| |laurent| |viewThetaDefault| + |constantKernel| |normalizeIfCan| |specialTrigs| |intensity| + |binarySearchTree| |bat1| |getStream| |modifyPointData| + |integralRepresents| |isPlus| |puiseux| |d03faf| |numericIfCan| + |branchPoint?| |elRow1!| |OMsend| |polygamma| |nthFactor| |acoshIfCan| + |qinterval| |monicModulo| |padicallyExpand| |complete| + |symmetricPower| |normalized?| |leftMult| |getBadValues| + |binaryFunction| |Beta| |halfExtendedResultant2| |inv| |curve?| + |oblateSpheroidal| |minRowIndex| |headRemainder| |bezoutMatrix| + |content| |toseInvertible?| |repeatUntilLoop| |makeSUP| + |binaryTournament| |ground?| |squareFreePolynomial| |SFunction| + |OMputBind| |rename!| |lastSubResultant| |multinomial| |shade| + |mulmod| |complexNumericIfCan| |ground| |movedPoints| |sign| |iiacos| + |commutator| |tab1| |simpson| |fractionPart| |rewriteSetWithReduction| + |prinpolINFO| |aspFilename| |nonLinearPart| |reverseLex| + |leadingMonomial| |readable?| |order| |purelyTranscendental?| + |whileLoop| |factorsOfDegree| |basisOfLeftAnnihilator| |zeroDim?| + |leadingCoefficient| |currentScope| |addPoint| |pureLex| |acosIfCan| + |rightDivide| |LowTriBddDenomInv| |createNormalPrimitivePoly| |imagj| + |critMTonD1| |getOperator| |rootProduct| |rightRegularRepresentation| + |primitiveMonomials| BY |cCot| |integrate| |linear?| |pade| + |parabolicCylindrical| |subResultantChain| |f02aef| |extend| + |sumOfKthPowerDivisors| |d02gbf| |reductum| |chiSquare| |inverse| + |minordet| |hermite| |uncouplingMatrices| |fortranTypeOf| |iicsc| + |dmpToHdmp| |doubleComplex?| |frobenius| |previous| |denomRicDE| + |e01baf| |say| |genericPosition| |purelyAlgebraicLeadingMonomial?| + |iflist2Result| |stoseIntegralLastSubResultant| |subtractIfCan| + |operation| |adaptive| |maxPoints3D| |modTree| |iicot| |var1Steps| + |lazyIrreducibleFactors| |totalfract| |OMputEndApp| |char| |init| + |appendPoint| |squareFreePrim| |thetaCoord| |algebraic?| |separate| + |separateDegrees| |pmComplexintegrate| |showTheFTable| |prefixRagits| + |unitNormal| |quotientByP| |structuralConstants| |parseString| + |plusInfinity| |wordsForStrongGenerators| |weighted| + |clearTheSymbolTable| |getDatabase| |d01asf| |fortranCompilerName| + |d01gaf| |minusInfinity| |pquo| |OMgetAttr| |complexForm| NOT + |leftRankPolynomial| |maximumExponent| |signatureAst| |ODESolve| + |torsion?| |c06gbf| |graphState| |showClipRegion| |primeFrobenius| + |generalPosition| OR |randomLC| |csubst| |hasPredicate?| |pushup| + |Gamma| |central?| |leftQuotient| |extractClosed| + |semiIndiceSubResultantEuclidean| |infRittWu?| AND |genericLeftTrace| + |palgint0| |float| |f01qcf| |lllip| |f2df| |setsubMatrix!| |d01apf| + |distFact| |just| |mkAnswer| |alphabetic?| |exponential| |nodeOf?| + |symbolIfCan| |balancedFactorisation| |acothIfCan| |getProperties| + |outputArgs| |createIrreduciblePoly| |ricDsolve| |print| + |exponential1| |iifact| |type| |computeInt| |imagI| |loopPoints| + |upperCase?| |leftOne| |resolve| |OMsetEncoding| + |halfExtendedSubResultantGcd2| |outputAsScript| + |cyclotomicFactorization| |satisfy?| |pdf2df| |ScanArabic| + |preprocess| |extendedEuclidean| |musserTrials| |keys| |dfRange| + |drawComplex| |generalizedContinuumHypothesisAssumed?| + |OMunhandledSymbol| |outputSpacing| |lowerCase| |printingInfo?| + |read!| |se2rfi| |leadingIdeal| |integralMatrixAtInfinity| |external?| + |rightRankPolynomial| |rootPoly| |log2| |singularitiesOf| |scopes| + |rk4f| |mainMonomial| |currentSubProgram| |approxNthRoot| + |incrementKthElement| |fortranLiteral| |writeLine!| |quotedOperators| + |coord| |s19aaf| |lazyResidueClass| |signAround| |polygon| |rootBound| + |Ci| GE |stopTableGcd!| |c06ekf| |rk4a| |credPol| |e01saf| + |topPredicate| |setCondition!| |surface| |upDateBranches| * GT + |denominator| |pole?| |removeRoughlyRedundantFactorsInPols| + |bitLength| |poisson| |redPo| |deepestTail| |changeName| + |invmultisect| LE |univariatePolynomials| |genericLeftDiscriminant| + |entry?| |e04ycf| |rdregime| |roughBase?| |prepareSubResAlgo| + |numerators| |fullDisplay| LT |elColumn2!| |stosePrepareSubResAlgo| + |moreAlgebraic?| |predicate| |lepol| |isExpt| |startTableInvSet!| + |outputForm| |boundOfCauchy| |integer?| = |trivialIdeal?| |morphism| + |cap| |packageCall| |d03eef| |radicalRoots| |lighting| |Is| + |invertibleElseSplit?| |largest| |mainValue| |prepareDecompose| + |charClass| |column| |reify| |sn| |gcdPolynomial| |completeSmith| < + |cAtan| |parabolic| |OMgetString| |computeBasis| + |getMultiplicationMatrix| |problemPoints| |conjug| |rdHack1| + |compound?| > |isTimes| |hasoln| |taylorIfCan| |permutations| + |linSolve| |rightQuotient| |untab| |s19acf| |low| <= |schwerpunkt| + |leftRank| |OMgetEndBind| |dioSolve| |roman| |polyRDE| |printInfo!| + |cschIfCan| |bumptab| >= |df2ef| |varList| |derivationCoordinates| + |deref| |palgint| |directSum| |zeroDimPrimary?| |rootsOf| + |selectMultiDimensionalRoutines| |radPoly| |clipSurface| |infieldint| + |laguerreL| |symbolTableOf| |seed| |characteristicSet| |f01rdf| + |att2Result| |plus!| |symmetricRemainder| |complexLimit| |parameters| + |property| |OMopenString| |primitivePart| |cfirst| |flexibleArray| + |create| |e02akf| |outputFixed| |showTheRoutinesTable| + |reciprocalPolynomial| |constantLeft| + |erf| |nextLatticePermutation| + |accuracyIF| |complementaryBasis| |conditionP| |addiag| |children| + |ipow| |collectUpper| |rubiksGroup| |unitVector| - |bfEntry| |s20acf| + |adaptive?| |explimitedint| |sh| |LyndonWordsList| |getOperands| + |prolateSpheroidal| |selectNonFiniteRoutines| / |updatD| |d02ejf| + |bubbleSort!| |units| |OMgetBVar| |divisorCascade| |makeCrit| + |infinity| |flagFactor| |firstSubsetGray| |retractIfCan| |henselFact| + |dilog| |implies| |unitCanonical| |getOrder| |compactFraction| + |ip4Address| |getIdentifier| |saturate| |setPredicates| |setref| |sin| + |routines| |leftTrace| |notelem| |fibonacci| |bright| + |algebraicVariables| |socf2socdf| |SturmHabichtCoefficients| + |trapezoidalo| |rur| |cos| |nonSingularModel| |gradient| + |listBranches| |truncate| |setEmpty!| |kernel| |row| |decimal| + |isEquiv| |plotPolar| |LazardQuotient2| |virtualDegree| |clearCache| + |tan| |position!| |complexElementary| |ptree| |hdmpToP| |redPol| + |draw| |iiacoth| |zoom| |returnTypeOf| |fixedPointExquo| + |fortranDouble| |key| |function| |cot| |code| |hasTopPredicate?| + |indicialEquation| |pointColorDefault| |sinhIfCan| |unaryFunction| + |bindings| |cyclic| |sncndn| |addPoint2| |sec| |getMeasure| + |partition| |reducedDiscriminant| |rightCharacteristicPolynomial| + |rank| |patternVariable| |makeFloatFunction| |removeSquaresIfCan| + |monomialIntPoly| |dequeue!| |csc| |eval| |d01bbf| |realElementary| + |dot| |delete!| |findCycle| |OMencodingUnknown| |airyBi| |e01daf| + |cross| |isQuotient| |asin| |rewriteIdealWithRemainder| + |leftCharacteristicPolynomial| |minGbasis| |vectorise| |makeObject| + |singularAtInfinity?| |iExquo| |nthr| |factorSquareFree| + |hostPlatform| |map| |acos| |repeating?| |normInvertible?| + |OMputFloat| |elliptic?| |changeThreshhold| |OMputInteger| |orbits| + |redpps| |quoByVar| |atan| |iisec| |currentEnv| + |eisensteinIrreducible?| |rischDE| |froot| |coef| |wholeRagits| + |baseRDE| |extractProperty| |e01sef| |tValues| |acot| + |basisOfCentroid| |increasePrecision| |dom| |iprint| |sqfree| + |minColIndex| |iisinh| |printCode| |discriminantEuclidean| + |atanhIfCan| |asec| |graeffe| |hypergeometric0F1| |OMgetVariable| + |square?| |perfectSqrt| |conditionsForIdempotents| |isList| |minPol| + |quadratic| |height| |acsc| |minIndex| |matrixConcat3D| |sech2cosh| + |stoseInvertibleSetsqfreg| |lists| |light| |linearlyDependentOverZ?| + |firstDenom| |viewSizeDefault| |leftFactorIfCan| |convert| |sinh| + |float?| |lowerCase?| |getSyntaxFormsFromFile| |f02wef| |coefChoose| + F2FG |solveLinearlyOverQ| |dictionary| |lazyGintegrate| |cosh| + |infLex?| |shrinkable| |maxdeg| |rischDEsys| |nextsubResultant2| + |iicoth| |over| |OMgetError| |typeList| |tanh| |ocf2ocdf| + |expintegrate| |title| |ridHack1| |rightDiscriminant| |cothIfCan| + |homogeneous?| |setAdaptive| |palginfieldint| |viewPosDefault| |lcm| + |coth| |copies| |knownInfBasis| |factorset| |OMencodingBinary| + |setRealSteps| |failed| |reseed| |lfextlimint| |realEigenvalues| + |minPoints3D| |expr| |sech| |toroidal| |iomode| |plot| |lift| + |diagonalMatrix| |imagE| |choosemon| |stoseInvertible?sqfreg| |iiacot| + |sequence| |e| |append| |csch| |operators| |explicitEntries?| + |curryRight| |reduce| |leastAffineMultiple| |chebyshevU| |edf2ef| + |bivariate?| |fortranComplex| |completeEchelonBasis| |gcd| |asinh| + |endSubProgram| |index?| |c06gqf| |OMsupportsCD?| |BasicMethod| + |nextNormalPrimitivePoly| |deleteRoutine!| |radicalOfLeftTraceForm| + |recoverAfterFail| |gcdcofactprim| |drawComplexVectorField| + |enumerate| |iidsum| |clip| |ParCondList| |discreteLog| |e01bff| |lex| + |variable| |contains?| |invertIfCan| |nothing| |deepestInitial| |f2st| + |balancedBinaryTree| |minimize| |resetBadValues| |radicalSimplify| + |iterators| |ode1| |datalist| |semiDegreeSubResultantEuclidean| + |meshFun2Var| |birth| |sorted?| |declare| |nextItem| |cyclePartition| + |simplifyExp| |elRow2!| |interReduce| |doubleResultant| |sts2stst| + |symbolTable| |quoted?| |subspace| |tail| |skewSFunction| |increment| + |splitConstant| |leftGcd| |genericRightTraceForm| |hasSolution?| + |cyclicGroup| |transcendenceDegree| |monomial?| |symmetricGroup| + |numberOfComponents| |aQuartic| |qqq| |setClipValue| |rules| |eq?| + |mapUnivariate| |multiplyCoefficients| |f07aef| |edf2df| |basis| + |string?| |removeSinSq| |outputList| |safeFloor| |e02adf| + |numberOfCycles| |cAcsch| |lambda| |bsolve| |multiEuclideanTree| + |unknown| |noncommutativeJordanAlgebra?| |f01qdf| |width| |subNode?| + |curveColorPalette| |head| |regime| |minus!| |completeEval| + |shallowExpand| |algSplitSimple| |parent| |certainlySubVariety?| + |createMultiplicationTable| |imagK| |basisOfRightAnnihilator| + |setScreenResolution| |algint| |key?| |elliptic| |qPot| + |algebraicCoefficients?| |byte| |failed?| |explicitlyFinite?| |split| + |cot2trig| |idealSimplify| |removeSuperfluousQuasiComponents| + |plenaryPower| |c05pbf| |leadingBasisTerm| |pushuconst| |unit| + |rightFactorIfCan| |getMultiplicationTable| |OMbindTCP| |s17def| + |power| |oddInfiniteProduct| |setStatus!| |cyclotomicDecomposition| + FG2F |leftExtendedGcd| |bfKeys| |s17aff| |OMputVariable| |seriesSolve| + |basicSet| |ratDenom| |int| |superscript| |monicDivide| + |showScalarValues| |makeFR| |li| |Vectorise| + |characteristicPolynomial| |ramifiedAtInfinity?| |adaptive3D?| + |axesColorDefault| |s18aff| |OMlistSymbols| |validExponential| + |sizePascalTriangle| |exQuo| |lagrange| |ignore?| |optional| + |definingInequation| |permutationRepresentation| |OMputEndBVar| + |pushNewContour| |conjugates| |numberOfChildren| |cartesian| |testDim| + |triangSolve| |horizConcat| |lazyVariations| |lyndon| |iiasec| |twist| + |semiLastSubResultantEuclidean| |addmod| |lazyPseudoQuotient| + |transcendentalDecompose| |leaf?| |createNormalElement| + |separateFactors| |binomThmExpt| |internalSubQuasiComponent?| |cLog| + |mdeg| |nthFlag| |expressIdealMember| |setMinPoints3D| + |tubeRadiusDefault| |changeVar| |resultantEuclidean| |janko2| + |findBinding| |rightMult| |rroot| |setleaves!| |sort!| |newSubProgram| + |mr| |factorial| |pushFortranOutputStack| |mesh?| |e02ajf| + |viewWriteAvailable| |nextSublist| |deepCopy| |qroot| |cExp| + |components| |polarCoordinates| |e02agf| |tanintegrate| |torsionIfCan| + |factorAndSplit| |setVariableOrder| |double| |log| |leadingTerm| + |bezoutResultant| |reverse!| |setleft!| |coleman| |makeprod| + |indiceSubResultantEuclidean| |exprToGenUPS| |f04qaf| |addMatch| + |irreducible?| |topFortranOutputStack| SEGMENT |scan| |arbitrary| + |sumOfSquares| |cSinh| |mainVariable| |test| |zCoord| |numFunEvals| + |companionBlocks| |commaSeparate| |critM| |Aleph| |expandLog| + |setProperties!| |showIntensityFunctions| |subCase?| |rational?| + |divideIfCan| |cubic| |bitTruth| |zeroDimensional?| + |indicialEquationAtInfinity| |relationsIdeal| |pop!| |sylvesterMatrix| + |directory| |reducedForm| |subResultantGcd| |prem| |primlimintfrac| + |leftDivide| |/\\| |readLine!| |iiatanh| |PollardSmallFactor| + |iiasinh| |exprToXXP| |printInfo| |generate| |diff| + |reduceByQuasiMonic| |eq| |useSingleFactorBound| |\\/| + |numberOfComputedEntries| |removeSinhSq| |comparison| + |stoseInvertible?| |orthonormalBasis| |sizeLess?| |OMgetAtp| |range| + |iter| |countable?| |unrankImproperPartitions1| |prefix| |dark| + |duplicates?| |removeZeroes| |declare!| |tryFunctionalDecomposition| + |incrementBy| |cycleTail| |fixedDivisor| |karatsubaDivide| |element?| + |flatten| |block| |lowerCase!| |setrest!| |OMgetSymbol| |stFuncN| + |parts| |capacity| |triangularSystems| |expand| |semicolonSeparate| + |controlPanel| |reindex| |nil| |lyndon?| |s18dcf| |commonDenominator| + |showTheIFTable| |insertMatch| |concat| |finiteBound| |mantissa| + |filterWhile| |ode| |makeViewport2D| |perspective| |primitivePart!| + |generalizedEigenvector| |transform| |genericLeftMinimalPolynomial| + |s01eaf| |reducedContinuedFraction| |changeBase| |filterUntil| + |wronskianMatrix| |e04naf| |leftUnit| |critT| |e02dcf| + |basisOfMiddleNucleus| |rightRemainder| |varselect| + |replaceKthElement| |select| |OMwrite| |ScanFloatIgnoreSpacesIfCan| + |logGamma| |frst| |lintgcd| |divideExponents| |makingStats?| + |approximate| |df2mf| |complexSolve| |iCompose| |reduced?| + |setPosition| |tubeRadius| |fixPredicate| |popFortranOutputStack| + |univariateSolve| |complex| |makeEq| |f02bbf| |hdmpToDmp| + |contractSolve| |groebnerIdeal| |exp| |zeroSquareMatrix| + |lazyPseudoRemainder| |triangulate| |component| |primlimitedint| + |segment| |one?| |divisors| |leftExactQuotient| |logpart| |hMonic| + |makeVariable| |unit?| |rk4qc| |extractIfCan| |extensionDegree| + |tryFunctionalDecomposition?| |clearTheIFTable| |hasHi| + |partialNumerators| |antiAssociative?| |infieldIntegrate| |generators| + |realSolve| |PDESolve| |integralMatrix| |fortranLiteralLine| |hex| + |shufflein| |outerProduct| |leftRecip| |constantOpIfCan| + |countRealRootsMultiple| |solve1| |negative?| |shellSort| |makeRecord| + |internalDecompose| |inverseColeman| |showAllElements| |equiv| + |squareMatrix| |rename| |initiallyReduced?| |prinb| |f02aff| |remove| + |perfectNthPower?| |mergeFactors| |mightHaveRoots| + |factorSquareFreePolynomial| |moduleSum| |innerint| |gethi| |back| + |zeroSetSplitIntoTriangularSystems| |sum| |members| |badNum| |sincos| + |scalarTypeOf| |rowEch| |sylvesterSequence| |stFunc1| |compBound| + |positive?| |last| |divisor| |meshPar1Var| |setTopPredicate| + |checkPrecision| |semiSubResultantGcdEuclidean2| |f02abf| + |positiveRemainder| |subMatrix| |nextIrreduciblePoly| |cCoth| |assoc| + |unmakeSUP| |rootSplit| |addPointLast| |setnext!| |polynomialZeros| + |second| |isNot| |lquo| |iiacsc| |OMconnOutDevice| |trunc| |cosIfCan| + |intcompBasis| |OMgetEndError| |unitsColorDefault| + |linearAssociatedLog| |normalizeAtInfinity| |third| |HenselLift| + |d02bbf| |bringDown| |leftScalarTimes!| |setPrologue!| |signature| + |tube| |close!| |presub| |monic?| |palgextint| |palgLODE| |lp| + |domainOf| |e02bbf| |pseudoQuotient| |medialSet| |commutativeEquality| + |extendedint| |sechIfCan| |lfintegrate| |stirling1| + |dimensionOfIrreducibleRepresentation| |removeSuperfluousCases| + |exponents| |internalSubPolSet?| |zeroSetSplit| |LazardQuotient| + |noKaratsuba| |primintfldpoly| |lhs| |category| |isConnected?| + |e02gaf| |cyclicCopy| |createLowComplexityNormalBasis| |c05adf| + |space| |integralAtInfinity?| |qualifier| |cSec| |rhs| |domain| + |initTable!| |primitive?| |imagJ| |setRow!| |realZeros| |testModulus| + |void| |iisqrt3| |limit| |tan2cot| |package| |f04mbf| |iilog| + |setLabelValue| |genericLeftNorm| |subset?| |checkForZero| |setelt!| + |show| |tan2trig| |setelt| |thenBranch| |vark| |multiEuclidean| + |zero?| |rischNormalize| |getGoodPrime| |systemCommand| |f01maf| + |nthRootIfCan| |mainCoefficients| |removeZero| |shuffle| + |closedCurve?| |mpsode| |powerSum| |genericRightMinimalPolynomial| + |associatedSystem| |completeHensel| |trace| |s15aef| |copy| + |squareFreeFactors| |stiffnessAndStabilityFactor| |setMaxPoints3D| + |insertionSort!| |zeroOf| |ramified?| |formula| |internalIntegrate| + |eulerPhi| |supRittWu?| |prindINFO| |possiblyNewVariety?| + |fixedPoints| |scale| |randomR| |halfExtendedSubResultantGcd1| + |update| |leadingSupport| |normal| |numberOfDivisors| |leftFactor| + |componentUpperBound| |stiffnessAndStabilityOfODEIF| + |nextsousResultant2| |mapGen| |iteratedInitials| |alternative?| |sort| + |cup| |npcoef| |dimensions| |autoCoerce| |nlde| |e02aef| |clipBoolean| + |push!| |associatedEquations| |polCase| |build| |computeCycleLength| + |linearPolynomials| |rowEchelonLocal| |irreducibleFactors| + |quasiMonicPolynomials| |solveRetract| |splitLinear| |collectUnder| + |nrows| |cond| |standardBasisOfCyclicSubmodule| + |solveLinearPolynomialEquationByFractions| |mainSquareFreePart| + |f01bsf| |laguerre| |e01bef| |interpolate| |matrixDimensions| + |squareTop| |ncols| |intermediateResultsIF| |OMlistCDs| |mathieu22| + |hash| |prime?| |mapExponents| |exptMod| |f02fjf| |viewZoomDefault| + |random| |generalTwoFactor| |position| |complement| |randnum| |count| + |c06fuf| |stronglyReduce| |outputFloating| |limitPlus| |match?| + |OMconnInDevice| |basisOfRightNucleus| |polyred| + |numberOfPrimitivePoly| |makeTerm| |repeating| |yellow| |parents| + |associator| |rightLcm| |rarrow| |lieAlgebra?| + |rewriteSetByReducingWithParticularGenerators| |sin2csc| |newLine| + |lazy?| |antiCommutative?| |printStats!| |complexRoots| |s18def| + |functionIsOscillatory| |e04mbf| |substring?| |nil?| |leastMonomial| + |returnType!| |clikeUniv| |symbol?| |child| |f04faf| |coth2trigh| + |e02bdf| |clearTheFTable| |palgLODE0| |primextintfrac| |call| |open?| + |sayLength| |bit?| |objectOf| |e04gcf| |eigenvector| |scaleRoots| + |suffix?| |gcdprim| |debug| |f02xef| |setOrder| |summation| + |rootDirectory| |iiexp| |digamma| |roughEqualIdeals?| |lo| + |generalizedContinuumHypothesisAssumed| |finite?| D |diagonals| + |revert| |raisePolynomial| |extendedIntegrate| |diagonal| |option?| + |roughUnitIdeal?| |unravel| |s19adf| |hcrf| |linearlyDependent?| + |nthExponent| |cyclicSubmodule| |empty?| |e02bef| |OMUnknownSymbol?| + |cardinality| |dflist| |palglimint0| |leader| |interpretString| + |s18aef| |rightZero| |totolex| |lifting1| |arg1| + |removeRedundantFactors| |f02adf| |rootSimp| |viewWriteDefault| + |mkIntegral| |unprotectedRemoveRedundantFactors| |cAsinh| |arg2| + |constantRight| |simpsono| |headReduced?| |polar| |readInt8!| |f04adf| + |super| |removeIrreducibleRedundantFactors| |wreath| |sPol| + |clearTable!| |direction| |palgextint0| |ScanFloatIgnoreSpaces| + |insertRoot!| |curveColor| |qfactor| |colorDef| |const| |adjoint| + |conditions| |zag| |OMserve| |semiSubResultantGcdEuclidean1| + |yCoordinates| |tubePlot| |s17dhf| |lazyPremWithDefault| + |trailingCoefficient| |match| |setfirst!| |uniform01| |UP2ifCan| + |removeRedundantFactorsInPols| |abs| |OMgetEndAtp| |copy!| + |OMgetEndAttr| |listYoungTableaus| |zero| |internalIntegrate0| + |beauzamyBound| |cAcosh| |c06fpf| |coerceImages| |cCos| + |noLinearFactor?| |lineColorDefault| |minimumExponent| |invertibleSet| + |result| |startTable!| |removeCosSq| |setlast!| |FormatRoman| + |areEquivalent?| |curryLeft| |showTheSymbolTable| |tanh2coth| |And| + |cycles| |bivariateSLPEBR| |insertTop!| |rootNormalize| |tanSum| + |basisOfRightNucloid| |OMParseError?| |push| |makeResult| + |HermiteIntegrate| |Or| |dihedral| |move| |setColumn!| |reset| + |partialDenominators| |s13adf| |expenseOfEvaluationIF| + |exteriorDifferential| |lifting| |exprex| |maxrow| |Not| |critMonD1| + |distdfact| |merge!| |integerIfCan| |maxRowIndex| |f01rcf| + |OMReadError?| |trapezoidal| |radicalEigenvectors| |presuper| |tree| + |more?| |write| |polyRicDE| |bumprow| |cSech| |applyRules| |asimpson| + |euclideanGroebner| |totalGroebner| |mainVariables| |gderiv| |save| + |pile| |makeMulti| |tanhIfCan| |normDeriv2| |getRef| |minPoly| + |innerSolve1| |extractSplittingLeaf| |mkPrim| |d01fcf| |printTypes| + |pToDmp| |null?| |baseRDEsys| |dn| |exprHasLogarithmicWeights| + |var2StepsDefault| |permutation| |s13aaf| |bottom!| |asinIfCan| + |antisymmetric?| |halfExtendedResultant1| |nextPartition| |ratPoly| + |groebnerFactorize| |id| |monomials| |mix| |radicalEigenvalues| + |setClosed| |factorials| |is?| |generalizedInverse| + |univariatePolynomial| |f04arf| |dimensionsOf| |midpoint| |reorder| + |numberOfComposites| |var2Steps| |rootKerSimp| |fixedPoint| |iiatan| + |f02bjf| |divideIfCan!| |elem?| |parametric?| |generator| |degree| + |logIfCan| |table| |dec| |composites| |solid| |edf2fi| |mainContent| + |RittWuCompare| |iidprod| |lowerPolynomial| |insert| |psolve| + |probablyZeroDim?| |exactQuotient!| |new| |fillPascalTriangle| + |finiteBasis| |sizeMultiplication| |solveInField| |recolor| + |infinite?| |euclideanNormalForm| |getConstant| |s17acf| |normalDenom| + |create3Space| |setLength!| |acotIfCan| |dimension| |readUInt8!| + |lazyIntegrate| |atoms| |algDsolve| |bivariatePolynomials| |options| + |jordanAlgebra?| |outlineRender| |allRootsOf| |absolutelyIrreducible?| + |critBonD| |numberOfFactors| |useEisensteinCriterion| + |selectOrPolynomials| |level| |decreasePrecision| |multiset| |debug3D| + |iiasin| |mathieu24| |expextendedint| |multiplyExponents| |iiasech| + |secIfCan| |weights| |d01aqf| |factorOfDegree| |changeMeasure| + |remove!| |imagi| |listOfLists| |every?| |heapSort| |hue| + |leftDiscriminant| |numberOfMonomials| ~ |logical?| |magnitude| + |splitSquarefree| |string| |constantOperator| |printStatement| + |e04fdf| |hconcat| |oddintegers| |s21bbf| |factorFraction| + |linearDependence| |matrix| |bumptab1| |printHeader| |numer| + |listConjugateBases| |e04dgf| |selectAndPolynomials| |indices| + |coHeight| |kroneckerDelta| |reflect| |open| |nonQsign| + |characteristic| |expandTrigProducts| |denom| |UnVectorise| + |cosh2sech| |integers| |d02bhf| |OMputEndAtp| |differentialVariables| + |readIfCan!| |typeLists| |loadNativeModule| |userOrdered?| UTS2UP + |OMputAtp| |monicDecomposeIfCan| |coordinate| |iicos| |pointLists| + |resetVariableOrder| |csch2sinh| |genericRightNorm| |c02agf| + |symmetricProduct| |pi| |s19abf| |points| |unexpand| |setProperty!| + |df2st| |setProperties| |generic| |extractTop!| |chainSubResultants| + |postfix| |withPredicates| |crushedSet| |left| |optional?| + |subPolSet?| |axes| |findConstructor| |algintegrate| |operations| + |c06ecf| |f01brf| |calcRanges| |fractRagits| |s13acf| |right| + |categories| |writeInt8!| |insertBottom!| |sec2cos| |weight| + |midpoints| |doublyTransitive?| |moebiusMu| |atanIfCan| |isOp| + |numberOfImproperPartitions| |computeCycleEntry| |measure2Result| + |singular?| |integralCoordinates| |overset?| |pointColor| + |rightExactQuotient| |removeRoughlyRedundantFactorsInContents| + |symmetricSquare| |po| |d01anf| |rationalApproximation| + |physicalLength| |bernoulliB| |terms| |squareFreeLexTriangular| |hclf| + |laurentIfCan| |whatInfinity| |tensorProduct| |asinhIfCan| + |definingPolynomial| |mindeg| |linearPart| |bracket| |monomRDEsys| + |subscriptedVariables| |LyndonWordsList1| |style| |laplacian| + |getPickedPoints| |ideal| |sinIfCan| |rquo| |rotate!| + |outputAsFortran| |submod| |alphabetic| |cscIfCan| |factorPolynomial| + |cyclicParents| |createPrimitivePoly| |setFieldInfo| |cPower| |latex| + |romberg| |freeOf?| |OMreceive| |slex| |nilFactor| |airyAi| |rst| + |character?| |mapUnivariateIfCan| |denominators| |constant?| + |createThreeSpace| |setProperty| |rootRadius| |nullary| |asecIfCan| + |newTypeLists| |bits| |degreeSubResultantEuclidean| |floor| + |selectPDERoutines| |asechIfCan| |llprop| |initiallyReduce| + |mappingAst| |difference| |fprindINFO| |matrixGcd| |omError| |sin?| + |kovacic| |blankSeparate| |bothWays| |subHeight| |branchIfCan| + |unrankImproperPartitions0| |messagePrint| |e02zaf| |karatsuba| + |shiftRoots| |FormatArabic| |sturmSequence| |elt| |red| + |inGroundField?| |generic?| |symbol| |aromberg| |numberOfHues| + |charthRoot| |retractable?| |reopen!| |powern| |e01sff| |f04maf| + |expression| |transcendent?| |lfunc| |c06ebf| |autoReduced?| |sample| + |edf2efi| |maxint| |semiResultantReduitEuclidean| + |mainDefiningPolynomial| |solveLinearPolynomialEquation| |integer| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| |shallowMutable| |canonical| |noetherian| |central| |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| diff --git a/src/share/algebra/interp.daase b/src/share/algebra/interp.daase index 02f055cb..33ace868 100644 --- a/src/share/algebra/interp.daase +++ b/src/share/algebra/interp.daase @@ -1,5296 +1,5296 @@ -(3198968 . 3451299487) -((-4294 (((-112) (-1 (-112) |#2| |#2|) $) 85) (((-112) $) NIL)) (-2441 (($ (-1 (-112) |#2| |#2|) $) 18) (($ $) NIL)) (-3750 ((|#2| $ (-564) |#2|) NIL) ((|#2| $ (-1226 (-564)) |#2|) 43)) (-2443 (($ $) 79)) (-3239 ((|#2| (-1 |#2| |#2| |#2|) $ |#2| |#2|) 51) ((|#2| (-1 |#2| |#2| |#2|) $ |#2|) 49) ((|#2| (-1 |#2| |#2| |#2|) $) 48)) (-3847 (((-564) (-1 (-112) |#2|) $) 27) (((-564) |#2| $) NIL) (((-564) |#2| $ (-564)) 95)) (-3534 (((-641 |#2|) $) 13)) (-2988 (($ (-1 (-112) |#2| |#2|) $ $) 62) (($ $ $) NIL)) (-1456 (($ (-1 |#2| |#2|) $) 37)) (-3123 (($ (-1 |#2| |#2|) $) NIL) (($ (-1 |#2| |#2| |#2|) $ $) 59)) (-4116 (($ 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -2797 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -2797 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-35) |has| |#1| (-1194)) ((-95) |has| |#1| (-1194)) ((-102) . T) ((-111 #0# #0#) -2797 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2797 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -2797 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -2797 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-858)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1018)) ((-612 (-169 (-379))) |has| |#1| (-1018)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-888 (-379))) |has| |#1| (-612 (-888 (-379)))) ((-612 (-888 (-564))) |has| |#1| (-612 (-888 (-564)))) ((-612 #1=(-1166 |#1|)) . 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T) ((-452) -2797 (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-493) |has| |#1| (-1194)) ((-514 (-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((-514 |#1| |#1|) |has| |#1| (-309 |#1|)) ((-556) -2797 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-644 #0#) -2797 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #0#) -2797 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-713 |#1|) . T) ((-713 $) -2797 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-720 |#1| #1#) . T) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . 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(|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2789 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2789 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2789 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2789 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2789 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2789 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2789 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2789 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2789 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2789 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2789 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2789 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2789 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2789 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-1514 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-3239 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3123 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -1514 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3239 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3123 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) -((-3123 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-3239 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-1514 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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(IF (|has| |t#2| (-722)) (PROGN (-6 (-722)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4403)) (-6 -4403) |%noBranch|) (IF (|has| |t#2| (-844)) (-6 (-844)) |%noBranch|) (IF (|has| |t#2| (-789)) (-6 (-789)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2797 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2797 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2797 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2797 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2797 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2797 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2797 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2797 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2797 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2797 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2797 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2797 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2797 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) +((-3482 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-3255 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3137 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3482 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3255 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3137 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) +((-3137 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-3255 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-3482 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2797 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . T) ((-172) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| |#1| (-612 (-536))) (|has| |#3| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| |#1| (-612 (-888 (-379)))) (|has| |#3| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| |#1| (-612 (-888 (-564)))) (|has| |#3| (-612 (-888 (-564))))) ((-231 |#1|) . T) ((-233) |has| |#1| (-233)) ((-290) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-309 $) . T) ((-326 |#1| |#4|) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2797 (|has| |#1| (-905)) (|has| |#1| (-452))) ((-514 |#2| |#1|) |has| |#1| (-233)) ((-514 |#2| $) |has| |#1| (-233)) ((-514 |#3| |#1|) . T) ((-514 |#3| $) . T) ((-514 $ $) . T) ((-556) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-644 #0#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1045)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2789 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1045))) ((-637 |#1|) |has| |#1| (-1045)) ((-713 #0#) |has| |#1| (-556)) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) -2789 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-846) . T) ((-896 (-1170)) |has| |#1| (-1045)) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . T) ((-916) |has| |#1| (-556)) ((-1034 (-407 (-564))) -2789 (|has| |#1| (-1034 (-407 (-564)))) (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))))) ((-1034 #1#) |has| |#1| (-556)) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 #2#) . T) ((-1034 #3#) |has| |#1| (-1045)) ((-1034 #4#) . T) ((-1034 |#1|) . T) ((-1051 #0#) |has| |#1| (-556)) ((-1051 |#1|) |has| |#1| (-172)) ((-1051 $) |has| |#1| (-556)) ((-1045) -2789 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1052) -2789 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1106) -2789 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-1094) . T) ((-1209) . 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T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) -((-2534 (((-641 (-1076)) $) 34)) (-2710 (($ $) 31)) (-2507 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-2674 (($ $) 14)) (-2686 ((|#2| $) 12)) (-2073 ((|#3| $) 10))) -(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -2534 ((-641 (-1076)) |#1|)) (-15 -2507 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2507 (|#1| |#1| (-1076) |#3|)) (-15 -2710 (|#1| |#1|)) (-15 -2507 (|#1| |#2| |#3|)) (-15 -2073 (|#3| |#1|)) (-15 -2674 (|#1| |#1|)) (-15 -2686 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) -NIL -(-10 -8 (-15 -2534 ((-641 (-1076)) |#1|)) (-15 -2507 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2507 (|#1| |#1| (-1076) |#3|)) (-15 -2710 (|#1| |#1|)) (-15 -2507 (|#1| |#2| |#3|)) (-15 -2073 (|#3| |#1|)) (-15 -2674 (|#1| |#1|)) (-15 -2686 (|#2| |#1|))) -((-2310 (((-112) $ $) 7)) (-3264 (((-112) $) 16)) (-2534 (((-641 (-1076)) $) 77)) (-3256 (((-1170) $) 106)) (-1864 (((-2 (|:| -2563 $) (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-767)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2797 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1076)) . T) ((-614 |#1|) . T) ((-614 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-858)) . T) ((-172) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1076) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| (-1076) (-612 (-888 (-379)))) (|has| |#1| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| (-1076) (-612 (-888 (-564)))) (|has| |#1| (-612 (-888 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2797 (|has| |#1| (-905)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #1#) |has| |#1| (-38 (-407 (-564)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 #2#) . T) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) -12 (|has| (-1076) (-882 (-379))) (|has| |#1| (-882 (-379)))) ((-882 (-564)) -12 (|has| (-1076) (-882 (-564))) (|has| |#1| (-882 (-564)))) ((-945 |#1| #0# #2#) . T) ((-905) |has| |#1| (-905)) ((-916) |has| |#1| (-363)) ((-1034 (-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 #2#) . T) ((-1034 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1051 |#1|) . T) ((-1051 $) -2797 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) +((-2560 (((-641 (-1076)) $) 34)) (-2730 (($ $) 31)) (-2532 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-2697 (($ $) 14)) (-2705 ((|#2| $) 12)) (-4122 ((|#3| $) 10))) +(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -2560 ((-641 (-1076)) |#1|)) (-15 -2532 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2532 (|#1| |#1| (-1076) |#3|)) (-15 -2730 (|#1| |#1|)) (-15 -2532 (|#1| |#2| |#3|)) (-15 -4122 (|#3| |#1|)) (-15 -2697 (|#1| |#1|)) (-15 -2705 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) +NIL +(-10 -8 (-15 -2560 ((-641 (-1076)) |#1|)) (-15 -2532 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2532 (|#1| |#1| (-1076) |#3|)) (-15 -2730 (|#1| |#1|)) (-15 -2532 (|#1| |#2| |#3|)) (-15 -4122 (|#3| |#1|)) (-15 -2697 (|#1| |#1|)) (-15 -2705 (|#2| |#1|))) +((-2331 (((-112) $ $) 7)) (-3779 (((-112) $) 16)) (-2560 (((-641 (-1076)) $) 77)) (-3282 (((-1170) $) 106)) (-2770 (((-2 (|:| -3376 $) (|:| 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(-172) (-368) (-612 (-564)) (-1145)) @@ -5306,4 +5306,4 @@ NIL NIL NIL NIL -((-3 3198953 3198958 3198963 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3198938 3198943 3198948 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3198923 3198928 3198933 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3198908 3198913 3198918 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3198077 3198783 3198860 "ZMOD" 3198865 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3197187 3197351 3197560 "ZLINDEP" 3197909 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3186487 3188255 3190227 "ZDSOLVE" 3195317 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3185733 3185874 3186063 "YSTREAM" 3186333 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3183534 3185034 3185238 "XRPOLY" 3185576 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3180114 3181405 3181980 "XPR" 3183006 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3177862 3179445 3179649 "XPOLY" 3179945 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3175645 3176987 3177042 "XPOLYC" 3177330 NIL XPOLYC (NIL T T) -9 NIL 3177443 NIL) (-1279 3172048 3174162 3174550 "XPBWPOLY" 3175303 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3167951 3170211 3170253 "XF" 3170874 NIL XF (NIL T) -9 NIL 3171274 NIL) (-1277 3167572 3167660 3167829 "XF-" 3167834 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3162898 3164161 3164216 "XFALG" 3166388 NIL XFALG (NIL T T) -9 NIL 3167177 NIL) (-1275 3162031 3162135 3162340 "XEXPPKG" 3162790 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3160167 3161881 3161977 "XDPOLY" 3161982 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159104 3159678 3159721 "XALG" 3159726 NIL XALG (NIL T) -9 NIL 3159837 NIL) (-1272 3152573 3157081 3157575 "WUTSET" 3158696 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3150856 3151625 3151948 "WP" 3152384 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3150485 3150678 3150748 "WHILEAST" 3150808 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3149984 3150202 3150296 "WHEREAST" 3150413 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3148870 3149068 3149363 "WFFINTBS" 3149781 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3146774 3147201 3147663 "WEIER" 3148442 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3145921 3146345 3146387 "VSPACE" 3146523 NIL VSPACE (NIL T) -9 NIL 3146597 NIL) (-1265 3145759 3145786 3145877 "VSPACE-" 3145882 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3145567 3145610 3145678 "VOID" 3145713 T VOID (NIL) -8 NIL NIL NIL) (-1263 3143703 3144062 3144468 "VIEW" 3145183 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140127 3140766 3141503 "VIEWDEF" 3142988 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3129458 3131675 3133848 "VIEW3D" 3137976 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3121736 3123369 3124948 "VIEW2D" 3127901 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117138 3121506 3121598 "VECTOR" 3121679 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3115715 3115974 3116292 "VECTOR2" 3116868 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3109242 3113499 3113542 "VECTCAT" 3114535 NIL VECTCAT (NIL T) -9 NIL 3115121 NIL) (-1256 3108256 3108510 3108900 "VECTCAT-" 3108905 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3107737 3107907 3108027 "VARIABLE" 3108171 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3107670 3107675 3107705 "UTYPE" 3107710 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3106500 3106654 3106916 "UTSODETL" 3107496 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3103940 3104400 3104924 "UTSODE" 3106041 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3095804 3101566 3102055 "UTS" 3103509 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3087039 3092371 3092414 "UTSCAT" 3093526 NIL UTSCAT (NIL T) -9 NIL 3094283 NIL) (-1249 3084387 3085109 3086098 "UTSCAT-" 3086103 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3084014 3084057 3084190 "UTS2" 3084338 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3078287 3080852 3080895 "URAGG" 3082965 NIL URAGG (NIL T) -9 NIL 3083688 NIL) (-1246 3075226 3076089 3077212 "URAGG-" 3077217 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3070942 3073840 3074312 "UPXSSING" 3074890 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3063035 3070189 3070462 "UPXS" 3070727 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056135 3062939 3063011 "UPXSCONS" 3063016 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3046372 3053130 3053192 "UPXSCCA" 3053766 NIL UPXSCCA (NIL T T) -9 NIL 3053999 NIL) (-1241 3046010 3046095 3046269 "UPXSCCA-" 3046274 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036100 3042631 3042674 "UPXSCAT" 3043322 NIL UPXSCAT (NIL T) -9 NIL 3043930 NIL) (-1239 3035530 3035609 3035788 "UPXS2" 3036015 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3034184 3034437 3034788 "UPSQFREE" 3035273 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3027964 3030986 3031041 "UPSCAT" 3032202 NIL UPSCAT (NIL T T) -9 NIL 3032976 NIL) (-1236 3027168 3027375 3027702 "UPSCAT-" 3027707 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3013010 3021016 3021059 "UPOLYC" 3023160 NIL UPOLYC (NIL T) -9 NIL 3024381 NIL) (-1234 3004338 3006764 3009911 "UPOLYC-" 3009916 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3003965 3004008 3004141 "UPOLYC2" 3004289 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2995531 3003648 3003777 "UP" 3003884 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2994870 2994977 2995141 "UPMP" 2995420 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2994423 2994504 2994643 "UPDIVP" 2994783 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2992991 2993240 2993556 "UPDECOMP" 2994172 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2992226 2992338 2992523 "UPCDEN" 2992875 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2991745 2991814 2991963 "UP2" 2992151 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2990260 2990949 2991226 "UNISEG" 2991503 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2989475 2989602 2989807 "UNISEG2" 2990103 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2988535 2988715 2988941 "UNIFACT" 2989291 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2972494 2987712 2987963 "ULS" 2988342 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2960520 2972398 2972470 "ULSCONS" 2972475 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943128 2955078 2955140 "ULSCCAT" 2955778 NIL ULSCCAT (NIL T T) -9 NIL 2956066 NIL) (-1220 2942178 2942423 2942811 "ULSCCAT-" 2942816 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2932045 2938490 2938533 "ULSCAT" 2939396 NIL ULSCAT (NIL T) -9 NIL 2940126 NIL) (-1218 2931475 2931554 2931733 "ULS2" 2931960 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2930592 2931075 2931182 "UINT8" 2931293 T UINT8 (NIL) -8 NIL NIL 2931378) (-1216 2929708 2930191 2930298 "UINT64" 2930409 T UINT64 (NIL) -8 NIL NIL 2930494) (-1215 2928824 2929307 2929414 "UINT32" 2929525 T UINT32 (NIL) -8 NIL NIL 2929610) (-1214 2927940 2928423 2928530 "UINT16" 2928641 T UINT16 (NIL) -8 NIL NIL 2928726) (-1213 2926335 2927266 2927296 "UFD" 2927508 T UFD (NIL) -9 NIL 2927622 NIL) (-1212 2926129 2926175 2926270 "UFD-" 2926275 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2925211 2925394 2925610 "UDVO" 2925935 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2923027 2923436 2923907 "UDPO" 2924775 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2922960 2922965 2922995 "TYPE" 2923000 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2922747 2922915 2922946 "TYPEAST" 2922951 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2921718 2921920 2922160 "TWOFACT" 2922541 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2920789 2921127 2921362 "TUPLE" 2921518 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2918480 2918999 2919538 "TUBETOOL" 2920272 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2917329 2917534 2917775 "TUBE" 2918273 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912085 2916301 2916584 "TS" 2917081 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2900752 2904844 2904941 "TSETCAT" 2910210 NIL TSETCAT (NIL T T T T) -9 NIL 2911741 NIL) (-1201 2895484 2897084 2898975 "TSETCAT-" 2898980 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2889746 2890593 2891535 "TRMANIP" 2894620 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2889187 2889250 2889413 "TRIMAT" 2889678 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2886983 2887220 2887584 "TRIGMNIP" 2888936 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2886503 2886616 2886646 "TRIGCAT" 2886859 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2886172 2886251 2886392 "TRIGCAT-" 2886397 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883065 2885030 2885311 "TREE" 2885926 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2882339 2882867 2882897 "TRANFUN" 2882932 T TRANFUN (NIL) -9 NIL 2882998 NIL) (-1193 2881618 2881809 2882089 "TRANFUN-" 2882094 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2881422 2881454 2881515 "TOPSP" 2881579 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2880770 2880885 2881039 "TOOLSIGN" 2881303 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2879431 2879947 2880186 "TEXTFILE" 2880553 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2877370 2877884 2878313 "TEX" 2879024 T TEX (NIL) -8 NIL NIL NIL) (-1188 2877151 2877182 2877254 "TEX1" 2877333 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2876799 2876862 2876952 "TEMUTL" 2877083 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2874953 2875233 2875558 "TBCMPPK" 2876522 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2866841 2873113 2873169 "TBAGG" 2873569 NIL TBAGG (NIL T T) -9 NIL 2873780 NIL) (-1184 2861911 2863399 2865153 "TBAGG-" 2865158 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2861295 2861402 2861547 "TANEXP" 2861800 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2854796 2861152 2861245 "TABLE" 2861250 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2854208 2854307 2854445 "TABLEAU" 2854693 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2848816 2850036 2851284 "TABLBUMP" 2852994 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848038 2848185 2848366 "SYSTEM" 2848657 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2844497 2845196 2845979 "SYSSOLP" 2847289 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2843531 2844009 2844128 "SYSNNI" 2844314 NIL SYSNNI (NIL NIL) -8 NIL NIL 2844399) (-1176 2842828 2843260 2843339 "SYSINT" 2843399 NIL SYSINT (NIL NIL) -8 NIL NIL 2843444) (-1175 2839187 2840106 2840816 "SYNTAX" 2842140 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2836345 2836947 2837579 "SYMTAB" 2838577 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2831594 2832496 2833479 "SYMS" 2835384 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2828856 2831052 2831282 "SYMPOLY" 2831399 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2828373 2828448 2828571 "SYMFUNC" 2828768 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2824419 2825685 2826498 "SYMBOL" 2827582 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2817958 2819647 2821367 "SWITCH" 2822721 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2811219 2816779 2817082 "SUTS" 2817713 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2803312 2810466 2810739 "SUPXS" 2811004 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2794827 2802930 2803056 "SUP" 2803221 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2793986 2794113 2794330 "SUPFRACF" 2794695 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2793607 2793666 2793779 "SUP2" 2793921 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792020 2792294 2792657 "SUMRF" 2793306 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2791334 2791400 2791599 "SUMFS" 2791941 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2775328 2790511 2790762 "SULS" 2791141 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2774957 2775150 2775220 "SUCHTAST" 2775280 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2774279 2774482 2774622 "SUCH" 2774865 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2768173 2769185 2770144 "SUBSPACE" 2773367 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2767603 2767693 2767857 "SUBRESP" 2768061 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2760968 2762268 2763579 "STTF" 2766339 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755141 2756261 2757408 "STTFNC" 2759868 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2746452 2748323 2750117 "STTAYLOR" 2753382 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2739696 2746316 2746399 "STRTBL" 2746404 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735087 2739651 2739682 "STRING" 2739687 T STRING (NIL) -8 NIL NIL NIL) (-1151 2729975 2734460 2734490 "STRICAT" 2734549 T STRICAT (NIL) -9 NIL 2734611 NIL) (-1150 2722778 2727594 2728205 "STREAM" 2729399 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2722288 2722365 2722509 "STREAM3" 2722695 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2721270 2721453 2721688 "STREAM2" 2722101 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2720958 2721010 2721103 "STREAM1" 2721212 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2719974 2720155 2720386 "STINPROD" 2720774 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2719552 2719736 2719766 "STEP" 2719846 T STEP (NIL) -9 NIL 2719924 NIL) (-1144 2713095 2719451 2719528 "STBL" 2719533 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2708269 2712316 2712359 "STAGG" 2712512 NIL STAGG (NIL T) -9 NIL 2712601 NIL) (-1142 2705971 2706573 2707445 "STAGG-" 2707450 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2704166 2705741 2705833 "STACK" 2705914 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2696889 2702307 2702763 "SREGSET" 2703796 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2689314 2690683 2692196 "SRDCMPK" 2695495 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2682281 2686754 2686784 "SRAGG" 2688087 T SRAGG (NIL) -9 NIL 2688695 NIL) (-1137 2681298 2681553 2681932 "SRAGG-" 2681937 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2675785 2680245 2680666 "SQMATRIX" 2680924 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2669532 2672503 2673230 "SPLTREE" 2675130 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2665522 2666188 2666834 "SPLNODE" 2668958 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2664569 2664802 2664832 "SPFCAT" 2665276 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2663306 2663516 2663780 "SPECOUT" 2664327 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2654958 2656702 2656732 "SPADXPT" 2661124 T SPADXPT (NIL) -9 NIL 2663158 NIL) (-1130 2654719 2654759 2654828 "SPADPRSR" 2654911 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2652901 2654674 2654705 "SPADAST" 2654710 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2644872 2646619 2646662 "SPACEC" 2651035 NIL SPACEC (NIL T) -9 NIL 2652851 NIL) (-1127 2643029 2644804 2644853 "SPACE3" 2644858 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2641781 2641952 2642243 "SORTPAK" 2642834 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2639831 2640134 2640553 "SOLVETRA" 2641445 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2638842 2639064 2639338 "SOLVESER" 2639604 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634053 2634943 2635945 "SOLVERAD" 2637894 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2629868 2630477 2631206 "SOLVEFOR" 2633420 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2624165 2629217 2629314 "SNTSCAT" 2629319 NIL SNTSCAT (NIL T T T T) -9 NIL 2629389 NIL) (-1120 2618298 2622488 2622879 "SMTS" 2623855 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2612738 2618186 2618263 "SMP" 2618268 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2610897 2611198 2611596 "SMITH" 2612435 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2603784 2607948 2608051 "SMATCAT" 2609402 NIL SMATCAT (NIL NIL T T T) -9 NIL 2609952 NIL) (-1116 2600724 2601547 2602725 "SMATCAT-" 2602730 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2598437 2599960 2600003 "SKAGG" 2600264 NIL SKAGG (NIL T) -9 NIL 2600399 NIL) (-1114 2594772 2597853 2598048 "SINT" 2598235 T SINT (NIL) -8 NIL NIL 2598408) (-1113 2594544 2594582 2594648 "SIMPAN" 2594728 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2593850 2594079 2594219 "SIG" 2594426 T SIG (NIL) -8 NIL NIL NIL) (-1111 2592688 2592909 2593184 "SIGNRF" 2593609 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2591493 2591644 2591935 "SIGNEF" 2592517 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2590826 2591076 2591200 "SIGAST" 2591391 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2588516 2588970 2589476 "SHP" 2590367 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2582416 2588417 2588493 "SHDP" 2588498 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582015 2582181 2582211 "SGROUP" 2582304 T SGROUP (NIL) -9 NIL 2582366 NIL) (-1105 2581873 2581899 2581972 "SGROUP-" 2581977 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2578708 2579406 2580129 "SGCF" 2581172 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573103 2578155 2578252 "SFRTCAT" 2578257 NIL SFRTCAT (NIL T T T T) -9 NIL 2578296 NIL) (-1102 2566524 2567542 2568678 "SFRGCD" 2572086 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2559651 2560723 2561909 "SFQCMPK" 2565457 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559273 2559362 2559472 "SFORT" 2559592 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2558418 2559113 2559234 "SEXOF" 2559239 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2557552 2558299 2558367 "SEX" 2558372 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553091 2553780 2553875 "SEXCAT" 2556812 NIL SEXCAT (NIL T T T T T) -9 NIL 2557390 NIL) (-1096 2550271 2553025 2553073 "SET" 2553078 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2548522 2548984 2549289 "SETMN" 2550012 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548128 2548254 2548284 "SETCAT" 2548401 T SETCAT (NIL) -9 NIL 2548486 NIL) (-1093 2547908 2547960 2548059 "SETCAT-" 2548064 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2544295 2546369 2546412 "SETAGG" 2547282 NIL SETAGG (NIL T) -9 NIL 2547622 NIL) (-1091 2543753 2543869 2544106 "SETAGG-" 2544111 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2543223 2543449 2543550 "SEQAST" 2543674 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2542422 2542716 2542777 "SEGXCAT" 2543063 NIL SEGXCAT (NIL T T) -9 NIL 2543183 NIL) (-1088 2541476 2542088 2542270 "SEG" 2542275 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2540455 2540669 2540712 "SEGCAT" 2541234 NIL SEGCAT (NIL T) -9 NIL 2541455 NIL) (-1086 2539504 2539834 2540034 "SEGBIND" 2540290 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539125 2539184 2539297 "SEGBIND2" 2539439 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2538725 2538926 2539003 "SEGAST" 2539070 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2537944 2538070 2538274 "SEG2" 2538569 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2537381 2537879 2537926 "SDVAR" 2537931 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2529663 2537151 2537281 "SDPOL" 2537286 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2528256 2528522 2528841 "SCPKG" 2529378 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2527416 2527589 2527782 "SCOPE" 2528085 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2526636 2526770 2526949 "SCACHE" 2527271 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2526308 2526468 2526498 "SASTCAT" 2526503 T SASTCAT (NIL) -9 NIL 2526516 NIL) (-1076 2525822 2526143 2526219 "SAOS" 2526254 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2525387 2525422 2525595 "SAERFFC" 2525781 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2519353 2525284 2525364 "SAE" 2525369 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2518946 2518981 2519140 "SAEFACT" 2519312 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2517267 2517581 2517982 "RURPK" 2518612 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2515903 2516182 2516494 "RULESET" 2517101 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513090 2513593 2514058 "RULE" 2515584 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2512729 2512884 2512967 "RULECOLD" 2513042 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2512519 2512547 2512618 "RTVALUE" 2512680 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2512017 2512236 2512330 "RSTRCAST" 2512447 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2506865 2507660 2508580 "RSETGCD" 2511216 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496122 2501174 2501271 "RSETCAT" 2505390 NIL RSETCAT (NIL T T T T) -9 NIL 2506487 NIL) (-1064 2494049 2494588 2495412 "RSETCAT-" 2495417 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486434 2487811 2489331 "RSDCMPK" 2492648 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484439 2484880 2484954 "RRCC" 2486040 NIL RRCC (NIL T T) -9 NIL 2486384 NIL) (-1061 2483790 2483964 2484243 "RRCC-" 2484248 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483260 2483486 2483587 "RPTAST" 2483711 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457258 2466853 2466920 "RPOLCAT" 2477584 NIL RPOLCAT (NIL T T T) -9 NIL 2480743 NIL) (-1058 2448756 2451096 2454218 "RPOLCAT-" 2454223 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2439803 2446967 2447449 "ROUTINE" 2448296 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2436628 2439429 2439569 "ROMAN" 2439685 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2434899 2435488 2435748 "ROIRC" 2436433 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431284 2433535 2433565 "RNS" 2433869 T RNS (NIL) -9 NIL 2434142 NIL) (-1053 2429793 2430176 2430710 "RNS-" 2430785 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429242 2429624 2429654 "RNG" 2429659 T RNG (NIL) -9 NIL 2429680 NIL) (-1051 2428634 2428996 2429039 "RMODULE" 2429101 NIL RMODULE (NIL T) -9 NIL 2429143 NIL) (-1050 2427470 2427564 2427900 "RMCAT2" 2428535 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424347 2426816 2427113 "RMATRIX" 2427232 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417289 2419523 2419638 "RMATCAT" 2422997 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2423979 NIL) (-1047 2416664 2416811 2417118 "RMATCAT-" 2417123 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416231 2416306 2416434 "RINTERP" 2416583 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415350 2415878 2415908 "RING" 2415964 T RING (NIL) -9 NIL 2416056 NIL) (-1044 2415142 2415186 2415283 "RING-" 2415288 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2413983 2414220 2414478 "RIDIST" 2414906 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405299 2413451 2413657 "RGCHAIN" 2413831 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2404675 2405055 2405096 "RGBCSPC" 2405154 NIL RGBCSPC (NIL T) -9 NIL 2405206 NIL) (-1040 2403859 2404214 2404255 "RGBCMDL" 2404487 NIL RGBCMDL (NIL T) -9 NIL 2404601 NIL) (-1039 2400853 2401467 2402137 "RF" 2403223 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400499 2400562 2400665 "RFFACTOR" 2400784 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400224 2400259 2400356 "RFFACT" 2400458 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398341 2398705 2399087 "RFDIST" 2399864 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2397794 2397886 2398049 "RETSOL" 2398243 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397430 2397510 2397553 "RETRACT" 2397686 NIL RETRACT (NIL T) -9 NIL 2397773 NIL) (-1033 2397279 2397304 2397391 "RETRACT-" 2397396 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2396908 2397101 2397171 "RETAST" 2397231 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2389762 2396561 2396688 "RESULT" 2396803 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388380 2389031 2389230 "RESRING" 2389665 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2388016 2388065 2388163 "RESLATC" 2388317 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2387721 2387756 2387863 "REPSQ" 2387975 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385143 2385723 2386325 "REP" 2387141 T REP (NIL) -7 NIL NIL NIL) (-1026 2384840 2384875 2384986 "REPDB" 2385102 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2378740 2380129 2381352 "REP2" 2383652 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375117 2375798 2376606 "REP1" 2377967 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2367840 2373258 2373714 "REGSET" 2374747 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2366653 2366988 2367238 "REF" 2367625 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2366030 2366133 2366300 "REDORDER" 2366537 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2362025 2365243 2365470 "RECLOS" 2365858 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361077 2361258 2361473 "REALSOLV" 2361832 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2360923 2360964 2360994 "REAL" 2360999 T REAL (NIL) -9 NIL 2361034 NIL) (-1017 2357406 2358208 2359092 "REAL0Q" 2360088 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2353007 2353995 2355056 "REAL0" 2356387 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352505 2352724 2352818 "RDUCEAST" 2352935 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2351910 2351982 2352189 "RDIV" 2352427 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2350978 2351152 2351365 "RDIST" 2351732 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349575 2349862 2350234 "RDETRS" 2350686 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347387 2347841 2348379 "RDETR" 2349117 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2345998 2346276 2346680 "RDEEFS" 2347103 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344493 2344799 2345231 "RDEEF" 2345686 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2338746 2341629 2341659 "RCFIELD" 2342954 T RCFIELD (NIL) -9 NIL 2343684 NIL) (-1007 2336810 2337314 2338010 "RCFIELD-" 2338085 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333126 2334911 2334954 "RCAGG" 2336038 NIL RCAGG (NIL T) -9 NIL 2336503 NIL) (-1005 2332754 2332848 2333011 "RCAGG-" 2333016 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332089 2332201 2332366 "RATRET" 2332638 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2331642 2331709 2331830 "RATFACT" 2332017 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2330950 2331070 2331222 "RANDSRC" 2331512 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2330684 2330728 2330801 "RADUTIL" 2330899 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2323827 2329517 2329827 "RADIX" 2330408 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315475 2323671 2323799 "RADFF" 2323804 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315127 2315202 2315230 "RADCAT" 2315387 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2314912 2314960 2315057 "RADCAT-" 2315062 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313063 2314687 2314776 "QUEUE" 2314856 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2309631 2313000 2313045 "QUAT" 2313050 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309269 2309312 2309439 "QUATCT2" 2309582 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2303008 2306318 2306358 "QUATCAT" 2307138 NIL QUATCAT (NIL T) -9 NIL 2307904 NIL) (-992 2299152 2300189 2301576 "QUATCAT-" 2301670 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2296672 2298236 2298277 "QUAGG" 2298652 NIL QUAGG (NIL T) -9 NIL 2298827 NIL) (-990 2296304 2296497 2296565 "QQUTAST" 2296624 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295229 2295702 2295874 "QFORM" 2296176 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286433 2291646 2291686 "QFCAT" 2292344 NIL QFCAT (NIL T) -9 NIL 2293345 NIL) (-987 2282005 2283206 2284797 "QFCAT-" 2284891 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2281643 2281686 2281813 "QFCAT2" 2281956 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281103 2281213 2281343 "QEQUAT" 2281533 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274250 2275322 2276506 "QCMPACK" 2280036 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2271826 2272247 2272675 "QALGSET" 2273905 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271071 2271245 2271477 "QALGSET2" 2271646 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2269761 2269985 2270302 "PWFFINTB" 2270844 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2267943 2268111 2268465 "PUSHVAR" 2269575 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2263861 2264915 2264956 "PTRANFN" 2266840 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262263 2262554 2262876 "PTPACK" 2263572 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2261895 2261952 2262061 "PTFUNC2" 2262200 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256422 2260767 2260808 "PTCAT" 2261104 NIL PTCAT (NIL T) -9 NIL 2261257 NIL) (-975 2256080 2256115 2256239 "PSQFR" 2256381 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2254675 2254973 2255307 "PSEUDLIN" 2255778 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241438 2243809 2246133 "PSETPK" 2252435 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234482 2237196 2237292 "PSETCAT" 2240313 NIL PSETCAT (NIL T T T T) -9 NIL 2241127 NIL) (-971 2232318 2232952 2233773 "PSETCAT-" 2233778 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2231667 2231832 2231860 "PSCURVE" 2232128 T PSCURVE (NIL) -9 NIL 2232295 NIL) (-969 2228015 2229505 2229570 "PSCAT" 2230414 NIL PSCAT (NIL T T T) -9 NIL 2230654 NIL) (-968 2227078 2227294 2227694 "PSCAT-" 2227699 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2225810 2226443 2226648 "PRTITION" 2226893 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225312 2225531 2225623 "PRTDAST" 2225738 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214402 2216616 2218804 "PRS" 2223174 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212260 2213752 2213792 "PRQAGG" 2213975 NIL PRQAGG (NIL T) -9 NIL 2214077 NIL) (-963 2211646 2211875 2211903 "PROPLOG" 2212088 T PROPLOG (NIL) -9 NIL 2212210 NIL) (-962 2210154 2210597 2210854 "PROPFRML" 2211422 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2209614 2209724 2209854 "PROPERTY" 2210044 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2203699 2207780 2208600 "PRODUCT" 2208840 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2201004 2203157 2203391 "PR" 2203510 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2200800 2200832 2200891 "PRINT" 2200965 T PRINT (NIL) -7 NIL NIL NIL) (-957 2200140 2200257 2200409 "PRIMES" 2200680 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2198205 2198606 2199072 "PRIMELT" 2199719 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2197934 2197983 2198011 "PRIMCAT" 2198135 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2194097 2197872 2197917 "PRIMARR" 2197922 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2193104 2193282 2193510 "PRIMARR2" 2193915 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2192747 2192803 2192914 "PREASSOC" 2193042 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2192222 2192355 2192383 "PPCURVE" 2192588 T PPCURVE (NIL) -9 NIL 2192724 NIL) (-950 2191844 2192017 2192100 "PORTNUM" 2192159 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2189203 2189602 2190194 "POLYROOT" 2191425 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2183140 2188807 2188967 "POLY" 2189076 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2182523 2182581 2182815 "POLYLIFT" 2183076 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2178798 2179247 2179876 "POLYCATQ" 2182068 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2165607 2170973 2171038 "POLYCAT" 2174552 NIL POLYCAT (NIL T T T) -9 NIL 2176480 NIL) (-944 2159056 2160918 2163302 "POLYCAT-" 2163307 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2158643 2158711 2158831 "POLY2UP" 2158982 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2158275 2158332 2158441 "POLY2" 2158580 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2156960 2157199 2157475 "POLUTIL" 2158049 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2155315 2155592 2155923 "POLTOPOL" 2156682 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2150830 2155251 2155297 "POINT" 2155302 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2149017 2149374 2149749 "PNTHEORY" 2150475 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2147436 2147733 2148145 "PMTOOLS" 2148715 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2147029 2147107 2147224 "PMSYM" 2147352 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2146539 2146608 2146782 "PMQFCAT" 2146954 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2145894 2146004 2146160 "PMPRED" 2146416 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2145290 2145376 2145537 "PMPREDFS" 2145795 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2143933 2144141 2144526 "PMPLCAT" 2145052 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2143465 2143544 2143696 "PMLSAGG" 2143848 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2142940 2143016 2143197 "PMKERNEL" 2143383 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2142557 2142632 2142745 "PMINS" 2142859 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2141985 2142054 2142270 "PMFS" 2142482 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2141213 2141331 2141536 "PMDOWN" 2141862 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2140376 2140535 2140717 "PMASS" 2141051 T PMASS (NIL) -7 NIL NIL NIL) (-925 2139650 2139761 2139924 "PMASSFS" 2140262 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2139305 2139373 2139467 "PLOTTOOL" 2139576 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2133912 2135116 2136264 "PLOT" 2138177 T PLOT (NIL) -8 NIL NIL NIL) (-922 2129716 2130760 2131681 "PLOT3D" 2133011 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2128628 2128805 2129040 "PLOT1" 2129520 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2104017 2108694 2113545 "PLEQN" 2123894 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2103335 2103457 2103637 "PINTERP" 2103882 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2103028 2103075 2103178 "PINTERPA" 2103282 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2102276 2102797 2102884 "PI" 2102924 T PI (NIL) -8 NIL NIL 2102991) (-916 2100665 2101614 2101642 "PID" 2101824 T PID (NIL) -9 NIL 2101958 NIL) (-915 2100390 2100427 2100515 "PICOERCE" 2100622 NIL PICOERCE (NIL T) -7 NIL NIL 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NIL NIL) (-878 2027139 2027202 2027304 "PARSURF" 2027449 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2026771 2026828 2026937 "PARSU2" 2027076 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2026535 2026575 2026642 "PARSER" 2026724 T PARSER (NIL) -7 NIL NIL NIL) (-875 2026156 2026219 2026321 "PARSCURV" 2026466 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2025788 2025845 2025954 "PARSC2" 2026093 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2025427 2025485 2025582 "PARPCURV" 2025724 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2025059 2025116 2025225 "PARPC2" 2025364 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2024579 2024665 2024784 "PAN2EXPR" 2024960 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2023383 2023700 2023928 "PALETTE" 2024371 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2021851 2022388 2022748 "PAIR" 2023069 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2015748 2021110 2021304 "PADICRC" 2021706 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2009004 2015094 2015278 "PADICRAT" 2015596 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2007346 2008941 2008986 "PADIC" 2008991 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2004548 2006086 2006126 "PADICCT" 2006707 NIL PADICCT (NIL NIL) -9 NIL 2006989 NIL) (-864 2003505 2003705 2003973 "PADEPAC" 2004335 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2002717 2002850 2003056 "PADE" 2003367 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2001131 2001925 2002205 "OWP" 2002521 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2000651 2000837 2000934 "OVERSET" 2001054 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1999724 2000256 2000428 "OVAR" 2000519 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1998988 1999109 1999270 "OUT" 1999583 T OUT (NIL) -7 NIL NIL NIL) (-858 1987886 1990097 1992297 "OUTFORM" 1996808 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1987222 1987483 1987610 "OUTBFILE" 1987779 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1986529 1986694 1986722 "OUTBCON" 1987040 T OUTBCON (NIL) -9 NIL 1987206 NIL) (-855 1986130 1986242 1986399 "OUTBCON-" 1986404 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1985537 1985859 1985948 "OSI" 1986061 T OSI (NIL) -8 NIL NIL NIL) (-853 1985093 1985405 1985433 "OSGROUP" 1985438 T OSGROUP (NIL) -9 NIL 1985460 NIL) (-852 1983838 1984065 1984350 "ORTHPOL" 1984840 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1981416 1983673 1983794 "OREUP" 1983799 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1978846 1981107 1981234 "ORESUP" 1981358 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1976374 1976874 1977435 "OREPCTO" 1978335 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1970190 1972365 1972406 "OREPCAT" 1974754 NIL OREPCAT (NIL T) -9 NIL 1975858 NIL) (-847 1967337 1968119 1969177 "OREPCAT-" 1969182 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1966514 1966786 1966814 "ORDSET" 1967123 T ORDSET (NIL) -9 NIL 1967287 NIL) (-845 1966033 1966155 1966348 "ORDSET-" 1966353 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1964659 1965424 1965452 "ORDRING" 1965654 T ORDRING (NIL) -9 NIL 1965779 NIL) (-843 1964304 1964398 1964542 "ORDRING-" 1964547 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1963710 1964147 1964175 "ORDMON" 1964180 T ORDMON (NIL) -9 NIL 1964201 NIL) (-841 1962872 1963019 1963214 "ORDFUNS" 1963559 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1962236 1962629 1962657 "ORDFIN" 1962722 T ORDFIN (NIL) -9 NIL 1962796 NIL) (-839 1958822 1960822 1961231 "ORDCOMP" 1961860 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1958088 1958215 1958401 "ORDCOMP2" 1958682 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954696 1955579 1956393 "OPTPROB" 1957294 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1951498 1952137 1952841 "OPTPACK" 1954012 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1949211 1949951 1949979 "OPTCAT" 1950798 T OPTCAT (NIL) -9 NIL 1951448 NIL) (-834 1948654 1948888 1948993 "OPSIG" 1949126 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1948422 1948461 1948527 "OPQUERY" 1948608 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1945580 1946733 1947237 "OP" 1947951 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1945115 1945286 1945327 "OPERCAT" 1945462 NIL OPERCAT (NIL T) -9 NIL 1945530 NIL) (-830 1944961 1944988 1945074 "OPERCAT-" 1945079 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1941800 1943758 1944127 "ONECOMP" 1944625 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1941105 1941220 1941394 "ONECOMP2" 1941672 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1940524 1940630 1940760 "OMSERVER" 1940995 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1937412 1939964 1940004 "OMSAGG" 1940065 NIL OMSAGG (NIL T) -9 NIL 1940129 NIL) (-825 1936035 1936298 1936580 "OMPKG" 1937150 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1935465 1935568 1935596 "OM" 1935895 T OM (NIL) -9 NIL NIL NIL) (-823 1934039 1935014 1935183 "OMLO" 1935346 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1932964 1933111 1933338 "OMEXPR" 1933865 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1932282 1932510 1932646 "OMERR" 1932848 T OMERR (NIL) -8 NIL NIL NIL) (-820 1931460 1931703 1931863 "OMERRK" 1932142 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1930938 1931137 1931245 "OMENC" 1931372 T OMENC (NIL) -8 NIL NIL NIL) (-818 1924833 1926018 1927189 "OMDEV" 1929787 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1923902 1924073 1924267 "OMCONN" 1924659 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1922515 1923465 1923493 "OINTDOM" 1923498 T OINTDOM (NIL) -9 NIL 1923519 NIL) (-815 1918321 1919505 1920221 "OFMONOID" 1921831 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1917759 1918258 1918303 "ODVAR" 1918308 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1915209 1917504 1917659 "ODR" 1917664 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1907545 1914985 1915111 "ODPOL" 1915116 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1901415 1907417 1907522 "ODP" 1907527 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1900181 1900396 1900671 "ODETOOLS" 1901189 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1897148 1897806 1898522 "ODESYS" 1899514 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1892030 1892938 1893963 "ODERTRIC" 1896223 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1891456 1891538 1891732 "ODERED" 1891942 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1888344 1888892 1889569 "ODERAT" 1890879 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1885301 1885768 1886365 "ODEPRRIC" 1887873 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1883271 1883840 1884326 "ODEPROB" 1884835 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1879791 1880276 1880923 "ODEPRIM" 1882750 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1879040 1879142 1879402 "ODEPAL" 1879683 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1875202 1875993 1876857 "ODEPACK" 1878196 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1874235 1874342 1874571 "ODEINT" 1875091 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1868336 1869761 1871208 "ODEIFTBL" 1872808 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1863671 1864457 1865416 "ODEEF" 1867495 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1863006 1863095 1863325 "ODECONST" 1863576 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1861157 1861792 1861820 "ODECAT" 1862425 T ODECAT (NIL) -9 NIL 1862956 NIL) (-795 1858056 1860869 1860988 "OCT" 1861070 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1857694 1857737 1857864 "OCTCT2" 1858007 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1852460 1854868 1854908 "OC" 1856005 NIL OC (NIL T) -9 NIL 1856863 NIL) (-792 1849687 1850435 1851425 "OC-" 1851519 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1849065 1849507 1849535 "OCAMON" 1849540 T OCAMON (NIL) -9 NIL 1849561 NIL) (-790 1848622 1848937 1848965 "OASGP" 1848970 T OASGP (NIL) -9 NIL 1848990 NIL) (-789 1847909 1848372 1848400 "OAMONS" 1848440 T OAMONS (NIL) -9 NIL 1848483 NIL) (-788 1847349 1847756 1847784 "OAMON" 1847789 T OAMON (NIL) -9 NIL 1847809 NIL) (-787 1846653 1847145 1847173 "OAGROUP" 1847178 T OAGROUP (NIL) -9 NIL 1847198 NIL) (-786 1846343 1846393 1846481 "NUMTUBE" 1846597 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1839916 1841434 1842970 "NUMQUAD" 1844827 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1835672 1836660 1837685 "NUMODE" 1838911 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1833053 1833907 1833935 "NUMINT" 1834858 T NUMINT (NIL) -9 NIL 1835622 NIL) (-782 1832001 1832198 1832416 "NUMFMT" 1832855 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1818360 1821305 1823837 "NUMERIC" 1829508 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1812757 1817809 1817904 "NTSCAT" 1817909 NIL NTSCAT (NIL T T T T) -9 NIL 1817948 NIL) (-779 1811951 1812116 1812309 "NTPOLFN" 1812596 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1799783 1808776 1809588 "NSUP" 1811172 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1799415 1799472 1799581 "NSUP2" 1799720 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1789398 1799189 1799322 "NSMP" 1799327 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1787830 1788131 1788488 "NREP" 1789086 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1786421 1786673 1787031 "NPCOEF" 1787573 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1785487 1785602 1785818 "NORMRETR" 1786302 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1783528 1783818 1784227 "NORMPK" 1785195 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1783213 1783241 1783365 "NORMMA" 1783494 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1783040 1783170 1783199 "NONE" 1783204 T NONE (NIL) -8 NIL NIL NIL) (-769 1782829 1782858 1782927 "NONE1" 1783004 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1782312 1782374 1782560 "NODE1" 1782761 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1780582 1781406 1781661 "NNI" 1782008 T NNI (NIL) -8 NIL NIL 1782243) (-766 1779002 1779315 1779679 "NLINSOL" 1780250 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1775270 1776238 1777137 "NIPROB" 1778123 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1774027 1774261 1774563 "NFINTBAS" 1775032 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1773201 1773677 1773718 "NETCLT" 1773890 NIL NETCLT (NIL T) -9 NIL 1773972 NIL) (-762 1771909 1772140 1772421 "NCODIV" 1772969 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1771671 1771708 1771783 "NCNTFRAC" 1771866 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1769851 1770215 1770635 "NCEP" 1771296 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1768748 1769495 1769523 "NASRING" 1769633 T NASRING (NIL) -9 NIL 1769713 NIL) (-758 1768543 1768587 1768681 "NASRING-" 1768686 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1767696 1768195 1768223 "NARNG" 1768340 T NARNG (NIL) -9 NIL 1768431 NIL) (-756 1767388 1767455 1767589 "NARNG-" 1767594 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1766267 1766474 1766709 "NAGSP" 1767173 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1757539 1759223 1760896 "NAGS" 1764614 T NAGS (NIL) -7 NIL NIL NIL) (-753 1756087 1756395 1756726 "NAGF07" 1757228 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1750625 1751916 1753223 "NAGF04" 1754800 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1743593 1745207 1746840 "NAGF02" 1749012 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1738817 1739917 1741034 "NAGF01" 1742496 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1732445 1734011 1735596 "NAGE04" 1737252 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1723614 1725735 1727865 "NAGE02" 1730335 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1719567 1720514 1721478 "NAGE01" 1722670 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1717362 1717896 1718454 "NAGD03" 1719029 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1709112 1711040 1712994 "NAGD02" 1715428 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1702923 1704348 1705788 "NAGD01" 1707692 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1699132 1699954 1700791 "NAGC06" 1702106 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1697597 1697929 1698285 "NAGC05" 1698796 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1696973 1697092 1697236 "NAGC02" 1697473 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1696033 1696590 1696630 "NAALG" 1696709 NIL NAALG (NIL T) -9 NIL 1696770 NIL) (-739 1695868 1695897 1695987 "NAALG-" 1695992 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1689818 1690926 1692113 "MULTSQFR" 1694764 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1689137 1689212 1689396 "MULTFACT" 1689730 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1682222 1686100 1686153 "MTSCAT" 1687223 NIL MTSCAT (NIL T T) -9 NIL 1687737 NIL) (-735 1681934 1681988 1682080 "MTHING" 1682162 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1681726 1681759 1681819 "MSYSCMD" 1681894 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1677835 1680481 1680801 "MSET" 1681439 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1674930 1677396 1677437 "MSETAGG" 1677442 NIL MSETAGG (NIL T) -9 NIL 1677476 NIL) (-731 1670798 1672309 1673054 "MRING" 1674230 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1670364 1670431 1670562 "MRF2" 1670725 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1669982 1670017 1670161 "MRATFAC" 1670323 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1667594 1667889 1668320 "MPRFF" 1669687 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1661646 1667448 1667545 "MPOLY" 1667550 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1661136 1661171 1661379 "MPCPF" 1661605 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1660650 1660693 1660877 "MPC3" 1661087 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1659845 1659926 1660147 "MPC2" 1660565 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1658146 1658483 1658873 "MONOTOOL" 1659505 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1657397 1657688 1657716 "MONOID" 1657935 T MONOID (NIL) -9 NIL 1658082 NIL) (-721 1656943 1657062 1657243 "MONOID-" 1657248 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1647794 1653710 1653769 "MONOGEN" 1654443 NIL MONOGEN (NIL T T) -9 NIL 1654899 NIL) (-719 1645012 1645747 1646747 "MONOGEN-" 1646866 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1643871 1644291 1644319 "MONADWU" 1644711 T MONADWU (NIL) -9 NIL 1644949 NIL) (-717 1643243 1643402 1643650 "MONADWU-" 1643655 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1642628 1642846 1642874 "MONAD" 1643081 T MONAD (NIL) -9 NIL 1643193 NIL) (-715 1642313 1642391 1642523 "MONAD-" 1642528 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1640629 1641226 1641505 "MOEBIUS" 1642066 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1640021 1640399 1640439 "MODULE" 1640444 NIL MODULE (NIL T) -9 NIL 1640470 NIL) (-712 1639589 1639685 1639875 "MODULE-" 1639880 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1637296 1637953 1638280 "MODRING" 1639413 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1634267 1635401 1635922 "MODOP" 1636825 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1632882 1633334 1633611 "MODMONOM" 1634130 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1622679 1631173 1631587 "MODMON" 1632519 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1619862 1621523 1621799 "MODFIELD" 1622554 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1618866 1619143 1619333 "MMLFORM" 1619692 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1618392 1618435 1618614 "MMAP" 1618817 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1616601 1617342 1617383 "MLO" 1617806 NIL MLO (NIL T) -9 NIL 1618048 NIL) (-703 1613967 1614483 1615085 "MLIFT" 1616082 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1613358 1613442 1613596 "MKUCFUNC" 1613878 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1612957 1613027 1613150 "MKRECORD" 1613281 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1612004 1612166 1612394 "MKFUNC" 1612768 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1611392 1611496 1611652 "MKFLCFN" 1611887 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610669 1610771 1610956 "MKBCFUNC" 1611285 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607403 1610223 1610359 "MINT" 1610553 T MINT (NIL) -8 NIL NIL NIL) (-696 1606215 1606458 1606735 "MHROWRED" 1607158 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601622 1604750 1605155 "MFLOAT" 1605830 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600979 1601055 1601226 "MFINFACT" 1601534 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597294 1598142 1599026 "MESH" 1600115 T MESH (NIL) -7 NIL NIL NIL) (-692 1595684 1595996 1596349 "MDDFACT" 1596981 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592526 1594843 1594884 "MDAGG" 1595139 NIL MDAGG (NIL T) -9 NIL 1595282 NIL) (-690 1582296 1591819 1592026 "MCMPLX" 1592339 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581437 1581583 1581783 "MCDEN" 1582145 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579327 1579597 1579977 "MCALCFN" 1581167 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578252 1578492 1578725 "MAYBE" 1579133 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575864 1576387 1576949 "MATSTOR" 1577723 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571869 1575236 1575484 "MATRIX" 1575649 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567633 1568342 1569078 "MATLIN" 1571226 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557787 1560925 1561002 "MATCAT" 1565882 NIL MATCAT (NIL T T T) -9 NIL 1567299 NIL) (-682 1554143 1555164 1556520 "MATCAT-" 1556525 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552737 1552890 1553223 "MATCAT2" 1553978 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550849 1551173 1551557 "MAPPKG3" 1552412 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549830 1550003 1550225 "MAPPKG2" 1550673 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548329 1548613 1548940 "MAPPKG1" 1549536 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547435 1547735 1547912 "MAPPAST" 1548172 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1547046 1547104 1547227 "MAPHACK3" 1547371 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546638 1546699 1546813 "MAPHACK2" 1546978 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1546075 1546179 1546321 "MAPHACK1" 1546529 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544181 1544775 1545079 "MAGMA" 1545803 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543687 1543905 1543996 "MACROAST" 1544110 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1540153 1541926 1542387 "M3D" 1543259 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534307 1538522 1538563 "LZSTAGG" 1539345 NIL LZSTAGG (NIL T) -9 NIL 1539640 NIL) (-669 1530264 1531438 1532895 "LZSTAGG-" 1532900 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527378 1528155 1528642 "LWORD" 1529809 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526981 1527182 1527257 "LSTAST" 1527323 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1520174 1526752 1526886 "LSQM" 1526891 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519398 1519537 1519765 "LSPP" 1520029 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517210 1517511 1517967 "LSMP" 1519087 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513989 1514663 1515393 "LSMP1" 1516512 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507914 1513156 1513197 "LSAGG" 1513259 NIL LSAGG (NIL T) -9 NIL 1513337 NIL) (-661 1504609 1505533 1506746 "LSAGG-" 1506751 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502235 1503753 1504002 "LPOLY" 1504404 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501817 1501902 1502025 "LPEFRAC" 1502144 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1500164 1500911 1501164 "LO" 1501649 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499816 1499928 1499956 "LOGIC" 1500067 T LOGIC (NIL) -9 NIL 1500148 NIL) (-656 1499678 1499701 1499772 "LOGIC-" 1499777 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498871 1499011 1499204 "LODOOPS" 1499534 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496321 1498787 1498853 "LODO" 1498858 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494859 1495094 1495447 "LODOF" 1496068 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491207 1493612 1493653 "LODOCAT" 1494091 NIL LODOCAT (NIL T) -9 NIL 1494302 NIL) (-651 1490940 1490998 1491125 "LODOCAT-" 1491130 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488287 1490781 1490899 "LODO2" 1490904 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485749 1488224 1488269 "LODO1" 1488274 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484609 1484774 1485086 "LODEEF" 1485572 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479895 1482739 1482780 "LNAGG" 1483727 NIL LNAGG (NIL T) -9 NIL 1484171 NIL) (-646 1479042 1479256 1479598 "LNAGG-" 1479603 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475205 1475967 1476606 "LMOPS" 1478457 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474600 1474962 1475003 "LMODULE" 1475064 NIL LMODULE (NIL T) -9 NIL 1475106 NIL) (-643 1471846 1474245 1474368 "LMDICT" 1474510 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471572 1471754 1471814 "LITERAL" 1471819 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464803 1470518 1470816 "LIST" 1471307 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464328 1464402 1464541 "LIST3" 1464723 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463335 1463513 1463741 "LIST2" 1464146 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461469 1461781 1462180 "LIST2MAP" 1462982 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460191 1460835 1460876 "LINEXP" 1461131 NIL LINEXP (NIL T) -9 NIL 1461280 NIL) (-636 1458838 1459098 1459395 "LINDEP" 1459943 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455605 1456324 1457101 "LIMITRF" 1458093 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453880 1454176 1454592 "LIMITPS" 1455300 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448335 1453391 1453619 "LIE" 1453701 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447384 1447827 1447867 "LIECAT" 1448007 NIL LIECAT (NIL T) -9 NIL 1448158 NIL) (-631 1447225 1447252 1447340 "LIECAT-" 1447345 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439837 1446674 1446839 "LIB" 1447080 T LIB (NIL) -8 NIL NIL NIL) (-629 1435472 1436355 1437290 "LGROBP" 1438954 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433338 1433612 1433974 "LF" 1435193 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432178 1432870 1432898 "LFCAT" 1433105 T LFCAT (NIL) -9 NIL 1433244 NIL) (-626 1429080 1429710 1430398 "LEXTRIPK" 1431542 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425851 1426650 1427153 "LEXP" 1428660 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425354 1425572 1425664 "LETAST" 1425779 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423752 1424065 1424466 "LEADCDET" 1425036 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422942 1423016 1423245 "LAZM3PK" 1423673 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417886 1421019 1421557 "LAUPOL" 1422454 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417451 1417495 1417663 "LAPLACE" 1417836 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415417 1416552 1416803 "LA" 1417284 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414490 1415048 1415089 "LALG" 1415151 NIL LALG (NIL T) -9 NIL 1415210 NIL) (-617 1414204 1414263 1414399 "LALG-" 1414404 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1414039 1414063 1414104 "KVTFROM" 1414166 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412839 1413256 1413485 "KTVLOGIC" 1413830 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412674 1412698 1412739 "KRCFROM" 1412801 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411578 1411765 1412064 "KOVACIC" 1412474 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411413 1411437 1411478 "KONVERT" 1411540 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411248 1411272 1411313 "KOERCE" 1411375 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408982 1409742 1410135 "KERNEL" 1410887 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408484 1408565 1408695 "KERNEL2" 1408896 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402335 1407023 1407077 "KDAGG" 1407454 NIL KDAGG (NIL T T) -9 NIL 1407660 NIL) (-607 1401864 1401988 1402193 "KDAGG-" 1402198 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1395039 1401525 1401680 "KAFILE" 1401742 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389494 1394550 1394778 "JORDAN" 1394860 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388900 1389143 1389264 "JOINAST" 1389393 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388746 1388805 1388860 "JAVACODE" 1388865 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1385045 1386951 1387005 "IXAGG" 1387934 NIL IXAGG (NIL T T) -9 NIL 1388393 NIL) (-601 1383964 1384270 1384689 "IXAGG-" 1384694 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379544 1383886 1383945 "IVECTOR" 1383950 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378310 1378547 1378813 "ITUPLE" 1379311 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376746 1376923 1377229 "ITRIGMNP" 1378132 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375491 1375695 1375978 "ITFUN3" 1376522 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1375123 1375180 1375289 "ITFUN2" 1375428 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372952 1373985 1374284 "ITAYLOR" 1374857 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361924 1367089 1368252 "ISUPS" 1371822 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1361028 1361168 1361404 "ISUMP" 1361771 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356292 1360829 1360908 "ISTRING" 1360981 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355795 1356013 1356105 "ISAST" 1356220 T ISAST (NIL) -8 NIL NIL NIL) (-590 1355005 1355086 1355302 "IRURPK" 1355709 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353941 1354142 1354382 "IRSN" 1354785 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351970 1352325 1352761 "IRRF2F" 1353579 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351717 1351755 1351831 "IRREDFFX" 1351926 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350332 1350591 1350890 "IROOT" 1351450 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346963 1348016 1348708 "IR" 1349672 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344576 1345071 1345637 "IR2" 1346441 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343648 1343761 1343982 "IR2F" 1344459 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343439 1343473 1343533 "IPRNTPK" 1343608 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1340046 1343328 1343397 "IPF" 1343402 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338400 1339971 1340028 "IPADIC" 1340033 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337739 1337960 1338090 "IP4ADDR" 1338290 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337239 1337443 1337553 "IOMODE" 1337649 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336312 1336836 1336963 "IOBFILE" 1337132 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335800 1336216 1336244 "IOBCON" 1336249 T IOBCON (NIL) -9 NIL 1336270 NIL) (-575 1335297 1335355 1335545 "INVLAPLA" 1335736 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324945 1327299 1329685 "INTTR" 1332961 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321289 1322031 1322895 "INTTOOLS" 1324130 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320875 1320966 1321083 "INTSLPE" 1321192 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318856 1320798 1320857 "INTRVL" 1320862 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316458 1316970 1317545 "INTRF" 1318341 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315869 1315966 1316108 "INTRET" 1316356 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313866 1314255 1314725 "INTRAT" 1315477 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1311094 1311677 1312303 "INTPM" 1313351 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307796 1308396 1309141 "INTPAF" 1310480 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302975 1303937 1304988 "INTPACK" 1306765 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299879 1302704 1302831 "INT" 1302868 T INT (NIL) -8 NIL NIL NIL) (-563 1299131 1299283 1299491 "INTHERTR" 1299721 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298570 1298650 1298838 "INTHERAL" 1299045 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296416 1296859 1297316 "INTHEORY" 1298133 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287724 1289345 1291124 "INTG0" 1294768 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268297 1273087 1277897 "INTFTBL" 1282934 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267546 1267684 1267857 "INTFACT" 1268156 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264931 1265377 1265941 "INTEF" 1267100 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263390 1264103 1264131 "INTDOM" 1264432 T INTDOM (NIL) -9 NIL 1264639 NIL) (-555 1262759 1262933 1263175 "INTDOM-" 1263180 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259246 1261143 1261197 "INTCAT" 1261996 NIL INTCAT (NIL T) -9 NIL 1262316 NIL) (-553 1258718 1258821 1258949 "INTBIT" 1259138 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257389 1257543 1257857 "INTALG" 1258563 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256846 1256936 1257106 "INTAF" 1257293 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250300 1256656 1256796 "INTABL" 1256801 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249631 1250070 1250135 "INT8" 1250169 T INT8 (NIL) -8 NIL NIL 1250214) (-548 1248961 1249400 1249465 "INT64" 1249499 T INT64 (NIL) -8 NIL NIL 1249544) (-547 1248291 1248730 1248795 "INT32" 1248829 T INT32 (NIL) -8 NIL NIL 1248874) (-546 1247621 1248060 1248125 "INT16" 1248159 T INT16 (NIL) -8 NIL NIL 1248204) (-545 1242628 1245310 1245338 "INS" 1246272 T INS (NIL) -9 NIL 1246937 NIL) (-544 1239868 1240639 1241613 "INS-" 1241686 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238643 1238870 1239168 "INPSIGN" 1239621 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237761 1237878 1238075 "INPRODPF" 1238523 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236655 1236772 1237009 "INPRODFF" 1237641 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235655 1235807 1236067 "INNMFACT" 1236491 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234852 1234949 1235137 "INMODGCD" 1235554 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233360 1233605 1233929 "INFSP" 1234597 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232544 1232661 1232844 "INFPROD0" 1233240 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229426 1230609 1231124 "INFORM" 1232037 T INFORM (NIL) -8 NIL NIL NIL) (-535 1229036 1229096 1229194 "INFORM1" 1229361 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228559 1228648 1228762 "INFINITY" 1228942 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227735 1228279 1228380 "INETCLTS" 1228478 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226351 1226601 1226922 "INEP" 1227483 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225627 1226248 1226313 "INDE" 1226318 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225191 1225259 1225376 "INCRMAPS" 1225554 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1224009 1224460 1224666 "INBFILE" 1225005 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219309 1220245 1221189 "INBFF" 1223097 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218217 1218486 1218514 "INBCON" 1219027 T INBCON (NIL) -9 NIL 1219293 NIL) (-526 1217469 1217692 1217968 "INBCON-" 1217973 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216975 1217193 1217284 "INAST" 1217398 T INAST (NIL) -8 NIL NIL NIL) (-524 1216429 1216654 1216760 "IMPTAST" 1216889 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212923 1216273 1216377 "IMATRIX" 1216382 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211635 1211758 1212073 "IMATQF" 1212779 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209855 1210082 1210419 "IMATLIN" 1211391 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204481 1209779 1209837 "ILIST" 1209842 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202434 1204341 1204454 "IIARRAY2" 1204459 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197859 1202345 1202409 "IFF" 1202414 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197233 1197476 1197592 "IFAST" 1197763 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192276 1196525 1196713 "IFARRAY" 1197090 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191483 1192180 1192253 "IFAMON" 1192258 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1191067 1191132 1191186 "IEVALAB" 1191393 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190742 1190810 1190970 "IEVALAB-" 1190975 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190400 1190656 1190719 "IDPO" 1190724 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189677 1190289 1190364 "IDPOAMS" 1190369 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1189011 1189566 1189641 "IDPOAM" 1189646 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1188096 1188346 1188399 "IDPC" 1188812 NIL IDPC (NIL T T) -9 NIL 1188961 NIL) (-508 1187592 1187988 1188061 "IDPAM" 1188066 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186995 1187484 1187557 "IDPAG" 1187562 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186667 1186831 1186906 "IDENT" 1186940 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182922 1183770 1184665 "IDECOMP" 1185824 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175786 1176845 1177892 "IDEAL" 1181958 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174950 1175062 1175261 "ICDEN" 1175670 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1174048 1174430 1174577 "ICARD" 1174823 T ICARD (NIL) -8 NIL NIL NIL) (-501 1172108 1172421 1172826 "IBPTOOLS" 1173725 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167742 1171728 1171841 "IBITS" 1172027 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164465 1165041 1165736 "IBATOOL" 1167159 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162244 1162706 1163239 "IBACHIN" 1164000 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1160121 1162090 1162193 "IARRAY2" 1162198 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156275 1160047 1160104 "IARRAY1" 1160109 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150259 1154687 1155168 "IAN" 1155814 T IAN (NIL) -8 NIL NIL NIL) (-494 1149770 1149827 1150000 "IALGFACT" 1150196 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149298 1149411 1149439 "HYPCAT" 1149646 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148836 1148953 1149139 "HYPCAT-" 1149144 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148458 1148631 1148714 "HOSTNAME" 1148773 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148303 1148340 1148381 "HOMOTOP" 1148386 NIL HOMOTOP (NIL T) -9 NIL 1148419 NIL) (-489 1144982 1146313 1146354 "HOAGG" 1147335 NIL HOAGG (NIL T) -9 NIL 1148014 NIL) (-488 1143576 1143975 1144501 "HOAGG-" 1144506 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137607 1143171 1143320 "HEXADEC" 1143447 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136355 1136577 1136840 "HEUGCD" 1137384 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135458 1136192 1136322 "HELLFDIV" 1136327 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133685 1135235 1135323 "HEAP" 1135402 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132975 1133237 1133371 "HEADAST" 1133571 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126889 1132890 1132952 "HDP" 1132957 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120632 1126524 1126676 "HDMP" 1126790 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119956 1120096 1120260 "HB" 1120488 T HB (NIL) -7 NIL NIL NIL) (-479 1113453 1119802 1119906 "HASHTBL" 1119911 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112956 1113174 1113266 "HASAST" 1113381 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110761 1112578 1112760 "HACKPI" 1112794 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106456 1110614 1110727 "GTSET" 1110732 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099982 1106334 1106432 "GSTBL" 1106437 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092287 1099013 1099278 "GSERIES" 1099773 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091454 1091845 1091873 "GROUP" 1092076 T GROUP (NIL) -9 NIL 1092210 NIL) (-472 1090820 1090979 1091230 "GROUP-" 1091235 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089187 1089508 1089895 "GROEBSOL" 1090497 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088127 1088389 1088440 "GRMOD" 1088969 NIL GRMOD (NIL T T) -9 NIL 1089137 NIL) (-469 1087895 1087931 1088059 "GRMOD-" 1088064 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083212 1084249 1085249 "GRIMAGE" 1086915 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081678 1081939 1082263 "GRDEF" 1082908 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081122 1081238 1081379 "GRAY" 1081557 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080335 1080715 1080766 "GRALG" 1080919 NIL GRALG (NIL T T) -9 NIL 1081012 NIL) (-464 1079996 1080069 1080232 "GRALG-" 1080237 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076800 1079581 1079759 "GPOLSET" 1079903 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076154 1076211 1076469 "GOSPER" 1076737 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071913 1072592 1073118 "GMODPOL" 1075853 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070918 1071102 1071340 "GHENSEL" 1071725 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064969 1065812 1066839 "GENUPS" 1070002 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064666 1064717 1064806 "GENUFACT" 1064912 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064078 1064155 1064320 "GENPGCD" 1064584 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063552 1063587 1063800 "GENMFACT" 1064037 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062118 1062375 1062682 "GENEEZ" 1063295 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056019 1061729 1061891 "GDMP" 1062041 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045388 1049790 1050896 "GCNAALG" 1055002 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043807 1044643 1044671 "GCDDOM" 1044926 T GCDDOM (NIL) -9 NIL 1045083 NIL) (-451 1043277 1043404 1043619 "GCDDOM-" 1043624 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041949 1042134 1042438 "GB" 1043056 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030565 1032895 1035287 "GBINTERN" 1039640 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028402 1028694 1029115 "GBF" 1030240 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027183 1027348 1027615 "GBEUCLID" 1028218 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026532 1026657 1026806 "GAUSSFAC" 1027054 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024899 1025201 1025515 "GALUTIL" 1026251 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023207 1023481 1023805 "GALPOLYU" 1024626 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020572 1020862 1021269 "GALFACTU" 1022904 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012378 1013877 1015485 "GALFACT" 1019004 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009766 1010424 1010452 "FVFUN" 1011608 T FVFUN (NIL) -9 NIL 1012328 NIL) (-440 1009032 1009214 1009242 "FVC" 1009533 T FVC (NIL) -9 NIL 1009716 NIL) (-439 1008702 1008857 1008925 "FUNDESC" 1008984 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008344 1008499 1008580 "FUNCTION" 1008654 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006115 1006666 1007132 "FT" 1007898 T FT (NIL) -8 NIL NIL NIL) (-436 1004933 1005416 1005619 "FTEM" 1005932 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003189 1003478 1003882 "FSUPFACT" 1004624 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001586 1001875 1002207 "FST" 1002877 T FST (NIL) -8 NIL NIL NIL) (-433 1000757 1000863 1001058 "FSRED" 1001468 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999435 999691 1000045 "FSPRMELT" 1000472 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996520 996958 997457 "FSPECF" 998998 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978574 987023 987063 "FS" 990911 NIL FS (NIL T) -9 NIL 993200 NIL) (-429 967221 970214 974270 "FS-" 974567 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966735 966789 966966 "FSINT" 967162 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 965054 965728 966031 "FSERIES" 966514 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 964068 964184 964415 "FSCINT" 964934 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960302 963012 963053 "FSAGG" 963423 NIL FSAGG (NIL T) -9 NIL 963682 NIL) (-424 958064 958665 959461 "FSAGG-" 959556 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 957106 957249 957476 "FSAGG2" 957917 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954760 955040 955594 "FS2UPS" 956824 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954342 954385 954540 "FS2" 954711 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953199 953370 953679 "FS2EXPXP" 954167 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952625 952740 952892 "FRUTIL" 953079 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944065 948120 949478 "FR" 951299 NIL FR (NIL T) -8 NIL NIL NIL) (-417 939140 941783 941823 "FRNAALG" 943219 NIL FRNAALG (NIL T) -9 NIL 943826 NIL) (-416 934813 935889 937164 "FRNAALG-" 937914 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934451 934494 934621 "FRNAAF2" 934764 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932858 933305 933600 "FRMOD" 934263 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930636 931241 931558 "FRIDEAL" 932649 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929831 929918 930207 "FRIDEAL2" 930543 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928964 929378 929419 "FRETRCT" 929424 NIL FRETRCT (NIL T) -9 NIL 929600 NIL) (-410 928076 928307 928658 "FRETRCT-" 928663 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925280 926464 926523 "FRAMALG" 927405 NIL FRAMALG (NIL T T) -9 NIL 927697 NIL) (-408 923414 923869 924499 "FRAMALG-" 924722 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917362 922889 923165 "FRAC" 923170 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916998 917055 917162 "FRAC2" 917299 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916634 916691 916798 "FR2" 916935 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911299 914159 914187 "FPS" 915306 T FPS (NIL) -9 NIL 915863 NIL) (-403 910748 910857 911021 "FPS-" 911167 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908194 909837 909865 "FPC" 910090 T FPC (NIL) -9 NIL 910232 NIL) (-401 907987 908027 908124 "FPC-" 908129 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906865 907475 907516 "FPATMAB" 907521 NIL FPATMAB (NIL T) -9 NIL 907673 NIL) (-399 904565 905041 905467 "FPARFRAC" 906502 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899958 900457 901139 "FORTRAN" 903997 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897674 898174 898713 "FORT" 899439 T FORT (NIL) -7 NIL NIL NIL) (-396 895350 895912 895940 "FORTFN" 897000 T FORTFN (NIL) -9 NIL 897624 NIL) (-395 895114 895164 895192 "FORTCAT" 895251 T FORTCAT (NIL) -9 NIL 895313 NIL) (-394 893247 893730 894120 "FORMULA" 894744 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893035 893065 893134 "FORMULA1" 893211 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892558 892610 892783 "FORDER" 892977 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891654 891818 892011 "FOP" 892385 T FOP (NIL) -7 NIL NIL NIL) (-390 890262 890934 891108 "FNLA" 891536 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889017 889406 889434 "FNCAT" 889894 T FNCAT (NIL) -9 NIL 890154 NIL) (-388 888583 888976 889004 "FNAME" 889009 T FNAME (NIL) -8 NIL NIL NIL) (-387 887238 888175 888203 "FMTC" 888208 T FMTC (NIL) -9 NIL 888244 NIL) (-386 883598 884761 885390 "FMONOID" 886642 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882817 883340 883489 "FM" 883494 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880241 880887 880915 "FMFUN" 882059 T FMFUN (NIL) -9 NIL 882767 NIL) (-383 879510 879691 879719 "FMC" 880009 T FMC (NIL) -9 NIL 880191 NIL) (-382 876704 877538 877592 "FMCAT" 878787 NIL FMCAT (NIL T T) -9 NIL 879282 NIL) (-381 875597 876470 876570 "FM1" 876649 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873371 873787 874281 "FLOATRP" 875148 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866972 871100 871721 "FLOAT" 872770 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864410 864910 865488 "FLOATCP" 866439 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863211 864023 864064 "FLINEXP" 864069 NIL FLINEXP (NIL T) -9 NIL 864162 NIL) (-376 862365 862600 862928 "FLINEXP-" 862933 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861441 861585 861809 "FLASORT" 862217 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858658 859500 859552 "FLALG" 860779 NIL FLALG (NIL T T) -9 NIL 861246 NIL) (-373 852442 856144 856185 "FLAGG" 857447 NIL FLAGG (NIL T) -9 NIL 858099 NIL) (-372 851168 851507 851997 "FLAGG-" 852002 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850210 850353 850580 "FLAGG2" 851021 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847177 848159 848218 "FINRALG" 849346 NIL FINRALG (NIL T T) -9 NIL 849854 NIL) (-369 846337 846566 846905 "FINRALG-" 846910 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845743 845956 845984 "FINITE" 846180 T FINITE (NIL) -9 NIL 846287 NIL) (-367 838201 840362 840402 "FINAALG" 844069 NIL FINAALG (NIL T) -9 NIL 845522 NIL) (-366 833533 834583 835727 "FINAALG-" 837106 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832928 833288 833391 "FILE" 833463 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831612 831924 831978 "FILECAT" 832662 NIL FILECAT (NIL T T) -9 NIL 832878 NIL) (-363 829472 830974 831002 "FIELD" 831042 T FIELD (NIL) -9 NIL 831122 NIL) (-362 828092 828477 828988 "FIELD-" 828993 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825969 826727 827074 "FGROUP" 827778 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825059 825223 825443 "FGLMICPK" 825801 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820918 824984 825041 "FFX" 825046 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820519 820580 820715 "FFSLPE" 820851 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816508 817291 818087 "FFPOLY" 819755 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816012 816048 816257 "FFPOLY2" 816466 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811882 815931 815994 "FFP" 815999 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807307 811793 811857 "FF" 811862 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802460 806650 806840 "FFNBX" 807161 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797416 801595 801853 "FFNBP" 802314 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792076 796700 796911 "FFNB" 797249 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790908 791106 791421 "FFINTBAS" 791873 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787128 789315 789343 "FFIELDC" 789963 T FFIELDC (NIL) -9 NIL 790339 NIL) (-348 785790 786161 786658 "FFIELDC-" 786663 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785359 785405 785529 "FFHOM" 785732 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783054 783541 784058 "FFF" 784874 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778699 782796 782897 "FFCGX" 782997 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774347 778431 778538 "FFCGP" 778642 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769557 774074 774182 "FFCG" 774283 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751382 760428 760514 "FFCAT" 765679 NIL FFCAT (NIL T T T) -9 NIL 767130 NIL) (-341 746580 747627 748941 "FFCAT-" 750171 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745991 746034 746269 "FFCAT2" 746531 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735188 738963 740183 "FEXPR" 744843 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734188 734623 734664 "FEVALAB" 734748 NIL FEVALAB (NIL T) -9 NIL 735009 NIL) (-337 733347 733557 733895 "FEVALAB-" 733900 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731940 732730 732933 "FDIV" 733246 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729006 729721 729836 "FDIVCAT" 731404 NIL FDIVCAT (NIL T T T T) -9 NIL 731841 NIL) (-334 728768 728795 728965 "FDIVCAT-" 728970 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727988 728075 728352 "FDIV2" 728675 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726674 726933 727222 "FCPAK1" 727719 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725800 726174 726315 "FCOMP" 726565 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709529 712950 716488 "FC" 722282 T FC (NIL) -8 NIL NIL NIL) (-329 702100 706093 706133 "FAXF" 707935 NIL FAXF (NIL T) -9 NIL 708627 NIL) (-328 699376 700034 700859 "FAXF-" 701324 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694476 698752 698928 "FARRAY" 699233 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689721 691761 691814 "FAMR" 692837 NIL FAMR (NIL T T) -9 NIL 693297 NIL) (-325 688611 688913 689348 "FAMR-" 689353 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687807 688533 688586 "FAMONOID" 688591 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685619 686303 686356 "FAMONC" 687297 NIL FAMONC (NIL T T) -9 NIL 687683 NIL) (-322 684311 685373 685510 "FAGROUP" 685515 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682106 682425 682828 "FACUTIL" 683992 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681205 681390 681612 "FACTFUNC" 681916 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673602 680456 680668 "EXPUPXS" 681061 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671085 671625 672211 "EXPRTUBE" 673036 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667279 667871 668608 "EXPRODE" 670424 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652645 665934 666362 "EXPR" 666883 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647052 647639 648452 "EXPR2UPS" 651943 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646688 646745 646852 "EXPR2" 646989 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638085 645820 646117 "EXPEXPAN" 646525 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637912 638042 638071 "EXIT" 638076 T EXIT (NIL) -8 NIL NIL NIL) (-311 637419 637636 637727 "EXITAST" 637841 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637046 637108 637221 "EVALCYC" 637351 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636587 636705 636746 "EVALAB" 636916 NIL EVALAB (NIL T) -9 NIL 637020 NIL) (-308 636068 636190 636411 "EVALAB-" 636416 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633528 634804 634832 "EUCDOM" 635387 T EUCDOM (NIL) -9 NIL 635737 NIL) (-306 631933 632375 632965 "EUCDOM-" 632970 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619471 622231 624981 "ESTOOLS" 629203 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619103 619160 619269 "ESTOOLS2" 619408 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618854 618896 618976 "ESTOOLS1" 619055 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612759 614487 614515 "ES" 617283 T ES (NIL) -9 NIL 618692 NIL) (-301 607706 608993 610810 "ES-" 610974 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604080 604841 605621 "ESCONT" 606946 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603825 603857 603939 "ESCONT1" 604042 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603500 603550 603650 "ES2" 603769 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603130 603188 603297 "ES1" 603436 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602346 602475 602651 "ERROR" 602974 T ERROR (NIL) -7 NIL NIL NIL) (-295 595849 602205 602296 "EQTBL" 602301 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588400 591163 592612 "EQ" 594433 NIL -2056 (NIL T) -8 NIL NIL NIL) (-293 588032 588089 588198 "EQ2" 588337 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583321 584370 585463 "EP" 586971 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581899 582196 582508 "ENV" 583029 T ENV (NIL) -8 NIL NIL NIL) (-290 581070 581598 581626 "ENTIRER" 581631 T ENTIRER (NIL) -9 NIL 581677 NIL) (-289 577564 579025 579395 "EMR" 580869 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576708 576893 576947 "ELTAGG" 577327 NIL ELTAGG (NIL T T) -9 NIL 577538 NIL) (-287 576427 576489 576630 "ELTAGG-" 576635 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576216 576245 576299 "ELTAB" 576383 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575342 575488 575687 "ELFUTS" 576067 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575084 575140 575168 "ELEMFUN" 575273 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574954 574975 575043 "ELEMFUN-" 575048 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569845 573054 573095 "ELAGG" 574035 NIL ELAGG (NIL T) -9 NIL 574498 NIL) (-281 568130 568564 569227 "ELAGG-" 569232 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566795 567073 567366 "ELABEXPR" 567857 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559659 561462 562289 "EFUPXS" 566071 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553109 554910 555720 "EFULS" 558935 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550531 550889 551368 "EFSTRUC" 552741 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539602 541168 542728 "EF" 549046 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538703 539087 539236 "EAB" 539473 T EAB (NIL) -8 NIL NIL NIL) (-274 537912 538662 538690 "E04UCFA" 538695 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537121 537871 537899 "E04NAFA" 537904 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536330 537080 537108 "E04MBFA" 537113 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535539 536289 536317 "E04JAFA" 536322 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534750 535498 535526 "E04GCFA" 535531 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533961 534709 534737 "E04FDFA" 534742 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533170 533920 533948 "E04DGFA" 533953 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527343 528695 530059 "E04AGNT" 531826 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526049 526529 526569 "DVARCAT" 527044 NIL DVARCAT (NIL T) -9 NIL 527243 NIL) (-265 525253 525465 525779 "DVARCAT-" 525784 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518145 525052 525181 "DSMP" 525186 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512954 514090 515158 "DROPT" 517097 T DROPT (NIL) -8 NIL NIL NIL) (-262 512619 512678 512776 "DROPT1" 512889 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507734 508860 509997 "DROPT0" 511502 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506079 506404 506790 "DRAWPT" 507368 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500666 501589 502668 "DRAW" 505053 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500299 500352 500470 "DRAWHACK" 500607 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499030 499299 499590 "DRAWCX" 500028 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498545 498614 498765 "DRAWCURV" 498956 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489013 490975 493090 "DRAWCFUN" 496450 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485826 487708 487749 "DQAGG" 488378 NIL DQAGG (NIL T) -9 NIL 488651 NIL) (-253 474097 480804 480887 "DPOLCAT" 482739 NIL DPOLCAT (NIL T T T T) -9 NIL 483284 NIL) (-252 468933 470282 472240 "DPOLCAT-" 472245 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 462082 468794 468892 "DPMO" 468897 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 455134 461862 462029 "DPMM" 462034 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454766 455053 455101 "DOMCTOR" 455106 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454061 454288 454425 "DOMAIN" 454649 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447804 453696 453848 "DMP" 453962 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447404 447460 447604 "DLP" 447742 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441274 446731 446921 "DLIST" 447246 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 438118 440127 440168 "DLAGG" 440718 NIL DLAGG (NIL T) -9 NIL 440948 NIL) (-243 436923 437561 437589 "DIVRING" 437681 T DIVRING (NIL) -9 NIL 437764 NIL) (-242 436160 436350 436650 "DIVRING-" 436655 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434262 434619 435025 "DISPLAY" 435774 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428198 434176 434239 "DIRPROD" 434244 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 427046 427249 427514 "DIRPROD2" 427991 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416303 422261 422314 "DIRPCAT" 422724 NIL DIRPCAT (NIL NIL T) -9 NIL 423564 NIL) (-237 413629 414271 415152 "DIRPCAT-" 415489 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412916 413076 413262 "DIOSP" 413463 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409618 411828 411869 "DIOPS" 412303 NIL DIOPS (NIL T) -9 NIL 412532 NIL) (-234 409167 409281 409472 "DIOPS-" 409477 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408051 408653 408681 "DIFRING" 408868 T DIFRING (NIL) -9 NIL 408978 NIL) (-232 407697 407774 407926 "DIFRING-" 407931 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405494 406740 406781 "DIFEXT" 407144 NIL DIFEXT (NIL T) -9 NIL 407438 NIL) (-230 403779 404207 404873 "DIFEXT-" 404878 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401101 403311 403352 "DIAGG" 403357 NIL DIAGG (NIL T) -9 NIL 403377 NIL) (-228 400485 400642 400894 "DIAGG-" 400899 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395950 399444 399721 "DHMATRIX" 400254 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391562 392471 393481 "DFSFUN" 394960 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386667 390493 390805 "DFLOAT" 391270 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384895 385176 385572 "DFINTTLS" 386375 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381951 382916 383316 "DERHAM" 384561 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379800 381726 381815 "DEQUEUE" 381895 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379015 379148 379344 "DEGRED" 379662 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375410 376155 377008 "DEFINTRF" 378243 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372937 373406 374005 "DEFINTEF" 374929 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372314 372557 372672 "DEFAST" 372842 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366345 371909 372058 "DECIMAL" 372185 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363855 364315 364821 "DDFACT" 365889 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363451 363494 363645 "DBLRESP" 363806 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361350 361684 362044 "DBASE" 363218 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360619 360830 360976 "DATAARY" 361249 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359752 360578 360606 "D03FAFA" 360611 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358886 359711 359739 "D03EEFA" 359744 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356836 357302 357791 "D03AGNT" 358417 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356152 356795 356823 "D02EJFA" 356828 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355468 356111 356139 "D02CJFA" 356144 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354784 355427 355455 "D02BHFA" 355460 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354100 354743 354771 "D02BBFA" 354776 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347297 348886 350492 "D02AGNT" 352514 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345065 345588 346134 "D01WGTS" 346771 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344159 345024 345052 "D01TRNS" 345057 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343254 344118 344146 "D01GBFA" 344151 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342349 343213 343241 "D01FCFA" 343246 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341444 342308 342336 "D01ASFA" 342341 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340539 341403 341431 "D01AQFA" 341436 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339634 340498 340526 "D01APFA" 340531 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338729 339593 339621 "D01ANFA" 339626 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337824 338688 338716 "D01AMFA" 338721 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336919 337783 337811 "D01ALFA" 337816 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336014 336878 336906 "D01AKFA" 336911 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335109 335973 336001 "D01AJFA" 336006 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328404 329957 331518 "D01AGNT" 333568 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327741 327869 328021 "CYCLOTOM" 328272 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324476 325189 325916 "CYCLES" 327034 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323788 323922 324093 "CVMP" 324337 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321559 321817 322193 "CTRIGMNP" 323516 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321054 321353 321426 "CTOR" 321506 T CTOR (NIL) -8 NIL NIL NIL) (-186 320590 320785 320886 "CTORKIND" 320973 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319938 320197 320225 "CTORCAT" 320407 T CTORCAT (NIL) -9 NIL 320520 NIL) (-184 319536 319647 319806 "CTORCAT-" 319811 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319052 319239 319337 "CTORCALL" 319458 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318426 318525 318678 "CSTTOOLS" 318949 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314225 314882 315640 "CRFP" 317738 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313727 313946 314038 "CRCEAST" 314153 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312774 312959 313187 "CRAPACK" 313531 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312158 312259 312463 "CPMATCH" 312650 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311883 311911 312017 "CPIMA" 312124 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308247 308919 309637 "COORDSYS" 311218 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307655 307777 307920 "CONTOUR" 308124 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303573 305658 306150 "CONTFRAC" 307195 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303453 303474 303502 "CONDUIT" 303539 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302618 303146 303174 "COMRING" 303179 T COMRING (NIL) -9 NIL 303231 NIL) (-171 301699 301976 302160 "COMPPROP" 302454 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301360 301395 301523 "COMPLPAT" 301658 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291409 301169 301278 "COMPLEX" 301283 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291045 291102 291209 "COMPLEX2" 291346 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290763 290798 290896 "COMPFACT" 291004 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274917 285145 285185 "COMPCAT" 286189 NIL COMPCAT (NIL T) -9 NIL 287585 NIL) (-165 264428 267356 270983 "COMPCAT-" 271339 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264157 264185 264288 "COMMUPC" 264394 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263951 263985 264044 "COMMONOP" 264118 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263534 263702 263789 "COMM" 263884 T COMM (NIL) -8 NIL NIL NIL) (-161 263137 263338 263413 "COMMAAST" 263479 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262386 262580 262608 "COMBOPC" 262946 T COMBOPC (NIL) -9 NIL 263121 NIL) (-159 261282 261492 261734 "COMBINAT" 262176 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 257479 258053 258693 "COMBF" 260704 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256264 256595 256830 "COLOR" 257264 T COLOR (NIL) -8 NIL NIL NIL) (-156 255767 255985 256077 "COLONAST" 256192 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255407 255454 255579 "CMPLXRT" 255714 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254882 255107 255206 "CLLCTAST" 255328 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250382 251412 252492 "CLIP" 253822 T CLIP (NIL) -7 NIL NIL NIL) (-152 248755 249488 249727 "CLIF" 250209 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244977 246901 246942 "CLAGG" 247871 NIL CLAGG (NIL T) -9 NIL 248407 NIL) (-150 243399 243856 244439 "CLAGG-" 244444 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242943 243028 243168 "CINTSLPE" 243308 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240444 240915 241463 "CHVAR" 242471 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239679 240207 240235 "CHARZ" 240240 T CHARZ (NIL) -9 NIL 240255 NIL) (-146 239433 239473 239551 "CHARPOL" 239633 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238552 239113 239141 "CHARNZ" 239188 T CHARNZ (NIL) -9 NIL 239244 NIL) (-144 236541 237242 237577 "CHAR" 238237 T CHAR (NIL) -8 NIL NIL NIL) (-143 236267 236328 236356 "CFCAT" 236467 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235512 235623 235805 "CDEN" 236151 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231504 234665 234945 "CCLASS" 235252 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230811 230954 231117 "CATEGORY" 231361 T -10 (NIL) -8 NIL NIL NIL) (-139 230443 230730 230778 "CATCTOR" 230783 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229921 230146 230244 "CATAST" 230365 T CATAST (NIL) -8 NIL NIL NIL) (-137 229424 229642 229734 "CASEAST" 229849 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224460 225453 226206 "CARTEN" 228727 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 223568 223716 223937 "CARTEN2" 224307 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221910 222718 222975 "CARD" 223331 T CARD (NIL) -8 NIL NIL NIL) (-133 221513 221714 221789 "CAPSLAST" 221855 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220885 221213 221241 "CACHSET" 221373 T CACHSET (NIL) -9 NIL 221450 NIL) (-131 220381 220677 220705 "CABMON" 220755 T CABMON (NIL) -9 NIL 220811 NIL) (-130 219881 220085 220195 "BYTEORD" 220291 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218884 219415 219557 "BYTE" 219720 T BYTE (NIL) -8 NIL NIL 219842) (-128 214284 218389 218561 "BYTEBUF" 218732 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211841 213976 214083 "BTREE" 214210 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209338 211489 211611 "BTOURN" 211751 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206755 208808 208849 "BTCAT" 208917 NIL BTCAT (NIL T) -9 NIL 208994 NIL) (-124 206422 206502 206651 "BTCAT-" 206656 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201714 205565 205593 "BTAGG" 205815 T BTAGG (NIL) -9 NIL 205976 NIL) (-122 201204 201329 201535 "BTAGG-" 201540 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198247 200482 200697 "BSTREE" 201021 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197385 197511 197695 "BRILL" 198103 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194084 196111 196152 "BRAGG" 196801 NIL BRAGG (NIL T) -9 NIL 197059 NIL) (-118 192613 193019 193574 "BRAGG-" 193579 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185869 191959 192143 "BPADICRT" 192461 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184211 185806 185851 "BPADIC" 185856 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183909 183939 184053 "BOUNDZRO" 184175 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179021 180193 181138 "BOP" 182984 T BOP (NIL) -8 NIL NIL NIL) (-113 176642 177086 177606 "BOP1" 178534 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175344 176066 176259 "BOOLEAN" 176469 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174706 175084 175138 "BMODULE" 175143 NIL BMODULE (NIL T T) -9 NIL 175208 NIL) (-110 170534 174504 174577 "BITS" 174653 T BITS (NIL) -8 NIL NIL NIL) (-109 169946 170068 170210 "BINDING" 170412 T BINDING (NIL) -8 NIL NIL NIL) (-108 163980 169543 169691 "BINARY" 169818 T BINARY (NIL) -8 NIL NIL NIL) (-107 161807 163235 163276 "BGAGG" 163536 NIL BGAGG (NIL T) -9 NIL 163673 NIL) (-106 161638 161670 161761 "BGAGG-" 161766 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160736 161022 161227 "BFUNCT" 161453 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159426 159604 159892 "BEZOUT" 160560 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155943 158278 158608 "BBTREE" 159129 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155677 155730 155758 "BASTYPE" 155877 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155530 155558 155631 "BASTYPE-" 155636 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154964 155040 155192 "BALFACT" 155441 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153847 154379 154565 "AUTOMOR" 154809 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153573 153578 153604 "ATTREG" 153609 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151852 152270 152622 "ATTRBUT" 153239 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151487 151680 151746 "ATTRAST" 151804 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151023 151136 151162 "ATRIG" 151363 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150832 150873 150960 "ATRIG-" 150965 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150503 150663 150689 "ASTCAT" 150694 T ASTCAT (NIL) -9 NIL 150724 NIL) (-92 150230 150289 150408 "ASTCAT-" 150413 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148427 150006 150094 "ASTACK" 150173 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146932 147229 147594 "ASSOCEQ" 148109 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145964 146591 146715 "ASP9" 146839 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145727 145912 145951 "ASP8" 145956 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144595 145332 145474 "ASP80" 145616 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143493 144230 144362 "ASP7" 144494 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142447 143170 143288 "ASP78" 143406 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141416 142127 142244 "ASP77" 142361 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140328 141054 141185 "ASP74" 141316 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139228 139963 140095 "ASP73" 140227 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138332 139054 139154 "ASP6" 139159 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137276 138009 138127 "ASP55" 138245 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136225 136950 137069 "ASP50" 137188 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135313 135926 136036 "ASP4" 136146 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134401 135014 135124 "ASP49" 135234 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133185 133940 134108 "ASP42" 134290 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131961 132718 132888 "ASP41" 133072 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130911 131638 131756 "ASP35" 131874 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130676 130859 130898 "ASP34" 130903 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130413 130480 130556 "ASP33" 130631 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129306 130048 130180 "ASP31" 130312 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129071 129254 129293 "ASP30" 129298 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128806 128875 128951 "ASP29" 129026 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128571 128754 128793 "ASP28" 128798 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128336 128519 128558 "ASP27" 128563 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127420 128034 128145 "ASP24" 128256 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126496 127222 127334 "ASP20" 127339 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125584 126197 126307 "ASP1" 126417 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124526 125258 125377 "ASP19" 125496 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124263 124330 124406 "ASP12" 124481 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123115 123862 124006 "ASP10" 124150 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121014 122959 123050 "ARRAY2" 123055 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116827 120662 120776 "ARRAY1" 120931 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115859 116032 116253 "ARRAY12" 116650 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110218 112089 112164 "ARR2CAT" 114794 NIL ARR2CAT (NIL T T T) -9 NIL 115552 NIL) (-56 107652 108396 109350 "ARR2CAT-" 109355 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107279 107404 "ARITY" 107545 T ARITY (NIL) -8 NIL NIL NIL) (-54 105744 105896 106202 "APPRULE" 106832 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105395 105443 105562 "APPLYORE" 105690 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104369 104660 104855 "ANY" 105218 T ANY (NIL) -8 NIL NIL NIL) (-51 103647 103770 103927 "ANY1" 104243 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101204 102084 102411 "ANTISYM" 103371 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100911 101007 "ANON" 101126 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file +((-3 3199079 3199084 3199089 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3199064 3199069 3199074 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3199049 3199054 3199059 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3199034 3199039 3199044 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3198203 3198909 3198986 "ZMOD" 3198991 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3197313 3197477 3197686 "ZLINDEP" 3198035 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3186613 3188381 3190353 "ZDSOLVE" 3195443 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3185859 3186000 3186189 "YSTREAM" 3186459 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3183660 3185160 3185364 "XRPOLY" 3185702 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3180240 3181531 3182106 "XPR" 3183132 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3177988 3179571 3179775 "XPOLY" 3180071 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3175771 3177113 3177168 "XPOLYC" 3177456 NIL XPOLYC (NIL T T) -9 NIL 3177569 NIL) (-1279 3172174 3174288 3174676 "XPBWPOLY" 3175429 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3168077 3170337 3170379 "XF" 3171000 NIL XF (NIL T) -9 NIL 3171400 NIL) (-1277 3167698 3167786 3167955 "XF-" 3167960 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3163024 3164287 3164342 "XFALG" 3166514 NIL XFALG (NIL T T) -9 NIL 3167303 NIL) (-1275 3162157 3162261 3162466 "XEXPPKG" 3162916 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3160293 3162007 3162103 "XDPOLY" 3162108 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159230 3159804 3159847 "XALG" 3159852 NIL XALG (NIL T) -9 NIL 3159963 NIL) (-1272 3152699 3157207 3157701 "WUTSET" 3158822 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3150982 3151751 3152074 "WP" 3152510 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3150611 3150804 3150874 "WHILEAST" 3150934 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3150110 3150328 3150422 "WHEREAST" 3150539 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3148996 3149194 3149489 "WFFINTBS" 3149907 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3146900 3147327 3147789 "WEIER" 3148568 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3146047 3146471 3146513 "VSPACE" 3146649 NIL VSPACE (NIL T) -9 NIL 3146723 NIL) (-1265 3145885 3145912 3146003 "VSPACE-" 3146008 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3145693 3145736 3145804 "VOID" 3145839 T VOID (NIL) -8 NIL NIL NIL) (-1263 3143829 3144188 3144594 "VIEW" 3145309 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140253 3140892 3141629 "VIEWDEF" 3143114 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3129584 3131801 3133974 "VIEW3D" 3138102 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3121862 3123495 3125074 "VIEW2D" 3128027 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117264 3121632 3121724 "VECTOR" 3121805 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3115841 3116100 3116418 "VECTOR2" 3116994 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3109368 3113625 3113668 "VECTCAT" 3114661 NIL VECTCAT (NIL T) -9 NIL 3115247 NIL) (-1256 3108382 3108636 3109026 "VECTCAT-" 3109031 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3107863 3108033 3108153 "VARIABLE" 3108297 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3107796 3107801 3107831 "UTYPE" 3107836 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3106626 3106780 3107042 "UTSODETL" 3107622 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3104066 3104526 3105050 "UTSODE" 3106167 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3095930 3101692 3102181 "UTS" 3103635 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3087165 3092497 3092540 "UTSCAT" 3093652 NIL UTSCAT (NIL T) -9 NIL 3094409 NIL) (-1249 3084513 3085235 3086224 "UTSCAT-" 3086229 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3084140 3084183 3084316 "UTS2" 3084464 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3078413 3080978 3081021 "URAGG" 3083091 NIL URAGG (NIL T) -9 NIL 3083814 NIL) (-1246 3075352 3076215 3077338 "URAGG-" 3077343 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3071068 3073966 3074438 "UPXSSING" 3075016 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3063161 3070315 3070588 "UPXS" 3070853 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056261 3063065 3063137 "UPXSCONS" 3063142 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3046498 3053256 3053318 "UPXSCCA" 3053892 NIL UPXSCCA (NIL T T) -9 NIL 3054125 NIL) (-1241 3046136 3046221 3046395 "UPXSCCA-" 3046400 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036226 3042757 3042800 "UPXSCAT" 3043448 NIL UPXSCAT (NIL T) -9 NIL 3044056 NIL) (-1239 3035656 3035735 3035914 "UPXS2" 3036141 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3034310 3034563 3034914 "UPSQFREE" 3035399 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3028090 3031112 3031167 "UPSCAT" 3032328 NIL UPSCAT (NIL T T) -9 NIL 3033102 NIL) (-1236 3027294 3027501 3027828 "UPSCAT-" 3027833 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3013136 3021142 3021185 "UPOLYC" 3023286 NIL UPOLYC (NIL T) -9 NIL 3024507 NIL) (-1234 3004464 3006890 3010037 "UPOLYC-" 3010042 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3004091 3004134 3004267 "UPOLYC2" 3004415 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2995657 3003774 3003903 "UP" 3004010 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2994996 2995103 2995267 "UPMP" 2995546 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2994549 2994630 2994769 "UPDIVP" 2994909 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2993117 2993366 2993682 "UPDECOMP" 2994298 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2992352 2992464 2992649 "UPCDEN" 2993001 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2991871 2991940 2992089 "UP2" 2992277 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2990386 2991075 2991352 "UNISEG" 2991629 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2989601 2989728 2989933 "UNISEG2" 2990229 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2988661 2988841 2989067 "UNIFACT" 2989417 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2972620 2987838 2988089 "ULS" 2988468 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2960646 2972524 2972596 "ULSCONS" 2972601 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943254 2955204 2955266 "ULSCCAT" 2955904 NIL ULSCCAT (NIL T T) -9 NIL 2956192 NIL) (-1220 2942304 2942549 2942937 "ULSCCAT-" 2942942 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2932171 2938616 2938659 "ULSCAT" 2939522 NIL ULSCAT (NIL T) -9 NIL 2940252 NIL) (-1218 2931601 2931680 2931859 "ULS2" 2932086 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2930718 2931201 2931308 "UINT8" 2931419 T UINT8 (NIL) -8 NIL NIL 2931504) (-1216 2929834 2930317 2930424 "UINT64" 2930535 T UINT64 (NIL) -8 NIL NIL 2930620) (-1215 2928950 2929433 2929540 "UINT32" 2929651 T UINT32 (NIL) -8 NIL NIL 2929736) (-1214 2928066 2928549 2928656 "UINT16" 2928767 T UINT16 (NIL) -8 NIL NIL 2928852) (-1213 2926461 2927392 2927422 "UFD" 2927634 T UFD (NIL) -9 NIL 2927748 NIL) (-1212 2926255 2926301 2926396 "UFD-" 2926401 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2925337 2925520 2925736 "UDVO" 2926061 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2923153 2923562 2924033 "UDPO" 2924901 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2923086 2923091 2923121 "TYPE" 2923126 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2922873 2923041 2923072 "TYPEAST" 2923077 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2921844 2922046 2922286 "TWOFACT" 2922667 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2920915 2921253 2921488 "TUPLE" 2921644 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2918606 2919125 2919664 "TUBETOOL" 2920398 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2917455 2917660 2917901 "TUBE" 2918399 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912211 2916427 2916710 "TS" 2917207 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2900878 2904970 2905067 "TSETCAT" 2910336 NIL TSETCAT (NIL T T T T) -9 NIL 2911867 NIL) (-1201 2895610 2897210 2899101 "TSETCAT-" 2899106 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2889872 2890719 2891661 "TRMANIP" 2894746 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2889313 2889376 2889539 "TRIMAT" 2889804 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2887109 2887346 2887710 "TRIGMNIP" 2889062 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2886629 2886742 2886772 "TRIGCAT" 2886985 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2886298 2886377 2886518 "TRIGCAT-" 2886523 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883191 2885156 2885437 "TREE" 2886052 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2882465 2882993 2883023 "TRANFUN" 2883058 T TRANFUN (NIL) -9 NIL 2883124 NIL) (-1193 2881744 2881935 2882215 "TRANFUN-" 2882220 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2881548 2881580 2881641 "TOPSP" 2881705 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2880896 2881011 2881165 "TOOLSIGN" 2881429 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2879557 2880073 2880312 "TEXTFILE" 2880679 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2877496 2878010 2878439 "TEX" 2879150 T TEX (NIL) -8 NIL NIL NIL) (-1188 2877277 2877308 2877380 "TEX1" 2877459 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2876925 2876988 2877078 "TEMUTL" 2877209 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2875079 2875359 2875684 "TBCMPPK" 2876648 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2866967 2873239 2873295 "TBAGG" 2873695 NIL TBAGG (NIL T T) -9 NIL 2873906 NIL) (-1184 2862037 2863525 2865279 "TBAGG-" 2865284 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2861421 2861528 2861673 "TANEXP" 2861926 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2854922 2861278 2861371 "TABLE" 2861376 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2854334 2854433 2854571 "TABLEAU" 2854819 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2848942 2850162 2851410 "TABLBUMP" 2853120 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848164 2848311 2848492 "SYSTEM" 2848783 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2844623 2845322 2846105 "SYSSOLP" 2847415 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2843657 2844135 2844254 "SYSNNI" 2844440 NIL SYSNNI (NIL NIL) -8 NIL NIL 2844525) (-1176 2842954 2843386 2843465 "SYSINT" 2843525 NIL SYSINT (NIL NIL) -8 NIL NIL 2843570) (-1175 2839313 2840232 2840942 "SYNTAX" 2842266 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2836471 2837073 2837705 "SYMTAB" 2838703 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2831720 2832622 2833605 "SYMS" 2835510 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2828982 2831178 2831408 "SYMPOLY" 2831525 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2828499 2828574 2828697 "SYMFUNC" 2828894 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2824545 2825811 2826624 "SYMBOL" 2827708 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818084 2819773 2821493 "SWITCH" 2822847 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2811345 2816905 2817208 "SUTS" 2817839 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2803438 2810592 2810865 "SUPXS" 2811130 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2794953 2803056 2803182 "SUP" 2803347 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794112 2794239 2794456 "SUPFRACF" 2794821 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2793733 2793792 2793905 "SUP2" 2794047 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792146 2792420 2792783 "SUMRF" 2793432 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2791460 2791526 2791725 "SUMFS" 2792067 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2775454 2790637 2790888 "SULS" 2791267 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775083 2775276 2775346 "SUCHTAST" 2775406 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2774405 2774608 2774748 "SUCH" 2774991 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2768299 2769311 2770270 "SUBSPACE" 2773493 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2767729 2767819 2767983 "SUBRESP" 2768187 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761094 2762394 2763705 "STTF" 2766465 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755267 2756387 2757534 "STTFNC" 2759994 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2746578 2748449 2750243 "STTAYLOR" 2753508 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2739822 2746442 2746525 "STRTBL" 2746530 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735213 2739777 2739808 "STRING" 2739813 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730101 2734586 2734616 "STRICAT" 2734675 T STRICAT (NIL) -9 NIL 2734737 NIL) (-1150 2722904 2727720 2728331 "STREAM" 2729525 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2722414 2722491 2722635 "STREAM3" 2722821 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2721396 2721579 2721814 "STREAM2" 2722227 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721084 2721136 2721229 "STREAM1" 2721338 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720100 2720281 2720512 "STINPROD" 2720900 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2719678 2719862 2719892 "STEP" 2719972 T STEP (NIL) -9 NIL 2720050 NIL) (-1144 2713221 2719577 2719654 "STBL" 2719659 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2708395 2712442 2712485 "STAGG" 2712638 NIL STAGG (NIL T) -9 NIL 2712727 NIL) (-1142 2706097 2706699 2707571 "STAGG-" 2707576 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2704292 2705867 2705959 "STACK" 2706040 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697015 2702433 2702889 "SREGSET" 2703922 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2689440 2690809 2692322 "SRDCMPK" 2695621 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2682407 2686880 2686910 "SRAGG" 2688213 T SRAGG (NIL) -9 NIL 2688821 NIL) (-1137 2681424 2681679 2682058 "SRAGG-" 2682063 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2675911 2680371 2680792 "SQMATRIX" 2681050 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2669658 2672629 2673356 "SPLTREE" 2675256 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2665648 2666314 2666960 "SPLNODE" 2669084 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2664695 2664928 2664958 "SPFCAT" 2665402 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2663432 2663642 2663906 "SPECOUT" 2664453 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655084 2656828 2656858 "SPADXPT" 2661250 T SPADXPT (NIL) -9 NIL 2663284 NIL) (-1130 2654845 2654885 2654954 "SPADPRSR" 2655037 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653027 2654800 2654831 "SPADAST" 2654836 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2644998 2646745 2646788 "SPACEC" 2651161 NIL SPACEC (NIL T) -9 NIL 2652977 NIL) (-1127 2643155 2644930 2644979 "SPACE3" 2644984 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2641907 2642078 2642369 "SORTPAK" 2642960 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2639957 2640260 2640679 "SOLVETRA" 2641571 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2638968 2639190 2639464 "SOLVESER" 2639730 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634179 2635069 2636071 "SOLVERAD" 2638020 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2629994 2630603 2631332 "SOLVEFOR" 2633546 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2624291 2629343 2629440 "SNTSCAT" 2629445 NIL SNTSCAT (NIL T T T T) -9 NIL 2629515 NIL) (-1120 2618424 2622614 2623005 "SMTS" 2623981 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2612864 2618312 2618389 "SMP" 2618394 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611023 2611324 2611722 "SMITH" 2612561 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2603910 2608074 2608177 "SMATCAT" 2609528 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610078 NIL) (-1116 2600850 2601673 2602851 "SMATCAT-" 2602856 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2598563 2600086 2600129 "SKAGG" 2600390 NIL SKAGG (NIL T) -9 NIL 2600525 NIL) (-1114 2594898 2597979 2598174 "SINT" 2598361 T SINT (NIL) -8 NIL NIL 2598534) (-1113 2594670 2594708 2594774 "SIMPAN" 2594854 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2593976 2594205 2594345 "SIG" 2594552 T SIG (NIL) -8 NIL NIL NIL) (-1111 2592814 2593035 2593310 "SIGNRF" 2593735 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2591619 2591770 2592061 "SIGNEF" 2592643 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2590952 2591202 2591326 "SIGAST" 2591517 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2588642 2589096 2589602 "SHP" 2590493 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2582542 2588543 2588619 "SHDP" 2588624 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582141 2582307 2582337 "SGROUP" 2582430 T SGROUP (NIL) -9 NIL 2582492 NIL) (-1105 2581999 2582025 2582098 "SGROUP-" 2582103 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2578834 2579532 2580255 "SGCF" 2581298 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573229 2578281 2578378 "SFRTCAT" 2578383 NIL SFRTCAT (NIL T T T T) -9 NIL 2578422 NIL) (-1102 2566650 2567668 2568804 "SFRGCD" 2572212 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2559777 2560849 2562035 "SFQCMPK" 2565583 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559399 2559488 2559598 "SFORT" 2559718 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2558544 2559239 2559360 "SEXOF" 2559365 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2557678 2558425 2558493 "SEX" 2558498 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553217 2553906 2554001 "SEXCAT" 2556938 NIL SEXCAT (NIL T T T T T) -9 NIL 2557516 NIL) (-1096 2550397 2553151 2553199 "SET" 2553204 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2548648 2549110 2549415 "SETMN" 2550138 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548254 2548380 2548410 "SETCAT" 2548527 T SETCAT (NIL) -9 NIL 2548612 NIL) (-1093 2548034 2548086 2548185 "SETCAT-" 2548190 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2544421 2546495 2546538 "SETAGG" 2547408 NIL SETAGG (NIL T) -9 NIL 2547748 NIL) (-1091 2543879 2543995 2544232 "SETAGG-" 2544237 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2543349 2543575 2543676 "SEQAST" 2543800 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2542548 2542842 2542903 "SEGXCAT" 2543189 NIL SEGXCAT (NIL T T) -9 NIL 2543309 NIL) (-1088 2541602 2542214 2542396 "SEG" 2542401 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2540581 2540795 2540838 "SEGCAT" 2541360 NIL SEGCAT (NIL T) -9 NIL 2541581 NIL) (-1086 2539630 2539960 2540160 "SEGBIND" 2540416 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539251 2539310 2539423 "SEGBIND2" 2539565 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2538851 2539052 2539129 "SEGAST" 2539196 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538070 2538196 2538400 "SEG2" 2538695 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2537507 2538005 2538052 "SDVAR" 2538057 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2529789 2537277 2537407 "SDPOL" 2537412 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2528382 2528648 2528967 "SCPKG" 2529504 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2527542 2527715 2527908 "SCOPE" 2528211 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2526762 2526896 2527075 "SCACHE" 2527397 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2526434 2526594 2526624 "SASTCAT" 2526629 T SASTCAT (NIL) -9 NIL 2526642 NIL) (-1076 2525948 2526269 2526345 "SAOS" 2526380 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2525513 2525548 2525721 "SAERFFC" 2525907 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2519479 2525410 2525490 "SAE" 2525495 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519072 2519107 2519266 "SAEFACT" 2519438 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2517393 2517707 2518108 "RURPK" 2518738 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516029 2516308 2516620 "RULESET" 2517227 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513216 2513719 2514184 "RULE" 2515710 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2512855 2513010 2513093 "RULECOLD" 2513168 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2512645 2512673 2512744 "RTVALUE" 2512806 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2512143 2512362 2512456 "RSTRCAST" 2512573 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2506991 2507786 2508706 "RSETGCD" 2511342 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496248 2501300 2501397 "RSETCAT" 2505516 NIL RSETCAT (NIL T T T T) -9 NIL 2506613 NIL) (-1064 2494175 2494714 2495538 "RSETCAT-" 2495543 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486560 2487937 2489457 "RSDCMPK" 2492774 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484565 2485006 2485080 "RRCC" 2486166 NIL RRCC (NIL T T) -9 NIL 2486510 NIL) (-1061 2483916 2484090 2484369 "RRCC-" 2484374 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483386 2483612 2483713 "RPTAST" 2483837 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457384 2466979 2467046 "RPOLCAT" 2477710 NIL RPOLCAT (NIL T T T) -9 NIL 2480869 NIL) (-1058 2448882 2451222 2454344 "RPOLCAT-" 2454349 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2439929 2447093 2447575 "ROUTINE" 2448422 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2436754 2439555 2439695 "ROMAN" 2439811 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2435025 2435614 2435874 "ROIRC" 2436559 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431410 2433661 2433691 "RNS" 2433995 T RNS (NIL) -9 NIL 2434268 NIL) (-1053 2429919 2430302 2430836 "RNS-" 2430911 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429368 2429750 2429780 "RNG" 2429785 T RNG (NIL) -9 NIL 2429806 NIL) (-1051 2428760 2429122 2429165 "RMODULE" 2429227 NIL RMODULE (NIL T) -9 NIL 2429269 NIL) (-1050 2427596 2427690 2428026 "RMCAT2" 2428661 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424473 2426942 2427239 "RMATRIX" 2427358 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417415 2419649 2419764 "RMATCAT" 2423123 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2424105 NIL) (-1047 2416790 2416937 2417244 "RMATCAT-" 2417249 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416357 2416432 2416560 "RINTERP" 2416709 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415476 2416004 2416034 "RING" 2416090 T RING (NIL) -9 NIL 2416182 NIL) (-1044 2415268 2415312 2415409 "RING-" 2415414 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2414109 2414346 2414604 "RIDIST" 2415032 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405425 2413577 2413783 "RGCHAIN" 2413957 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2404801 2405181 2405222 "RGBCSPC" 2405280 NIL RGBCSPC (NIL T) -9 NIL 2405332 NIL) (-1040 2403985 2404340 2404381 "RGBCMDL" 2404613 NIL RGBCMDL (NIL T) -9 NIL 2404727 NIL) (-1039 2400979 2401593 2402263 "RF" 2403349 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400625 2400688 2400791 "RFFACTOR" 2400910 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400350 2400385 2400482 "RFFACT" 2400584 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398467 2398831 2399213 "RFDIST" 2399990 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2397920 2398012 2398175 "RETSOL" 2398369 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397556 2397636 2397679 "RETRACT" 2397812 NIL RETRACT (NIL T) -9 NIL 2397899 NIL) (-1033 2397405 2397430 2397517 "RETRACT-" 2397522 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2397034 2397227 2397297 "RETAST" 2397357 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2389888 2396687 2396814 "RESULT" 2396929 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388506 2389157 2389356 "RESRING" 2389791 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2388142 2388191 2388289 "RESLATC" 2388443 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2387847 2387882 2387989 "REPSQ" 2388101 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385269 2385849 2386451 "REP" 2387267 T REP (NIL) -7 NIL NIL NIL) (-1026 2384966 2385001 2385112 "REPDB" 2385228 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2378866 2380255 2381478 "REP2" 2383778 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375243 2375924 2376732 "REP1" 2378093 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2367966 2373384 2373840 "REGSET" 2374873 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2366779 2367114 2367364 "REF" 2367751 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2366156 2366259 2366426 "REDORDER" 2366663 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2362151 2365369 2365596 "RECLOS" 2365984 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361203 2361384 2361599 "REALSOLV" 2361958 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2361049 2361090 2361120 "REAL" 2361125 T REAL (NIL) -9 NIL 2361160 NIL) (-1017 2357532 2358334 2359218 "REAL0Q" 2360214 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2353133 2354121 2355182 "REAL0" 2356513 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352631 2352850 2352944 "RDUCEAST" 2353061 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2352036 2352108 2352315 "RDIV" 2352553 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2351104 2351278 2351491 "RDIST" 2351858 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349701 2349988 2350360 "RDETRS" 2350812 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347513 2347967 2348505 "RDETR" 2349243 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2346124 2346402 2346806 "RDEEFS" 2347229 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344619 2344925 2345357 "RDEEF" 2345812 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2338872 2341755 2341785 "RCFIELD" 2343080 T RCFIELD (NIL) -9 NIL 2343810 NIL) (-1007 2336936 2337440 2338136 "RCFIELD-" 2338211 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333252 2335037 2335080 "RCAGG" 2336164 NIL RCAGG (NIL T) -9 NIL 2336629 NIL) (-1005 2332880 2332974 2333137 "RCAGG-" 2333142 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332215 2332327 2332492 "RATRET" 2332764 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2331768 2331835 2331956 "RATFACT" 2332143 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2331076 2331196 2331348 "RANDSRC" 2331638 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2330810 2330854 2330927 "RADUTIL" 2331025 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2323953 2329643 2329953 "RADIX" 2330534 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315601 2323797 2323925 "RADFF" 2323930 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315253 2315328 2315356 "RADCAT" 2315513 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2315038 2315086 2315183 "RADCAT-" 2315188 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313189 2314813 2314902 "QUEUE" 2314982 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2309757 2313126 2313171 "QUAT" 2313176 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309395 2309438 2309565 "QUATCT2" 2309708 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2303134 2306444 2306484 "QUATCAT" 2307264 NIL QUATCAT (NIL T) -9 NIL 2308030 NIL) (-992 2299278 2300315 2301702 "QUATCAT-" 2301796 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2296798 2298362 2298403 "QUAGG" 2298778 NIL QUAGG (NIL T) -9 NIL 2298953 NIL) (-990 2296430 2296623 2296691 "QQUTAST" 2296750 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295355 2295828 2296000 "QFORM" 2296302 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286559 2291772 2291812 "QFCAT" 2292470 NIL QFCAT (NIL T) -9 NIL 2293471 NIL) (-987 2282131 2283332 2284923 "QFCAT-" 2285017 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2281769 2281812 2281939 "QFCAT2" 2282082 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281229 2281339 2281469 "QEQUAT" 2281659 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274376 2275448 2276632 "QCMPACK" 2280162 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2271952 2272373 2272801 "QALGSET" 2274031 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271197 2271371 2271603 "QALGSET2" 2271772 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2269887 2270111 2270428 "PWFFINTB" 2270970 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2268069 2268237 2268591 "PUSHVAR" 2269701 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2263987 2265041 2265082 "PTRANFN" 2266966 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262389 2262680 2263002 "PTPACK" 2263698 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2262021 2262078 2262187 "PTFUNC2" 2262326 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256548 2260893 2260934 "PTCAT" 2261230 NIL PTCAT (NIL T) -9 NIL 2261383 NIL) (-975 2256206 2256241 2256365 "PSQFR" 2256507 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2254801 2255099 2255433 "PSEUDLIN" 2255904 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241564 2243935 2246259 "PSETPK" 2252561 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234608 2237322 2237418 "PSETCAT" 2240439 NIL PSETCAT (NIL T T T T) -9 NIL 2241253 NIL) (-971 2232444 2233078 2233899 "PSETCAT-" 2233904 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2231793 2231958 2231986 "PSCURVE" 2232254 T PSCURVE (NIL) -9 NIL 2232421 NIL) (-969 2228141 2229631 2229696 "PSCAT" 2230540 NIL PSCAT (NIL T T T) -9 NIL 2230780 NIL) (-968 2227204 2227420 2227820 "PSCAT-" 2227825 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2225936 2226569 2226774 "PRTITION" 2227019 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225438 2225657 2225749 "PRTDAST" 2225864 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214528 2216742 2218930 "PRS" 2223300 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212386 2213878 2213918 "PRQAGG" 2214101 NIL PRQAGG (NIL T) -9 NIL 2214203 NIL) (-963 2211772 2212001 2212029 "PROPLOG" 2212214 T PROPLOG (NIL) -9 NIL 2212336 NIL) (-962 2210280 2210723 2210980 "PROPFRML" 2211548 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2209740 2209850 2209980 "PROPERTY" 2210170 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2203825 2207906 2208726 "PRODUCT" 2208966 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2201130 2203283 2203517 "PR" 2203636 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2200926 2200958 2201017 "PRINT" 2201091 T PRINT (NIL) -7 NIL NIL NIL) (-957 2200266 2200383 2200535 "PRIMES" 2200806 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2198331 2198732 2199198 "PRIMELT" 2199845 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2198060 2198109 2198137 "PRIMCAT" 2198261 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2194223 2197998 2198043 "PRIMARR" 2198048 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2193230 2193408 2193636 "PRIMARR2" 2194041 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2192873 2192929 2193040 "PREASSOC" 2193168 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2192348 2192481 2192509 "PPCURVE" 2192714 T PPCURVE (NIL) -9 NIL 2192850 NIL) (-950 2191970 2192143 2192226 "PORTNUM" 2192285 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2189329 2189728 2190320 "POLYROOT" 2191551 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2183266 2188933 2189093 "POLY" 2189202 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2182649 2182707 2182941 "POLYLIFT" 2183202 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2178924 2179373 2180002 "POLYCATQ" 2182194 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2165733 2171099 2171164 "POLYCAT" 2174678 NIL POLYCAT (NIL T T T) -9 NIL 2176606 NIL) (-944 2159182 2161044 2163428 "POLYCAT-" 2163433 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2158769 2158837 2158957 "POLY2UP" 2159108 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2158401 2158458 2158567 "POLY2" 2158706 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2157086 2157325 2157601 "POLUTIL" 2158175 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2155441 2155718 2156049 "POLTOPOL" 2156808 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2150956 2155377 2155423 "POINT" 2155428 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2149143 2149500 2149875 "PNTHEORY" 2150601 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2147562 2147859 2148271 "PMTOOLS" 2148841 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2147155 2147233 2147350 "PMSYM" 2147478 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2146665 2146734 2146908 "PMQFCAT" 2147080 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2146020 2146130 2146286 "PMPRED" 2146542 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2145416 2145502 2145663 "PMPREDFS" 2145921 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2144059 2144267 2144652 "PMPLCAT" 2145178 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2143591 2143670 2143822 "PMLSAGG" 2143974 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2143066 2143142 2143323 "PMKERNEL" 2143509 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2142683 2142758 2142871 "PMINS" 2142985 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2142111 2142180 2142396 "PMFS" 2142608 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2141339 2141457 2141662 "PMDOWN" 2141988 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2140502 2140661 2140843 "PMASS" 2141177 T PMASS (NIL) -7 NIL NIL NIL) (-925 2139776 2139887 2140050 "PMASSFS" 2140388 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2139431 2139499 2139593 "PLOTTOOL" 2139702 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2134038 2135242 2136390 "PLOT" 2138303 T PLOT (NIL) -8 NIL NIL NIL) (-922 2129842 2130886 2131807 "PLOT3D" 2133137 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2128754 2128931 2129166 "PLOT1" 2129646 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2104143 2108820 2113671 "PLEQN" 2124020 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2103461 2103583 2103763 "PINTERP" 2104008 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2103154 2103201 2103304 "PINTERPA" 2103408 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2102402 2102923 2103010 "PI" 2103050 T PI (NIL) -8 NIL NIL 2103117) (-916 2100791 2101740 2101768 "PID" 2101950 T PID (NIL) -9 NIL 2102084 NIL) (-915 2100516 2100553 2100641 "PICOERCE" 2100748 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2099836 2099975 2100151 "PGROEB" 2100372 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2095423 2096237 2097142 "PGE" 2098951 T PGE (NIL) -7 NIL NIL NIL) (-912 2093546 2093793 2094159 "PGCD" 2095140 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2092884 2092987 2093148 "PFRPAC" 2093430 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2089552 2091432 2091785 "PFR" 2092563 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2087941 2088185 2088510 "PFOTOOLS" 2089299 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2086474 2086713 2087064 "PFOQ" 2087698 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2084947 2085159 2085522 "PFO" 2086258 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2081527 2084836 2084905 "PF" 2084910 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2078953 2080198 2080226 "PFECAT" 2080811 T PFECAT (NIL) -9 NIL 2081195 NIL) (-904 2078398 2078552 2078766 "PFECAT-" 2078771 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2077001 2077253 2077554 "PFBRU" 2078147 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2074866 2075219 2075651 "PFBR" 2076652 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2070775 2072242 2072918 "PERM" 2074223 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2066036 2066982 2067852 "PERMGRP" 2069938 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2064168 2065099 2065140 "PERMCAT" 2065586 NIL PERMCAT (NIL T) -9 NIL 2065891 NIL) (-898 2063821 2063862 2063986 "PERMAN" 2064121 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2061357 2063486 2063608 "PENDTREE" 2063732 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2059442 2060184 2060225 "PDRING" 2060882 NIL PDRING (NIL T) -9 NIL 2061168 NIL) (-895 2058545 2058763 2059125 "PDRING-" 2059130 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2055787 2056538 2057206 "PDEPROB" 2057897 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2053332 2053836 2054391 "PDEPACK" 2055252 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2052244 2052434 2052685 "PDECOMP" 2053131 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2049849 2050666 2050694 "PDECAT" 2051481 T PDECAT (NIL) -9 NIL 2052194 NIL) (-890 2049600 2049633 2049723 "PCOMP" 2049810 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2047805 2048401 2048698 "PBWLB" 2049329 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2040305 2041878 2043216 "PATTERN" 2046488 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2039937 2039994 2040103 "PATTERN2" 2040242 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2037694 2038082 2038539 "PATTERN1" 2039526 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2035089 2035643 2036124 "PATRES" 2037259 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2034653 2034720 2034852 "PATRES2" 2035016 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2032536 2032941 2033348 "PATMATCH" 2034320 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2032072 2032255 2032296 "PATMAB" 2032403 NIL PATMAB (NIL T) -9 NIL 2032486 NIL) (-881 2030617 2030926 2031184 "PATLRES" 2031877 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2030163 2030286 2030327 "PATAB" 2030332 NIL PATAB (NIL T) -9 NIL 2030504 NIL) (-879 2027644 2028176 2028749 "PARTPERM" 2029610 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2027265 2027328 2027430 "PARSURF" 2027575 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2026897 2026954 2027063 "PARSU2" 2027202 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2026661 2026701 2026768 "PARSER" 2026850 T PARSER (NIL) -7 NIL NIL NIL) (-875 2026282 2026345 2026447 "PARSCURV" 2026592 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2025914 2025971 2026080 "PARSC2" 2026219 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2025553 2025611 2025708 "PARPCURV" 2025850 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2025185 2025242 2025351 "PARPC2" 2025490 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2024705 2024791 2024910 "PAN2EXPR" 2025086 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2023509 2023826 2024054 "PALETTE" 2024497 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2021977 2022514 2022874 "PAIR" 2023195 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2015874 2021236 2021430 "PADICRC" 2021832 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2009130 2015220 2015404 "PADICRAT" 2015722 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2007472 2009067 2009112 "PADIC" 2009117 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2004674 2006212 2006252 "PADICCT" 2006833 NIL PADICCT (NIL NIL) -9 NIL 2007115 NIL) (-864 2003631 2003831 2004099 "PADEPAC" 2004461 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2002843 2002976 2003182 "PADE" 2003493 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2001257 2002051 2002331 "OWP" 2002647 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2000777 2000963 2001060 "OVERSET" 2001180 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1999850 2000382 2000554 "OVAR" 2000645 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1999114 1999235 1999396 "OUT" 1999709 T OUT (NIL) -7 NIL NIL NIL) (-858 1988012 1990223 1992423 "OUTFORM" 1996934 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1987348 1987609 1987736 "OUTBFILE" 1987905 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1986655 1986820 1986848 "OUTBCON" 1987166 T OUTBCON (NIL) -9 NIL 1987332 NIL) (-855 1986256 1986368 1986525 "OUTBCON-" 1986530 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1985663 1985985 1986074 "OSI" 1986187 T OSI (NIL) -8 NIL NIL NIL) (-853 1985219 1985531 1985559 "OSGROUP" 1985564 T OSGROUP (NIL) -9 NIL 1985586 NIL) (-852 1983964 1984191 1984476 "ORTHPOL" 1984966 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1981542 1983799 1983920 "OREUP" 1983925 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1978972 1981233 1981360 "ORESUP" 1981484 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1976500 1977000 1977561 "OREPCTO" 1978461 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1970316 1972491 1972532 "OREPCAT" 1974880 NIL OREPCAT (NIL T) -9 NIL 1975984 NIL) (-847 1967463 1968245 1969303 "OREPCAT-" 1969308 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1966640 1966912 1966940 "ORDSET" 1967249 T ORDSET (NIL) -9 NIL 1967413 NIL) (-845 1966159 1966281 1966474 "ORDSET-" 1966479 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1964785 1965550 1965578 "ORDRING" 1965780 T ORDRING (NIL) -9 NIL 1965905 NIL) (-843 1964430 1964524 1964668 "ORDRING-" 1964673 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1963836 1964273 1964301 "ORDMON" 1964306 T ORDMON (NIL) -9 NIL 1964327 NIL) (-841 1962998 1963145 1963340 "ORDFUNS" 1963685 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1962362 1962755 1962783 "ORDFIN" 1962848 T ORDFIN (NIL) -9 NIL 1962922 NIL) (-839 1958948 1960948 1961357 "ORDCOMP" 1961986 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1958214 1958341 1958527 "ORDCOMP2" 1958808 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954822 1955705 1956519 "OPTPROB" 1957420 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1951624 1952263 1952967 "OPTPACK" 1954138 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1949337 1950077 1950105 "OPTCAT" 1950924 T OPTCAT (NIL) -9 NIL 1951574 NIL) (-834 1948780 1949014 1949119 "OPSIG" 1949252 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1948548 1948587 1948653 "OPQUERY" 1948734 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1945706 1946859 1947363 "OP" 1948077 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1945241 1945412 1945453 "OPERCAT" 1945588 NIL OPERCAT (NIL T) -9 NIL 1945656 NIL) (-830 1945087 1945114 1945200 "OPERCAT-" 1945205 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1941926 1943884 1944253 "ONECOMP" 1944751 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1941231 1941346 1941520 "ONECOMP2" 1941798 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1940650 1940756 1940886 "OMSERVER" 1941121 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1937538 1940090 1940130 "OMSAGG" 1940191 NIL OMSAGG (NIL T) -9 NIL 1940255 NIL) (-825 1936161 1936424 1936706 "OMPKG" 1937276 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1935591 1935694 1935722 "OM" 1936021 T OM (NIL) -9 NIL NIL NIL) (-823 1934165 1935140 1935309 "OMLO" 1935472 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1933090 1933237 1933464 "OMEXPR" 1933991 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1932408 1932636 1932772 "OMERR" 1932974 T OMERR (NIL) -8 NIL NIL NIL) (-820 1931586 1931829 1931989 "OMERRK" 1932268 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1931064 1931263 1931371 "OMENC" 1931498 T OMENC (NIL) -8 NIL NIL NIL) (-818 1924959 1926144 1927315 "OMDEV" 1929913 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1924028 1924199 1924393 "OMCONN" 1924785 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1922641 1923591 1923619 "OINTDOM" 1923624 T OINTDOM (NIL) -9 NIL 1923645 NIL) (-815 1918447 1919631 1920347 "OFMONOID" 1921957 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1917885 1918384 1918429 "ODVAR" 1918434 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1915335 1917630 1917785 "ODR" 1917790 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1907671 1915111 1915237 "ODPOL" 1915242 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1901541 1907543 1907648 "ODP" 1907653 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1900307 1900522 1900797 "ODETOOLS" 1901315 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1897274 1897932 1898648 "ODESYS" 1899640 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1892156 1893064 1894089 "ODERTRIC" 1896349 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1891582 1891664 1891858 "ODERED" 1892068 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1888470 1889018 1889695 "ODERAT" 1891005 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1885427 1885894 1886491 "ODEPRRIC" 1887999 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1883397 1883966 1884452 "ODEPROB" 1884961 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1879917 1880402 1881049 "ODEPRIM" 1882876 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1879166 1879268 1879528 "ODEPAL" 1879809 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1875328 1876119 1876983 "ODEPACK" 1878322 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1874361 1874468 1874697 "ODEINT" 1875217 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1868462 1869887 1871334 "ODEIFTBL" 1872934 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1863797 1864583 1865542 "ODEEF" 1867621 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1863132 1863221 1863451 "ODECONST" 1863702 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1861283 1861918 1861946 "ODECAT" 1862551 T ODECAT (NIL) -9 NIL 1863082 NIL) (-795 1858182 1860995 1861114 "OCT" 1861196 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1857820 1857863 1857990 "OCTCT2" 1858133 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1852586 1854994 1855034 "OC" 1856131 NIL OC (NIL T) -9 NIL 1856989 NIL) (-792 1849813 1850561 1851551 "OC-" 1851645 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1849191 1849633 1849661 "OCAMON" 1849666 T OCAMON (NIL) -9 NIL 1849687 NIL) (-790 1848748 1849063 1849091 "OASGP" 1849096 T OASGP (NIL) -9 NIL 1849116 NIL) (-789 1848035 1848498 1848526 "OAMONS" 1848566 T OAMONS (NIL) -9 NIL 1848609 NIL) (-788 1847475 1847882 1847910 "OAMON" 1847915 T OAMON (NIL) -9 NIL 1847935 NIL) (-787 1846779 1847271 1847299 "OAGROUP" 1847304 T OAGROUP (NIL) -9 NIL 1847324 NIL) (-786 1846469 1846519 1846607 "NUMTUBE" 1846723 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1840042 1841560 1843096 "NUMQUAD" 1844953 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1835798 1836786 1837811 "NUMODE" 1839037 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1833179 1834033 1834061 "NUMINT" 1834984 T NUMINT (NIL) -9 NIL 1835748 NIL) (-782 1832127 1832324 1832542 "NUMFMT" 1832981 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1818486 1821431 1823963 "NUMERIC" 1829634 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1812883 1817935 1818030 "NTSCAT" 1818035 NIL NTSCAT (NIL T T T T) -9 NIL 1818074 NIL) (-779 1812077 1812242 1812435 "NTPOLFN" 1812722 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1799909 1808902 1809714 "NSUP" 1811298 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1799541 1799598 1799707 "NSUP2" 1799846 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1789524 1799315 1799448 "NSMP" 1799453 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1787956 1788257 1788614 "NREP" 1789212 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1786547 1786799 1787157 "NPCOEF" 1787699 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1785613 1785728 1785944 "NORMRETR" 1786428 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1783654 1783944 1784353 "NORMPK" 1785321 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1783339 1783367 1783491 "NORMMA" 1783620 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1783166 1783296 1783325 "NONE" 1783330 T NONE (NIL) -8 NIL NIL NIL) (-769 1782955 1782984 1783053 "NONE1" 1783130 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1782438 1782500 1782686 "NODE1" 1782887 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1780708 1781532 1781787 "NNI" 1782134 T NNI (NIL) -8 NIL NIL 1782369) (-766 1779128 1779441 1779805 "NLINSOL" 1780376 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1775396 1776364 1777263 "NIPROB" 1778249 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1774153 1774387 1774689 "NFINTBAS" 1775158 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1773327 1773803 1773844 "NETCLT" 1774016 NIL NETCLT (NIL T) -9 NIL 1774098 NIL) (-762 1772035 1772266 1772547 "NCODIV" 1773095 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1771797 1771834 1771909 "NCNTFRAC" 1771992 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1769977 1770341 1770761 "NCEP" 1771422 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1768874 1769621 1769649 "NASRING" 1769759 T NASRING (NIL) -9 NIL 1769839 NIL) (-758 1768669 1768713 1768807 "NASRING-" 1768812 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1767822 1768321 1768349 "NARNG" 1768466 T NARNG (NIL) -9 NIL 1768557 NIL) (-756 1767514 1767581 1767715 "NARNG-" 1767720 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1766393 1766600 1766835 "NAGSP" 1767299 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1757665 1759349 1761022 "NAGS" 1764740 T NAGS (NIL) -7 NIL NIL NIL) (-753 1756213 1756521 1756852 "NAGF07" 1757354 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1750751 1752042 1753349 "NAGF04" 1754926 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1743719 1745333 1746966 "NAGF02" 1749138 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1738943 1740043 1741160 "NAGF01" 1742622 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1732571 1734137 1735722 "NAGE04" 1737378 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1723740 1725861 1727991 "NAGE02" 1730461 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1719693 1720640 1721604 "NAGE01" 1722796 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1717488 1718022 1718580 "NAGD03" 1719155 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1709238 1711166 1713120 "NAGD02" 1715554 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1703049 1704474 1705914 "NAGD01" 1707818 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1699258 1700080 1700917 "NAGC06" 1702232 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1697723 1698055 1698411 "NAGC05" 1698922 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1697099 1697218 1697362 "NAGC02" 1697599 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1696159 1696716 1696756 "NAALG" 1696835 NIL NAALG (NIL T) -9 NIL 1696896 NIL) (-739 1695994 1696023 1696113 "NAALG-" 1696118 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1689944 1691052 1692239 "MULTSQFR" 1694890 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1689263 1689338 1689522 "MULTFACT" 1689856 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1682348 1686226 1686279 "MTSCAT" 1687349 NIL MTSCAT (NIL T T) -9 NIL 1687863 NIL) (-735 1682060 1682114 1682206 "MTHING" 1682288 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1681852 1681885 1681945 "MSYSCMD" 1682020 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1677961 1680607 1680927 "MSET" 1681565 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1675056 1677522 1677563 "MSETAGG" 1677568 NIL MSETAGG (NIL T) -9 NIL 1677602 NIL) (-731 1670924 1672435 1673180 "MRING" 1674356 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1670490 1670557 1670688 "MRF2" 1670851 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1670108 1670143 1670287 "MRATFAC" 1670449 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1667720 1668015 1668446 "MPRFF" 1669813 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1661772 1667574 1667671 "MPOLY" 1667676 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1661262 1661297 1661505 "MPCPF" 1661731 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1660776 1660819 1661003 "MPC3" 1661213 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1659971 1660052 1660273 "MPC2" 1660691 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1658272 1658609 1658999 "MONOTOOL" 1659631 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1657523 1657814 1657842 "MONOID" 1658061 T MONOID (NIL) -9 NIL 1658208 NIL) (-721 1657069 1657188 1657369 "MONOID-" 1657374 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1647920 1653836 1653895 "MONOGEN" 1654569 NIL MONOGEN (NIL T T) -9 NIL 1655025 NIL) (-719 1645138 1645873 1646873 "MONOGEN-" 1646992 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1643997 1644417 1644445 "MONADWU" 1644837 T MONADWU (NIL) -9 NIL 1645075 NIL) (-717 1643369 1643528 1643776 "MONADWU-" 1643781 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1642754 1642972 1643000 "MONAD" 1643207 T MONAD (NIL) -9 NIL 1643319 NIL) (-715 1642439 1642517 1642649 "MONAD-" 1642654 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1640755 1641352 1641631 "MOEBIUS" 1642192 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1640147 1640525 1640565 "MODULE" 1640570 NIL MODULE (NIL T) -9 NIL 1640596 NIL) (-712 1639715 1639811 1640001 "MODULE-" 1640006 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1637422 1638079 1638406 "MODRING" 1639539 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1634393 1635527 1636048 "MODOP" 1636951 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1633008 1633460 1633737 "MODMONOM" 1634256 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1622805 1631299 1631713 "MODMON" 1632645 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1619988 1621649 1621925 "MODFIELD" 1622680 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1618992 1619269 1619459 "MMLFORM" 1619818 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1618518 1618561 1618740 "MMAP" 1618943 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1616727 1617468 1617509 "MLO" 1617932 NIL MLO (NIL T) -9 NIL 1618174 NIL) (-703 1614093 1614609 1615211 "MLIFT" 1616208 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1613484 1613568 1613722 "MKUCFUNC" 1614004 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1613083 1613153 1613276 "MKRECORD" 1613407 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1612130 1612292 1612520 "MKFUNC" 1612894 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1611518 1611622 1611778 "MKFLCFN" 1612013 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610795 1610897 1611082 "MKBCFUNC" 1611411 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607529 1610349 1610485 "MINT" 1610679 T MINT (NIL) -8 NIL NIL NIL) (-696 1606341 1606584 1606861 "MHROWRED" 1607284 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601748 1604876 1605281 "MFLOAT" 1605956 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1601105 1601181 1601352 "MFINFACT" 1601660 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597420 1598268 1599152 "MESH" 1600241 T MESH (NIL) -7 NIL NIL NIL) (-692 1595810 1596122 1596475 "MDDFACT" 1597107 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592652 1594969 1595010 "MDAGG" 1595265 NIL MDAGG (NIL T) -9 NIL 1595408 NIL) (-690 1582422 1591945 1592152 "MCMPLX" 1592465 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581563 1581709 1581909 "MCDEN" 1582271 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579453 1579723 1580103 "MCALCFN" 1581293 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578378 1578618 1578851 "MAYBE" 1579259 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575990 1576513 1577075 "MATSTOR" 1577849 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571995 1575362 1575610 "MATRIX" 1575775 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567759 1568468 1569204 "MATLIN" 1571352 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557913 1561051 1561128 "MATCAT" 1566008 NIL MATCAT (NIL T T T) -9 NIL 1567425 NIL) (-682 1554269 1555290 1556646 "MATCAT-" 1556651 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552863 1553016 1553349 "MATCAT2" 1554104 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550975 1551299 1551683 "MAPPKG3" 1552538 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549956 1550129 1550351 "MAPPKG2" 1550799 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548455 1548739 1549066 "MAPPKG1" 1549662 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547561 1547861 1548038 "MAPPAST" 1548298 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1547172 1547230 1547353 "MAPHACK3" 1547497 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546764 1546825 1546939 "MAPHACK2" 1547104 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1546201 1546305 1546447 "MAPHACK1" 1546655 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544307 1544901 1545205 "MAGMA" 1545929 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543813 1544031 1544122 "MACROAST" 1544236 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1540279 1542052 1542513 "M3D" 1543385 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534433 1538648 1538689 "LZSTAGG" 1539471 NIL LZSTAGG (NIL T) -9 NIL 1539766 NIL) (-669 1530390 1531564 1533021 "LZSTAGG-" 1533026 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527504 1528281 1528768 "LWORD" 1529935 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1527107 1527308 1527383 "LSTAST" 1527449 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1520300 1526878 1527012 "LSQM" 1527017 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519524 1519663 1519891 "LSPP" 1520155 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517336 1517637 1518093 "LSMP" 1519213 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1514115 1514789 1515519 "LSMP1" 1516638 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1508040 1513282 1513323 "LSAGG" 1513385 NIL LSAGG (NIL T) -9 NIL 1513463 NIL) (-661 1504735 1505659 1506872 "LSAGG-" 1506877 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502361 1503879 1504128 "LPOLY" 1504530 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501943 1502028 1502151 "LPEFRAC" 1502270 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1500290 1501037 1501290 "LO" 1501775 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499942 1500054 1500082 "LOGIC" 1500193 T LOGIC (NIL) -9 NIL 1500274 NIL) (-656 1499804 1499827 1499898 "LOGIC-" 1499903 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498997 1499137 1499330 "LODOOPS" 1499660 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496447 1498913 1498979 "LODO" 1498984 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494985 1495220 1495573 "LODOF" 1496194 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491333 1493738 1493779 "LODOCAT" 1494217 NIL LODOCAT (NIL T) -9 NIL 1494428 NIL) (-651 1491066 1491124 1491251 "LODOCAT-" 1491256 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488413 1490907 1491025 "LODO2" 1491030 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485875 1488350 1488395 "LODO1" 1488400 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484735 1484900 1485212 "LODEEF" 1485698 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1480021 1482865 1482906 "LNAGG" 1483853 NIL LNAGG (NIL T) -9 NIL 1484297 NIL) (-646 1479168 1479382 1479724 "LNAGG-" 1479729 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475331 1476093 1476732 "LMOPS" 1478583 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474726 1475088 1475129 "LMODULE" 1475190 NIL LMODULE (NIL T) -9 NIL 1475232 NIL) (-643 1471972 1474371 1474494 "LMDICT" 1474636 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471698 1471880 1471940 "LITERAL" 1471945 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464929 1470644 1470942 "LIST" 1471433 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464454 1464528 1464667 "LIST3" 1464849 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463461 1463639 1463867 "LIST2" 1464272 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461595 1461907 1462306 "LIST2MAP" 1463108 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460317 1460961 1461002 "LINEXP" 1461257 NIL LINEXP (NIL T) -9 NIL 1461406 NIL) (-636 1458964 1459224 1459521 "LINDEP" 1460069 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455731 1456450 1457227 "LIMITRF" 1458219 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1454006 1454302 1454718 "LIMITPS" 1455426 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448461 1453517 1453745 "LIE" 1453827 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447510 1447953 1447993 "LIECAT" 1448133 NIL LIECAT (NIL T) -9 NIL 1448284 NIL) (-631 1447351 1447378 1447466 "LIECAT-" 1447471 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439963 1446800 1446965 "LIB" 1447206 T LIB (NIL) -8 NIL NIL NIL) (-629 1435598 1436481 1437416 "LGROBP" 1439080 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433464 1433738 1434100 "LF" 1435319 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432304 1432996 1433024 "LFCAT" 1433231 T LFCAT (NIL) -9 NIL 1433370 NIL) (-626 1429206 1429836 1430524 "LEXTRIPK" 1431668 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425977 1426776 1427279 "LEXP" 1428786 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425480 1425698 1425790 "LETAST" 1425905 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423878 1424191 1424592 "LEADCDET" 1425162 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1423068 1423142 1423371 "LAZM3PK" 1423799 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1418012 1421145 1421683 "LAUPOL" 1422580 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417577 1417621 1417789 "LAPLACE" 1417962 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415543 1416678 1416929 "LA" 1417410 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414616 1415174 1415215 "LALG" 1415277 NIL LALG (NIL T) -9 NIL 1415336 NIL) (-617 1414330 1414389 1414525 "LALG-" 1414530 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1414165 1414189 1414230 "KVTFROM" 1414292 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412965 1413382 1413611 "KTVLOGIC" 1413956 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412800 1412824 1412865 "KRCFROM" 1412927 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411704 1411891 1412190 "KOVACIC" 1412600 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411539 1411563 1411604 "KONVERT" 1411666 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411374 1411398 1411439 "KOERCE" 1411501 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1409108 1409868 1410261 "KERNEL" 1411013 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408610 1408691 1408821 "KERNEL2" 1409022 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402461 1407149 1407203 "KDAGG" 1407580 NIL KDAGG (NIL T T) -9 NIL 1407786 NIL) (-607 1401990 1402114 1402319 "KDAGG-" 1402324 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1395165 1401651 1401806 "KAFILE" 1401868 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389620 1394676 1394904 "JORDAN" 1394986 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1389026 1389269 1389390 "JOINAST" 1389519 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388872 1388931 1388986 "JAVACODE" 1388991 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1385171 1387077 1387131 "IXAGG" 1388060 NIL IXAGG (NIL T T) -9 NIL 1388519 NIL) (-601 1384090 1384396 1384815 "IXAGG-" 1384820 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379670 1384012 1384071 "IVECTOR" 1384076 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378436 1378673 1378939 "ITUPLE" 1379437 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376872 1377049 1377355 "ITRIGMNP" 1378258 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375617 1375821 1376104 "ITFUN3" 1376648 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1375249 1375306 1375415 "ITFUN2" 1375554 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1373078 1374111 1374410 "ITAYLOR" 1374983 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1362050 1367215 1368378 "ISUPS" 1371948 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1361154 1361294 1361530 "ISUMP" 1361897 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356418 1360955 1361034 "ISTRING" 1361107 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355921 1356139 1356231 "ISAST" 1356346 T ISAST (NIL) -8 NIL NIL NIL) (-590 1355131 1355212 1355428 "IRURPK" 1355835 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1354067 1354268 1354508 "IRSN" 1354911 T IRSN (NIL) -7 NIL NIL NIL) (-588 1352096 1352451 1352887 "IRRF2F" 1353705 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351843 1351881 1351957 "IRREDFFX" 1352052 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350458 1350717 1351016 "IROOT" 1351576 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1347089 1348142 1348834 "IR" 1349798 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344702 1345197 1345763 "IR2" 1346567 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343774 1343887 1344108 "IR2F" 1344585 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343565 1343599 1343659 "IPRNTPK" 1343734 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1340172 1343454 1343523 "IPF" 1343528 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338526 1340097 1340154 "IPADIC" 1340159 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337865 1338086 1338216 "IP4ADDR" 1338416 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337365 1337569 1337679 "IOMODE" 1337775 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336438 1336962 1337089 "IOBFILE" 1337258 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335926 1336342 1336370 "IOBCON" 1336375 T IOBCON (NIL) -9 NIL 1336396 NIL) (-575 1335423 1335481 1335671 "INVLAPLA" 1335862 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1325071 1327425 1329811 "INTTR" 1333087 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321415 1322157 1323021 "INTTOOLS" 1324256 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1321001 1321092 1321209 "INTSLPE" 1321318 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318982 1320924 1320983 "INTRVL" 1320988 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316584 1317096 1317671 "INTRF" 1318467 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315995 1316092 1316234 "INTRET" 1316482 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313992 1314381 1314851 "INTRAT" 1315603 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1311220 1311803 1312429 "INTPM" 1313477 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307922 1308522 1309267 "INTPAF" 1310606 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1303101 1304063 1305114 "INTPACK" 1306891 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1300005 1302830 1302957 "INT" 1302994 T INT (NIL) -8 NIL NIL NIL) (-563 1299257 1299409 1299617 "INTHERTR" 1299847 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298696 1298776 1298964 "INTHERAL" 1299171 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296542 1296985 1297442 "INTHEORY" 1298259 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287850 1289471 1291250 "INTG0" 1294894 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268423 1273213 1278023 "INTFTBL" 1283060 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267672 1267810 1267983 "INTFACT" 1268282 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1265057 1265503 1266067 "INTEF" 1267226 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263516 1264229 1264257 "INTDOM" 1264558 T INTDOM (NIL) -9 NIL 1264765 NIL) (-555 1262885 1263059 1263301 "INTDOM-" 1263306 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259372 1261269 1261323 "INTCAT" 1262122 NIL INTCAT (NIL T) -9 NIL 1262442 NIL) (-553 1258844 1258947 1259075 "INTBIT" 1259264 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257515 1257669 1257983 "INTALG" 1258689 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256972 1257062 1257232 "INTAF" 1257419 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250426 1256782 1256922 "INTABL" 1256927 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249757 1250196 1250261 "INT8" 1250295 T INT8 (NIL) -8 NIL NIL 1250340) (-548 1249087 1249526 1249591 "INT64" 1249625 T INT64 (NIL) -8 NIL NIL 1249670) (-547 1248417 1248856 1248921 "INT32" 1248955 T INT32 (NIL) -8 NIL NIL 1249000) (-546 1247747 1248186 1248251 "INT16" 1248285 T INT16 (NIL) -8 NIL NIL 1248330) (-545 1242754 1245436 1245464 "INS" 1246398 T INS (NIL) -9 NIL 1247063 NIL) (-544 1239994 1240765 1241739 "INS-" 1241812 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238769 1238996 1239294 "INPSIGN" 1239747 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237887 1238004 1238201 "INPRODPF" 1238649 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236781 1236898 1237135 "INPRODFF" 1237767 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235781 1235933 1236193 "INNMFACT" 1236617 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234978 1235075 1235263 "INMODGCD" 1235680 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233486 1233731 1234055 "INFSP" 1234723 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232670 1232787 1232970 "INFPROD0" 1233366 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229552 1230735 1231250 "INFORM" 1232163 T INFORM (NIL) -8 NIL NIL NIL) (-535 1229162 1229222 1229320 "INFORM1" 1229487 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228685 1228774 1228888 "INFINITY" 1229068 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227861 1228405 1228506 "INETCLTS" 1228604 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226477 1226727 1227048 "INEP" 1227609 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225753 1226374 1226439 "INDE" 1226444 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225317 1225385 1225502 "INCRMAPS" 1225680 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1224135 1224586 1224792 "INBFILE" 1225131 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219435 1220371 1221315 "INBFF" 1223223 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218343 1218612 1218640 "INBCON" 1219153 T INBCON (NIL) -9 NIL 1219419 NIL) (-526 1217595 1217818 1218094 "INBCON-" 1218099 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1217101 1217319 1217410 "INAST" 1217524 T INAST (NIL) -8 NIL NIL NIL) (-524 1216555 1216780 1216886 "IMPTAST" 1217015 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1213049 1216399 1216503 "IMATRIX" 1216508 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211761 1211884 1212199 "IMATQF" 1212905 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209981 1210208 1210545 "IMATLIN" 1211517 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204607 1209905 1209963 "ILIST" 1209968 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202560 1204467 1204580 "IIARRAY2" 1204585 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197985 1202471 1202535 "IFF" 1202540 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197359 1197602 1197718 "IFAST" 1197889 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192402 1196651 1196839 "IFARRAY" 1197216 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191609 1192306 1192379 "IFAMON" 1192384 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1191193 1191258 1191312 "IEVALAB" 1191519 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190868 1190936 1191096 "IEVALAB-" 1191101 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190526 1190782 1190845 "IDPO" 1190850 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189803 1190415 1190490 "IDPOAMS" 1190495 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1189137 1189692 1189767 "IDPOAM" 1189772 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1188222 1188472 1188525 "IDPC" 1188938 NIL IDPC (NIL T T) -9 NIL 1189087 NIL) (-508 1187718 1188114 1188187 "IDPAM" 1188192 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1187121 1187610 1187683 "IDPAG" 1187688 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186793 1186957 1187032 "IDENT" 1187066 T IDENT (NIL) -8 NIL NIL NIL) (-505 1183048 1183896 1184791 "IDECOMP" 1185950 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175912 1176971 1178018 "IDEAL" 1182084 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1175076 1175188 1175387 "ICDEN" 1175796 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1174174 1174556 1174703 "ICARD" 1174949 T ICARD (NIL) -8 NIL NIL NIL) (-501 1172234 1172547 1172952 "IBPTOOLS" 1173851 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167868 1171854 1171967 "IBITS" 1172153 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164591 1165167 1165862 "IBATOOL" 1167285 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162370 1162832 1163365 "IBACHIN" 1164126 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1160247 1162216 1162319 "IARRAY2" 1162324 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156401 1160173 1160230 "IARRAY1" 1160235 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150385 1154813 1155294 "IAN" 1155940 T IAN (NIL) -8 NIL NIL NIL) (-494 1149896 1149953 1150126 "IALGFACT" 1150322 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149424 1149537 1149565 "HYPCAT" 1149772 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148962 1149079 1149265 "HYPCAT-" 1149270 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148584 1148757 1148840 "HOSTNAME" 1148899 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148429 1148466 1148507 "HOMOTOP" 1148512 NIL HOMOTOP (NIL T) -9 NIL 1148545 NIL) (-489 1145108 1146439 1146480 "HOAGG" 1147461 NIL HOAGG (NIL T) -9 NIL 1148140 NIL) (-488 1143702 1144101 1144627 "HOAGG-" 1144632 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137733 1143297 1143446 "HEXADEC" 1143573 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136481 1136703 1136966 "HEUGCD" 1137510 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135584 1136318 1136448 "HELLFDIV" 1136453 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133811 1135361 1135449 "HEAP" 1135528 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1133101 1133363 1133497 "HEADAST" 1133697 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1127015 1133016 1133078 "HDP" 1133083 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120758 1126650 1126802 "HDMP" 1126916 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1120082 1120222 1120386 "HB" 1120614 T HB (NIL) -7 NIL NIL NIL) (-479 1113579 1119928 1120032 "HASHTBL" 1120037 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1113082 1113300 1113392 "HASAST" 1113507 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110887 1112704 1112886 "HACKPI" 1112920 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106582 1110740 1110853 "GTSET" 1110858 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1100108 1106460 1106558 "GSTBL" 1106563 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092413 1099139 1099404 "GSERIES" 1099899 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091580 1091971 1091999 "GROUP" 1092202 T GROUP (NIL) -9 NIL 1092336 NIL) (-472 1090946 1091105 1091356 "GROUP-" 1091361 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089313 1089634 1090021 "GROEBSOL" 1090623 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088253 1088515 1088566 "GRMOD" 1089095 NIL GRMOD (NIL T T) -9 NIL 1089263 NIL) (-469 1088021 1088057 1088185 "GRMOD-" 1088190 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083338 1084375 1085375 "GRIMAGE" 1087041 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081804 1082065 1082389 "GRDEF" 1083034 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081248 1081364 1081505 "GRAY" 1081683 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080461 1080841 1080892 "GRALG" 1081045 NIL GRALG (NIL T T) -9 NIL 1081138 NIL) (-464 1080122 1080195 1080358 "GRALG-" 1080363 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076926 1079707 1079885 "GPOLSET" 1080029 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076280 1076337 1076595 "GOSPER" 1076863 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1072039 1072718 1073244 "GMODPOL" 1075979 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1071044 1071228 1071466 "GHENSEL" 1071851 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1065095 1065938 1066965 "GENUPS" 1070128 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064792 1064843 1064932 "GENUFACT" 1065038 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064204 1064281 1064446 "GENPGCD" 1064710 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063678 1063713 1063926 "GENMFACT" 1064163 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062244 1062501 1062808 "GENEEZ" 1063421 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1056145 1061855 1062017 "GDMP" 1062167 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045514 1049916 1051022 "GCNAALG" 1055128 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043933 1044769 1044797 "GCDDOM" 1045052 T GCDDOM (NIL) -9 NIL 1045209 NIL) (-451 1043403 1043530 1043745 "GCDDOM-" 1043750 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1042075 1042260 1042564 "GB" 1043182 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030691 1033021 1035413 "GBINTERN" 1039766 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028528 1028820 1029241 "GBF" 1030366 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027309 1027474 1027741 "GBEUCLID" 1028344 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026658 1026783 1026932 "GAUSSFAC" 1027180 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1025025 1025327 1025641 "GALUTIL" 1026377 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023333 1023607 1023931 "GALPOLYU" 1024752 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020698 1020988 1021395 "GALFACTU" 1023030 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012504 1014003 1015611 "GALFACT" 1019130 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009892 1010550 1010578 "FVFUN" 1011734 T FVFUN (NIL) -9 NIL 1012454 NIL) (-440 1009158 1009340 1009368 "FVC" 1009659 T FVC (NIL) -9 NIL 1009842 NIL) (-439 1008828 1008983 1009051 "FUNDESC" 1009110 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008470 1008625 1008706 "FUNCTION" 1008780 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006241 1006792 1007258 "FT" 1008024 T FT (NIL) -8 NIL NIL NIL) (-436 1005059 1005542 1005745 "FTEM" 1006058 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003315 1003604 1004008 "FSUPFACT" 1004750 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001712 1002001 1002333 "FST" 1003003 T FST (NIL) -8 NIL NIL NIL) (-433 1000883 1000989 1001184 "FSRED" 1001594 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999561 999817 1000171 "FSPRMELT" 1000598 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996646 997084 997583 "FSPECF" 999124 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978700 987149 987189 "FS" 991037 NIL FS (NIL T) -9 NIL 993326 NIL) (-429 967347 970340 974396 "FS-" 974693 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966861 966915 967092 "FSINT" 967288 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 965180 965854 966157 "FSERIES" 966640 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 964194 964310 964541 "FSCINT" 965060 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960428 963138 963179 "FSAGG" 963549 NIL FSAGG (NIL T) -9 NIL 963808 NIL) (-424 958190 958791 959587 "FSAGG-" 959682 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 957232 957375 957602 "FSAGG2" 958043 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954886 955166 955720 "FS2UPS" 956950 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954468 954511 954666 "FS2" 954837 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953325 953496 953805 "FS2EXPXP" 954293 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952751 952866 953018 "FRUTIL" 953205 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944191 948246 949604 "FR" 951425 NIL FR (NIL T) -8 NIL NIL NIL) (-417 939266 941909 941949 "FRNAALG" 943345 NIL FRNAALG (NIL T) -9 NIL 943952 NIL) (-416 934939 936015 937290 "FRNAALG-" 938040 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934577 934620 934747 "FRNAAF2" 934890 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932984 933431 933726 "FRMOD" 934389 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930762 931367 931684 "FRIDEAL" 932775 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929957 930044 930333 "FRIDEAL2" 930669 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 929090 929504 929545 "FRETRCT" 929550 NIL FRETRCT (NIL T) -9 NIL 929726 NIL) (-410 928202 928433 928784 "FRETRCT-" 928789 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925406 926590 926649 "FRAMALG" 927531 NIL FRAMALG (NIL T T) -9 NIL 927823 NIL) (-408 923540 923995 924625 "FRAMALG-" 924848 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917488 923015 923291 "FRAC" 923296 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 917124 917181 917288 "FRAC2" 917425 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916760 916817 916924 "FR2" 917061 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911425 914285 914313 "FPS" 915432 T FPS (NIL) -9 NIL 915989 NIL) (-403 910874 910983 911147 "FPS-" 911293 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908320 909963 909991 "FPC" 910216 T FPC (NIL) -9 NIL 910358 NIL) (-401 908113 908153 908250 "FPC-" 908255 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906991 907601 907642 "FPATMAB" 907647 NIL FPATMAB (NIL T) -9 NIL 907799 NIL) (-399 904691 905167 905593 "FPARFRAC" 906628 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 900084 900583 901265 "FORTRAN" 904123 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897800 898300 898839 "FORT" 899565 T FORT (NIL) -7 NIL NIL NIL) (-396 895476 896038 896066 "FORTFN" 897126 T FORTFN (NIL) -9 NIL 897750 NIL) (-395 895240 895290 895318 "FORTCAT" 895377 T FORTCAT (NIL) -9 NIL 895439 NIL) (-394 893373 893856 894246 "FORMULA" 894870 T FORMULA (NIL) -8 NIL NIL NIL) (-393 893161 893191 893260 "FORMULA1" 893337 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892684 892736 892909 "FORDER" 893103 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891780 891944 892137 "FOP" 892511 T FOP (NIL) -7 NIL NIL NIL) (-390 890388 891060 891234 "FNLA" 891662 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 889143 889532 889560 "FNCAT" 890020 T FNCAT (NIL) -9 NIL 890280 NIL) (-388 888709 889102 889130 "FNAME" 889135 T FNAME (NIL) -8 NIL NIL NIL) (-387 887364 888301 888329 "FMTC" 888334 T FMTC (NIL) -9 NIL 888370 NIL) (-386 883724 884887 885516 "FMONOID" 886768 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882943 883466 883615 "FM" 883620 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880367 881013 881041 "FMFUN" 882185 T FMFUN (NIL) -9 NIL 882893 NIL) (-383 879636 879817 879845 "FMC" 880135 T FMC (NIL) -9 NIL 880317 NIL) (-382 876830 877664 877718 "FMCAT" 878913 NIL FMCAT (NIL T T) -9 NIL 879408 NIL) (-381 875723 876596 876696 "FM1" 876775 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873497 873913 874407 "FLOATRP" 875274 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 867098 871226 871847 "FLOAT" 872896 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864536 865036 865614 "FLOATCP" 866565 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863337 864149 864190 "FLINEXP" 864195 NIL FLINEXP (NIL T) -9 NIL 864288 NIL) (-376 862491 862726 863054 "FLINEXP-" 863059 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861567 861711 861935 "FLASORT" 862343 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858784 859626 859678 "FLALG" 860905 NIL FLALG (NIL T T) -9 NIL 861372 NIL) (-373 852568 856270 856311 "FLAGG" 857573 NIL FLAGG (NIL T) -9 NIL 858225 NIL) (-372 851294 851633 852123 "FLAGG-" 852128 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850336 850479 850706 "FLAGG2" 851147 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847303 848285 848344 "FINRALG" 849472 NIL FINRALG (NIL T T) -9 NIL 849980 NIL) (-369 846463 846692 847031 "FINRALG-" 847036 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845869 846082 846110 "FINITE" 846306 T FINITE (NIL) -9 NIL 846413 NIL) (-367 838327 840488 840528 "FINAALG" 844195 NIL FINAALG (NIL T) -9 NIL 845648 NIL) (-366 833659 834709 835853 "FINAALG-" 837232 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 833054 833414 833517 "FILE" 833589 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831738 832050 832104 "FILECAT" 832788 NIL FILECAT (NIL T T) -9 NIL 833004 NIL) (-363 829598 831100 831128 "FIELD" 831168 T FIELD (NIL) -9 NIL 831248 NIL) (-362 828218 828603 829114 "FIELD-" 829119 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 826095 826853 827200 "FGROUP" 827904 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825185 825349 825569 "FGLMICPK" 825927 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 821044 825110 825167 "FFX" 825172 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820645 820706 820841 "FFSLPE" 820977 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816634 817417 818213 "FFPOLY" 819881 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 816138 816174 816383 "FFPOLY2" 816592 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 812008 816057 816120 "FFP" 816125 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807433 811919 811983 "FF" 811988 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802586 806776 806966 "FFNBX" 807287 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797542 801721 801979 "FFNBP" 802440 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792202 796826 797037 "FFNB" 797375 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 791034 791232 791547 "FFINTBAS" 791999 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787254 789441 789469 "FFIELDC" 790089 T FFIELDC (NIL) -9 NIL 790465 NIL) (-348 785916 786287 786784 "FFIELDC-" 786789 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785485 785531 785655 "FFHOM" 785858 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783180 783667 784184 "FFF" 785000 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778825 782922 783023 "FFCGX" 783123 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774473 778557 778664 "FFCGP" 778768 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769683 774200 774308 "FFCG" 774409 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751508 760554 760640 "FFCAT" 765805 NIL FFCAT (NIL T T T) -9 NIL 767256 NIL) (-341 746706 747753 749067 "FFCAT-" 750297 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 746117 746160 746395 "FFCAT2" 746657 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735314 739089 740309 "FEXPR" 744969 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734314 734749 734790 "FEVALAB" 734874 NIL FEVALAB (NIL T) -9 NIL 735135 NIL) (-337 733473 733683 734021 "FEVALAB-" 734026 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 732066 732856 733059 "FDIV" 733372 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 729132 729847 729962 "FDIVCAT" 731530 NIL FDIVCAT (NIL T T T T) -9 NIL 731967 NIL) (-334 728894 728921 729091 "FDIVCAT-" 729096 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 728114 728201 728478 "FDIV2" 728801 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726800 727059 727348 "FCPAK1" 727845 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725926 726300 726441 "FCOMP" 726691 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709655 713076 716614 "FC" 722408 T FC (NIL) -8 NIL NIL NIL) (-329 702226 706219 706259 "FAXF" 708061 NIL FAXF (NIL T) -9 NIL 708753 NIL) (-328 699502 700160 700985 "FAXF-" 701450 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694602 698878 699054 "FARRAY" 699359 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689847 691887 691940 "FAMR" 692963 NIL FAMR (NIL T T) -9 NIL 693423 NIL) (-325 688737 689039 689474 "FAMR-" 689479 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687933 688659 688712 "FAMONOID" 688717 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685745 686429 686482 "FAMONC" 687423 NIL FAMONC (NIL T T) -9 NIL 687809 NIL) (-322 684437 685499 685636 "FAGROUP" 685641 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682232 682551 682954 "FACUTIL" 684118 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681331 681516 681738 "FACTFUNC" 682042 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673728 680582 680794 "EXPUPXS" 681187 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671211 671751 672337 "EXPRTUBE" 673162 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667405 667997 668734 "EXPRODE" 670550 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652771 666060 666488 "EXPR" 667009 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647178 647765 648578 "EXPR2UPS" 652069 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646814 646871 646978 "EXPR2" 647115 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638211 645946 646243 "EXPEXPAN" 646651 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 638038 638168 638197 "EXIT" 638202 T EXIT (NIL) -8 NIL NIL NIL) (-311 637545 637762 637853 "EXITAST" 637967 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637172 637234 637347 "EVALCYC" 637477 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636713 636831 636872 "EVALAB" 637042 NIL EVALAB (NIL T) -9 NIL 637146 NIL) (-308 636194 636316 636537 "EVALAB-" 636542 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633654 634930 634958 "EUCDOM" 635513 T EUCDOM (NIL) -9 NIL 635863 NIL) (-306 632059 632501 633091 "EUCDOM-" 633096 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619597 622357 625107 "ESTOOLS" 629329 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619229 619286 619395 "ESTOOLS2" 619534 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618980 619022 619102 "ESTOOLS1" 619181 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612885 614613 614641 "ES" 617409 T ES (NIL) -9 NIL 618818 NIL) (-301 607832 609119 610936 "ES-" 611100 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604206 604967 605747 "ESCONT" 607072 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603951 603983 604065 "ESCONT1" 604168 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603626 603676 603776 "ES2" 603895 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603256 603314 603423 "ES1" 603562 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602472 602601 602777 "ERROR" 603100 T ERROR (NIL) -7 NIL NIL NIL) (-295 595975 602331 602422 "EQTBL" 602427 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588526 591289 592738 "EQ" 594559 NIL -2064 (NIL T) -8 NIL NIL NIL) (-293 588158 588215 588324 "EQ2" 588463 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583447 584496 585589 "EP" 587097 NIL EP (NIL T) -7 NIL NIL NIL) (-291 582025 582322 582634 "ENV" 583155 T ENV (NIL) -8 NIL NIL NIL) (-290 581196 581724 581752 "ENTIRER" 581757 T ENTIRER (NIL) -9 NIL 581803 NIL) (-289 577690 579151 579521 "EMR" 580995 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576834 577019 577073 "ELTAGG" 577453 NIL ELTAGG (NIL T T) -9 NIL 577664 NIL) (-287 576553 576615 576756 "ELTAGG-" 576761 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576342 576371 576425 "ELTAB" 576509 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575468 575614 575813 "ELFUTS" 576193 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575210 575266 575294 "ELEMFUN" 575399 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 575080 575101 575169 "ELEMFUN-" 575174 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569971 573180 573221 "ELAGG" 574161 NIL ELAGG (NIL T) -9 NIL 574624 NIL) (-281 568256 568690 569353 "ELAGG-" 569358 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566921 567199 567492 "ELABEXPR" 567983 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559785 561588 562415 "EFUPXS" 566197 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553235 555036 555846 "EFULS" 559061 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550657 551015 551494 "EFSTRUC" 552867 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539728 541294 542854 "EF" 549172 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538829 539213 539362 "EAB" 539599 T EAB (NIL) -8 NIL NIL NIL) (-274 538038 538788 538816 "E04UCFA" 538821 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537247 537997 538025 "E04NAFA" 538030 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536456 537206 537234 "E04MBFA" 537239 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535665 536415 536443 "E04JAFA" 536448 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534876 535624 535652 "E04GCFA" 535657 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 534087 534835 534863 "E04FDFA" 534868 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533296 534046 534074 "E04DGFA" 534079 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527469 528821 530185 "E04AGNT" 531952 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526175 526655 526695 "DVARCAT" 527170 NIL DVARCAT (NIL T) -9 NIL 527369 NIL) (-265 525379 525591 525905 "DVARCAT-" 525910 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518271 525178 525307 "DSMP" 525312 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 513080 514216 515284 "DROPT" 517223 T DROPT (NIL) -8 NIL NIL NIL) (-262 512745 512804 512902 "DROPT1" 513015 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507860 508986 510123 "DROPT0" 511628 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506205 506530 506916 "DRAWPT" 507494 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500792 501715 502794 "DRAW" 505179 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500425 500478 500596 "DRAWHACK" 500733 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499156 499425 499716 "DRAWCX" 500154 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498671 498740 498891 "DRAWCURV" 499082 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 489139 491101 493216 "DRAWCFUN" 496576 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485952 487834 487875 "DQAGG" 488504 NIL DQAGG (NIL T) -9 NIL 488777 NIL) (-253 474223 480930 481013 "DPOLCAT" 482865 NIL DPOLCAT (NIL T T T T) -9 NIL 483410 NIL) (-252 469059 470408 472366 "DPOLCAT-" 472371 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 462208 468920 469018 "DPMO" 469023 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 455260 461988 462155 "DPMM" 462160 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454892 455179 455227 "DOMCTOR" 455232 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454187 454414 454551 "DOMAIN" 454775 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447930 453822 453974 "DMP" 454088 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447530 447586 447730 "DLP" 447868 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441400 446857 447047 "DLIST" 447372 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 438244 440253 440294 "DLAGG" 440844 NIL DLAGG (NIL T) -9 NIL 441074 NIL) (-243 437049 437687 437715 "DIVRING" 437807 T DIVRING (NIL) -9 NIL 437890 NIL) (-242 436286 436476 436776 "DIVRING-" 436781 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434388 434745 435151 "DISPLAY" 435900 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428324 434302 434365 "DIRPROD" 434370 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 427172 427375 427640 "DIRPROD2" 428117 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416429 422387 422440 "DIRPCAT" 422850 NIL DIRPCAT (NIL NIL T) -9 NIL 423690 NIL) (-237 413755 414397 415278 "DIRPCAT-" 415615 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 413042 413202 413388 "DIOSP" 413589 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409744 411954 411995 "DIOPS" 412429 NIL DIOPS (NIL T) -9 NIL 412658 NIL) (-234 409293 409407 409598 "DIOPS-" 409603 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408177 408779 408807 "DIFRING" 408994 T DIFRING (NIL) -9 NIL 409104 NIL) (-232 407823 407900 408052 "DIFRING-" 408057 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405620 406866 406907 "DIFEXT" 407270 NIL DIFEXT (NIL T) -9 NIL 407564 NIL) (-230 403905 404333 404999 "DIFEXT-" 405004 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401227 403437 403478 "DIAGG" 403483 NIL DIAGG (NIL T) -9 NIL 403503 NIL) (-228 400611 400768 401020 "DIAGG-" 401025 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 396076 399570 399847 "DHMATRIX" 400380 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391688 392597 393607 "DFSFUN" 395086 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386793 390619 390931 "DFLOAT" 391396 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 385021 385302 385698 "DFINTTLS" 386501 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 382077 383042 383442 "DERHAM" 384687 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379926 381852 381941 "DEQUEUE" 382021 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 379141 379274 379470 "DEGRED" 379788 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375536 376281 377134 "DEFINTRF" 378369 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 373063 373532 374131 "DEFINTEF" 375055 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372440 372683 372798 "DEFAST" 372968 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366471 372035 372184 "DECIMAL" 372311 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363981 364441 364947 "DDFACT" 366015 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363577 363620 363771 "DBLRESP" 363932 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361476 361810 362170 "DBASE" 363344 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360745 360956 361102 "DATAARY" 361375 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359878 360704 360732 "D03FAFA" 360737 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 359012 359837 359865 "D03EEFA" 359870 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356962 357428 357917 "D03AGNT" 358543 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356278 356921 356949 "D02EJFA" 356954 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355594 356237 356265 "D02CJFA" 356270 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354910 355553 355581 "D02BHFA" 355586 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354226 354869 354897 "D02BBFA" 354902 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347423 349012 350618 "D02AGNT" 352640 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345191 345714 346260 "D01WGTS" 346897 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344285 345150 345178 "D01TRNS" 345183 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343380 344244 344272 "D01GBFA" 344277 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342475 343339 343367 "D01FCFA" 343372 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341570 342434 342462 "D01ASFA" 342467 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340665 341529 341557 "D01AQFA" 341562 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339760 340624 340652 "D01APFA" 340657 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338855 339719 339747 "D01ANFA" 339752 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337950 338814 338842 "D01AMFA" 338847 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 337045 337909 337937 "D01ALFA" 337942 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 336140 337004 337032 "D01AKFA" 337037 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335235 336099 336127 "D01AJFA" 336132 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328530 330083 331644 "D01AGNT" 333694 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327867 327995 328147 "CYCLOTOM" 328398 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324602 325315 326042 "CYCLES" 327160 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323914 324048 324219 "CVMP" 324463 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321685 321943 322319 "CTRIGMNP" 323642 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321180 321479 321552 "CTOR" 321632 T CTOR (NIL) -8 NIL NIL NIL) (-186 320716 320911 321012 "CTORKIND" 321099 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 320064 320323 320351 "CTORCAT" 320533 T CTORCAT (NIL) -9 NIL 320646 NIL) (-184 319662 319773 319932 "CTORCAT-" 319937 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319178 319365 319463 "CTORCALL" 319584 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318552 318651 318804 "CSTTOOLS" 319075 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314351 315008 315766 "CRFP" 317864 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313853 314072 314164 "CRCEAST" 314279 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312900 313085 313313 "CRAPACK" 313657 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312284 312385 312589 "CPMATCH" 312776 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 312009 312037 312143 "CPIMA" 312250 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308373 309045 309763 "COORDSYS" 311344 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307781 307903 308046 "CONTOUR" 308250 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303699 305784 306276 "CONTFRAC" 307321 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303579 303600 303628 "CONDUIT" 303665 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302744 303272 303300 "COMRING" 303305 T COMRING (NIL) -9 NIL 303357 NIL) (-171 301825 302102 302286 "COMPPROP" 302580 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301486 301521 301649 "COMPLPAT" 301784 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291535 301295 301404 "COMPLEX" 301409 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291171 291228 291335 "COMPLEX2" 291472 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290889 290924 291022 "COMPFACT" 291130 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 275043 285271 285311 "COMPCAT" 286315 NIL COMPCAT (NIL T) -9 NIL 287711 NIL) (-165 264554 267482 271109 "COMPCAT-" 271465 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264283 264311 264414 "COMMUPC" 264520 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 264077 264111 264170 "COMMONOP" 264244 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263660 263828 263915 "COMM" 264010 T COMM (NIL) -8 NIL NIL NIL) (-161 263263 263464 263539 "COMMAAST" 263605 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262512 262706 262734 "COMBOPC" 263072 T COMBOPC (NIL) -9 NIL 263247 NIL) (-159 261408 261618 261860 "COMBINAT" 262302 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 257605 258179 258819 "COMBF" 260830 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256390 256721 256956 "COLOR" 257390 T COLOR (NIL) -8 NIL NIL NIL) (-156 255893 256111 256203 "COLONAST" 256318 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255533 255580 255705 "CMPLXRT" 255840 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 255008 255233 255332 "CLLCTAST" 255454 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250508 251538 252618 "CLIP" 253948 T CLIP (NIL) -7 NIL NIL NIL) (-152 248881 249614 249853 "CLIF" 250335 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 245103 247027 247068 "CLAGG" 247997 NIL CLAGG (NIL T) -9 NIL 248533 NIL) (-150 243525 243982 244565 "CLAGG-" 244570 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 243069 243154 243294 "CINTSLPE" 243434 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240570 241041 241589 "CHVAR" 242597 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239805 240333 240361 "CHARZ" 240366 T CHARZ (NIL) -9 NIL 240381 NIL) (-146 239559 239599 239677 "CHARPOL" 239759 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238678 239239 239267 "CHARNZ" 239314 T CHARNZ (NIL) -9 NIL 239370 NIL) (-144 236667 237368 237703 "CHAR" 238363 T CHAR (NIL) -8 NIL NIL NIL) (-143 236393 236454 236482 "CFCAT" 236593 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235638 235749 235931 "CDEN" 236277 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231630 234791 235071 "CCLASS" 235378 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230937 231080 231243 "CATEGORY" 231487 T -10 (NIL) -8 NIL NIL NIL) (-139 230569 230856 230904 "CATCTOR" 230909 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 230047 230272 230370 "CATAST" 230491 T CATAST (NIL) -8 NIL NIL NIL) (-137 229550 229768 229860 "CASEAST" 229975 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224586 225579 226332 "CARTEN" 228853 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 223694 223842 224063 "CARTEN2" 224433 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 222036 222844 223101 "CARD" 223457 T CARD (NIL) -8 NIL NIL NIL) (-133 221639 221840 221915 "CAPSLAST" 221981 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 221011 221339 221367 "CACHSET" 221499 T CACHSET (NIL) -9 NIL 221576 NIL) (-131 220507 220803 220831 "CABMON" 220881 T CABMON (NIL) -9 NIL 220937 NIL) (-130 220007 220211 220321 "BYTEORD" 220417 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 219010 219541 219683 "BYTE" 219846 T BYTE (NIL) -8 NIL NIL 219968) (-128 214410 218515 218687 "BYTEBUF" 218858 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211967 214102 214209 "BTREE" 214336 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209464 211615 211737 "BTOURN" 211877 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206881 208934 208975 "BTCAT" 209043 NIL BTCAT (NIL T) -9 NIL 209120 NIL) (-124 206548 206628 206777 "BTCAT-" 206782 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201840 205691 205719 "BTAGG" 205941 T BTAGG (NIL) -9 NIL 206102 NIL) (-122 201330 201455 201661 "BTAGG-" 201666 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198373 200608 200823 "BSTREE" 201147 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197511 197637 197821 "BRILL" 198229 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194210 196237 196278 "BRAGG" 196927 NIL BRAGG (NIL T) -9 NIL 197185 NIL) (-118 192739 193145 193700 "BRAGG-" 193705 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185995 192085 192269 "BPADICRT" 192587 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184337 185932 185977 "BPADIC" 185982 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 184035 184065 184179 "BOUNDZRO" 184301 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179021 180211 181181 "BOP" 183085 T BOP (NIL) -8 NIL NIL NIL) (-113 176642 177086 177606 "BOP1" 178534 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175344 176066 176259 "BOOLEAN" 176469 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174706 175084 175138 "BMODULE" 175143 NIL BMODULE (NIL T T) -9 NIL 175208 NIL) (-110 170534 174504 174577 "BITS" 174653 T BITS (NIL) -8 NIL NIL NIL) (-109 169946 170068 170210 "BINDING" 170412 T BINDING (NIL) -8 NIL NIL NIL) (-108 163980 169543 169691 "BINARY" 169818 T BINARY (NIL) -8 NIL NIL NIL) (-107 161807 163235 163276 "BGAGG" 163536 NIL BGAGG (NIL T) -9 NIL 163673 NIL) (-106 161638 161670 161761 "BGAGG-" 161766 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160736 161022 161227 "BFUNCT" 161453 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159426 159604 159892 "BEZOUT" 160560 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155943 158278 158608 "BBTREE" 159129 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155677 155730 155758 "BASTYPE" 155877 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155530 155558 155631 "BASTYPE-" 155636 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154964 155040 155192 "BALFACT" 155441 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153847 154379 154565 "AUTOMOR" 154809 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153573 153578 153604 "ATTREG" 153609 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151852 152270 152622 "ATTRBUT" 153239 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151487 151680 151746 "ATTRAST" 151804 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151023 151136 151162 "ATRIG" 151363 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150832 150873 150960 "ATRIG-" 150965 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150503 150663 150689 "ASTCAT" 150694 T ASTCAT (NIL) -9 NIL 150724 NIL) (-92 150230 150289 150408 "ASTCAT-" 150413 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148427 150006 150094 "ASTACK" 150173 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146932 147229 147594 "ASSOCEQ" 148109 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145964 146591 146715 "ASP9" 146839 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145727 145912 145951 "ASP8" 145956 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144595 145332 145474 "ASP80" 145616 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143493 144230 144362 "ASP7" 144494 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142447 143170 143288 "ASP78" 143406 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141416 142127 142244 "ASP77" 142361 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140328 141054 141185 "ASP74" 141316 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139228 139963 140095 "ASP73" 140227 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138332 139054 139154 "ASP6" 139159 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137276 138009 138127 "ASP55" 138245 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136225 136950 137069 "ASP50" 137188 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135313 135926 136036 "ASP4" 136146 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134401 135014 135124 "ASP49" 135234 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133185 133940 134108 "ASP42" 134290 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131961 132718 132888 "ASP41" 133072 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130911 131638 131756 "ASP35" 131874 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130676 130859 130898 "ASP34" 130903 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130413 130480 130556 "ASP33" 130631 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129306 130048 130180 "ASP31" 130312 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129071 129254 129293 "ASP30" 129298 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128806 128875 128951 "ASP29" 129026 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128571 128754 128793 "ASP28" 128798 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128336 128519 128558 "ASP27" 128563 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127420 128034 128145 "ASP24" 128256 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126496 127222 127334 "ASP20" 127339 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125584 126197 126307 "ASP1" 126417 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124526 125258 125377 "ASP19" 125496 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124263 124330 124406 "ASP12" 124481 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123115 123862 124006 "ASP10" 124150 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121014 122959 123050 "ARRAY2" 123055 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116827 120662 120776 "ARRAY1" 120931 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115859 116032 116253 "ARRAY12" 116650 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110218 112089 112164 "ARR2CAT" 114794 NIL ARR2CAT (NIL T T T) -9 NIL 115552 NIL) (-56 107652 108396 109350 "ARR2CAT-" 109355 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107279 107404 "ARITY" 107545 T ARITY (NIL) -8 NIL NIL NIL) (-54 105744 105896 106202 "APPRULE" 106832 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105395 105443 105562 "APPLYORE" 105690 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104369 104660 104855 "ANY" 105218 T ANY (NIL) -8 NIL NIL NIL) (-51 103647 103770 103927 "ANY1" 104243 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101204 102084 102411 "ANTISYM" 103371 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100723 100911 101007 "ANON" 101126 T ANON (NIL) -8 NIL NIL NIL) (-48 94847 99262 99716 "AN" 100287 T AN (NIL) -8 NIL NIL NIL) (-47 91095 92457 92508 "AMR" 93256 NIL AMR (NIL T T) -9 NIL 93856 NIL) (-46 90207 90428 90791 "AMR-" 90796 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74757 90124 90185 "ALIST" 90190 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71586 74351 74520 "ALGSC" 74675 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68141 68696 69303 "ALGPKG" 71026 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67418 67519 67703 "ALGMFACT" 68027 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63842 64497 "ALGMANIP" 66941 NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 54552 62781 62931 "ALGFF" 63088 NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 53748 53879 54058 "ALGFACT" 54410 NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 52805 53379 53417 "ALGEBRA" 53422 NIL ALGEBRA (NIL T) -9 NIL 53463 NIL) (-37 52523 52582 52714 "ALGEBRA-" 52719 NIL ALGEBRA- (NIL T T) -8 NIL NIL NIL) (-36 34782 50525 50577 "ALAGG" 50713 NIL ALAGG (NIL T T) -9 NIL 50874 NIL) (-35 34318 34431 34457 "AHYP" 34658 T AHYP (NIL) -9 NIL NIL NIL) (-34 33249 33497 33523 "AGG" 34022 T AGG (NIL) -9 NIL 34301 NIL) (-33 32683 32845 33059 "AGG-" 33064 NIL AGG- (NIL T) -8 NIL NIL NIL) (-32 30359 30782 31200 "AF" 32325 NIL AF (NIL T T) -7 NIL NIL NIL) (-31 29866 30084 30174 "ADDAST" 30287 T ADDAST (NIL) -8 NIL NIL NIL) (-30 29134 29393 29549 "ACPLOT" 29728 T ACPLOT (NIL) -8 NIL NIL NIL) (-29 18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 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 a4a5a790..1d017f6b 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,127 +1,97 @@ -(735619 . 3451299469) -(((*1 *2 *3 *4) - (-12 - (-5 *3 - (-641 - (-2 (|:| |eqzro| (-641 *8)) (|:| |neqzro| (-641 *8)) - (|:| |wcond| (-641 (-948 *5))) - (|:| |bsoln| - (-2 (|:| |partsol| (-1259 (-407 (-948 *5)))) - (|:| -3342 (-641 (-1259 (-407 (-948 *5)))))))))) - (-5 *4 (-1152)) (-4 *5 (-13 (-307) (-147))) (-4 *8 (-945 *5 *7 *6)) - (-4 *6 (-13 (-846) (-612 (-1170)))) (-4 *7 (-789)) (-5 *2 (-564)) - (-5 *1 (-920 *5 *6 *7 *8))))) -(((*1 *2 *3) - (-12 (-5 *3 (-641 (-481 *4 *5))) (-14 *4 (-641 (-1170))) - (-4 *5 (-452)) - (-5 *2 - (-2 (|:| |gblist| (-641 (-247 *4 *5))) - (|:| |gvlist| (-641 (-564))))) - (-5 *1 (-629 *4 *5))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 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(-5 *1 (-1095 *4 *5)) (-14 *4 *3) + (-14 *5 *3)))) +(((*1 *2 *1 *3 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-1219 *4)) (-4 *4 (-1045)) (-4 *4 (-556)) + (-5 *2 (-407 (-948 *4))))) + ((*1 *2 *1 *3) + (-12 (-5 *3 (-564)) (-4 *1 (-1219 *4)) (-4 *4 (-1045)) (-4 *4 (-556)) + (-5 *2 (-407 (-948 *4)))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-820))))) +(((*1 *1 *1 *2 *2) + (-12 (-5 *2 (-564)) (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3))))) (((*1 *2 *3) (-12 (-5 *3 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3346 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -2760 (-641 (-225))))) (-5 *2 (-641 (-1170))) (-5 *1 (-267)))) ((*1 *2 *3) (-12 (-5 *3 (-1166 *7)) (-4 *7 (-945 *6 *4 *5)) (-4 *4 (-789)) @@ -10555,7 +10191,7 @@ (-5 *1 (-946 *4 *5 *6 *7 *3)) (-4 *3 (-13 (-363) - (-10 -8 (-15 -2322 ($ *7)) (-15 -4189 (*7 $)) (-15 -4201 (*7 $))))))) + (-10 -8 (-15 -2344 ($ *7)) (-15 -4204 (*7 $)) (-15 -4216 (*7 $))))))) ((*1 *2 *1) (-12 (-4 *1 (-969 *3 *4 *5)) (-4 *3 (-1045)) (-4 *4 (-788)) (-4 *5 (-846)) (-5 *2 (-641 *5)))) @@ -10565,8 +10201,12 @@ ((*1 *2 *3) (-12 (-5 *3 (-407 (-948 *4))) (-4 *4 (-556)) (-5 *2 (-641 (-1170))) (-5 *1 (-1039 *4))))) -(((*1 *2 *2) (-12 (-5 *1 (-159 *2)) (-4 *2 (-545)))) - ((*1 *1 *2) (-12 (-5 *2 (-641 (-564))) (-5 *1 (-967))))) +(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-818))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-1166 *2)) (-4 *2 (-945 (-407 (-948 *6)) *5 *4)) + (-5 *1 (-728 *5 *4 *6 *2)) (-4 *5 (-789)) + (-4 *4 (-13 (-846) (-10 -8 (-15 -3193 ((-1170) $))))) + (-4 *6 (-556))))) (((*1 *2 *3) (-12 (-5 *3 (-1152)) (-5 *2 (-312)) (-5 *1 (-296)))) ((*1 *2 *3) (-12 (-5 *3 (-641 (-1152))) (-5 *2 (-312)) (-5 *1 (-296)))) @@ -10574,21 +10214,30 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-641 (-1152))) (-5 *3 (-1152)) (-5 *2 (-312)) (-5 *1 (-296))))) -(((*1 *2 *3 *4) - (-12 (-4 *2 (-1235 *4)) (-5 *1 (-803 *4 *2 *3 *5)) - (-4 *4 (-13 (-363) (-147) (-1034 (-407 (-564))))) (-4 *3 (-652 *2)) - (-4 *5 (-652 (-407 *2))))) +(((*1 *2 *1 *1) 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*4 *3 *5))))) +(((*1 *2 *3) + (-12 (-14 *4 (-641 (-1170))) (-4 *5 (-452)) + (-5 *2 + (-2 (|:| |glbase| (-641 (-247 *4 *5))) (|:| |glval| (-641 (-564))))) + (-5 *1 (-629 *4 *5)) (-5 *3 (-641 (-247 *4 *5)))))) (((*1 *2 *1) (-12 (-5 *2 (-1129)) (-5 *1 (-96)))) ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-109)))) ((*1 *2 *1) @@ -11194,24 +10761,15 @@ ((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-1069 *3)) (-14 *3 *2))) ((*1 *2 *1) (-12 (-5 *2 (-506)) (-5 *1 (-1109)))) ((*1 *1 *1) (-5 *1 (-1170)))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-556) (-147))) (-5 *1 (-537 *3 *2)) - (-4 *2 (-1250 *3)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-4 *4 (-1235 *3)) - (-4 *5 (-720 *3 *4)) (-5 *1 (-541 *3 *4 *5 *2)) (-4 *2 (-1250 *5)))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-363) (-368) (-612 (-564)))) (-5 *1 (-542 *3 *2)) - (-4 *2 (-1250 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1150 *3)) (-4 *3 (-13 (-556) (-147))) - (-5 *1 (-1146 *3))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1172 (-407 (-564)))) (-5 *1 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(-4 *4 (-1094)) + (-5 *1 (-113 *4)))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-114)) (-5 *2 (-1 *4 (-641 *4))) + (-5 *1 (-113 *4)) (-4 *4 (-1094)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *4 *4)) (-4 *4 (-644 *3)) (-4 *3 (-1045)) + (-5 *1 (-710 *3 *4)))) + ((*1 *1 *1 *2) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-832 *3))))) (((*1 *1) (-12 (-4 *1 (-465 *2 *3)) (-4 *2 (-172)) (-4 *3 (-23)))) ((*1 *1) (-5 *1 (-536))) ((*1 *1) (-4 *1 (-718))) ((*1 *1) (-4 *1 (-722))) ((*1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-1094)))) ((*1 *1) (-12 (-5 *1 (-889 *2)) (-4 *2 (-846))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1259 (-316 (-225)))) + (-5 *2 + (-2 (|:| |additions| (-564)) (|:| |multiplications| (-564)) + (|:| |exponentiations| (-564)) (|:| |functionCalls| (-564)))) + (-5 *1 (-305))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-564)) (|has| *1 (-6 -4407)) (-4 *1 (-1247 *3)) + (-4 *3 (-1209))))) (((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172)))) ((*1 *2 *3) (-12 (-4 *4 (-13 (-556) (-846) (-1034 (-564)))) (-5 *2 (-316 *4)) @@ -11263,23 +10901,11 @@ ((*1 *2 *2) (-12 (-4 *3 (-13 (-452) (-846) (-1034 (-564)) (-637 (-564)))) (-5 *1 (-1198 *3 *2)) (-4 *2 (-13 (-27) (-1194) (-430 *3)))))) -(((*1 *2 *2) - (-12 (-4 *3 (-1034 (-564))) (-4 *3 (-13 (-846) (-556))) - (-5 *1 (-32 *3 *2)) (-4 *2 (-430 *3)))) - ((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-1166 *4)) (-5 *1 (-165 *3 *4)) - (-4 *3 (-166 *4)))) - ((*1 *1 *1) (-12 (-4 *1 (-1045)) (-4 *1 (-302)))) - ((*1 *2) (-12 (-4 *1 (-329 *3)) (-4 *3 (-363)) (-5 *2 (-1166 *3)))) - ((*1 *2) (-12 (-4 *1 (-720 *3 *2)) (-4 *3 (-172)) (-4 *2 (-1235 *3)))) - ((*1 *2 *1) - (-12 (-4 *1 (-1062 *3 *2)) (-4 *3 (-13 (-844) (-363))) - (-4 *2 (-1235 *3))))) (((*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -4195 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3533 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 @@ -11297,7 +10923,7 @@ (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) - (|:| -4195 + (|:| -3533 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") @@ -11305,56 +10931,67 @@ "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-559))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-407 (-564))) (-5 *1 (-225)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-407 (-564))) (-5 *1 (-225)))) - ((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-407 (-564))) (-5 *1 (-379)))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-767)) (-5 *2 (-407 (-564))) (-5 *1 (-379))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| -1632 (-379)) (|:| -2420 (-1152)) - (|:| |explanations| (-641 (-1152))))) - (-5 *2 (-1031)) (-5 *1 (-305)))) - ((*1 *2 *3) +(((*1 *2 *1) (-12 (-4 *1 (-389)) (-5 *2 (-112))))) +(((*1 *1 *2) (-12 - (-5 *3 - (-2 (|:| -1632 (-379)) (|:| -2420 (-1152)) - (|:| |explanations| (-641 (-1152))) (|:| |extra| (-1031)))) - (-5 *2 (-1031)) (-5 *1 (-305))))) + (-5 *2 + (-641 + (-2 + (|:| -3090 + (-2 (|:| |xinit| (-225)) (|:| |xend| (-225)) + (|:| |fn| (-1259 (-316 (-225)))) + (|:| |yinit| (-641 (-225))) (|:| |intvals| (-641 (-225))) + (|:| |g| (-316 (-225))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -2538 + (-2 (|:| |stiffness| (-379)) (|:| |stability| (-379)) + (|:| |expense| (-379)) (|:| |accuracy| (-379)) + (|:| |intermediateResults| (-379))))))) + (-5 *1 (-799))))) +(((*1 *2 *2 *3) + (-12 (-5 *3 (-641 (-1170))) (-4 *4 (-1094)) + (-4 *5 (-13 (-1045) (-882 *4) (-846) (-612 (-888 *4)))) + (-5 *1 (-54 *4 *5 *2)) + (-4 *2 (-13 (-430 *5) (-882 *4) (-612 (-888 *4))))))) +(((*1 *1) (-5 *1 (-144))) ((*1 *1 *1) (-5 *1 (-858)))) +(((*1 *2 *3 *3 *4 *5 *3 *3 *4 *4 *4 *6) + (-12 (-5 *4 (-564)) (-5 *5 (-685 (-225))) + (-5 *6 (-3 (|:| |fn| (-388)) (|:| |fp| (-64 -2308)))) (-5 *3 (-225)) + (-5 *2 (-1031)) (-5 *1 (-744))))) 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*4))))) (((*1 *1) (-4 *1 (-23))) ((*1 *1) (-12 (-4 *1 (-470 *2 *3)) (-4 *2 (-172)) (-4 *3 (-23)))) ((*1 *1) (-5 *1 (-536))) ((*1 *1) (-12 (-5 *1 (-888 *2)) (-4 *2 (-1094))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1150 (-564))) (-5 *1 (-1154 *4)) (-4 *4 (-1045)) - (-5 *3 (-564))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-1259 *1)) (-4 *1 (-370 *4 *5)) (-4 *4 (-172)) + (-4 *5 (-1235 *4)) (-5 *2 (-685 *4)))) + ((*1 *2 *1) + (-12 (-4 *1 (-409 *3 *4)) (-4 *3 (-172)) (-4 *4 (-1235 *3)) + (-5 *2 (-685 *3))))) (((*1 *1 *1) (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) @@ -11364,66 +11001,45 @@ ((*1 *1 *2) (-12 (-5 *2 (-407 (-564))) (-4 *1 (-1008)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1008)) (-5 *2 (-917)))) ((*1 *1 *1) (-4 *1 (-1008)))) -(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-157)))) - ((*1 *2 *1) (-12 (-5 *2 (-157)) (-5 *1 (-870)))) - ((*1 *2 *3) (-12 (-5 *3 (-939 *2)) (-5 *1 (-978 *2)) (-4 *2 (-1045))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 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*3 (|[\|\|]| (-225))) (-5 *2 (-112)) (-5 *1 (-1175)))) ((*1 *2 *1 *3) (-12 (-5 *3 (|[\|\|]| (-564))) (-5 *2 (-112)) (-5 *1 (-1175))))) -(((*1 *2 *1) - (-12 (-4 *1 (-1097 *3 *4 *5 *6 *7)) (-4 *3 (-1094)) (-4 *4 (-1094)) - (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *7 (-1094)) (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-846)) (-5 *2 (-1181 (-641 *4))) (-5 *1 (-1180 *4)) + (-5 *3 (-641 *4))))) +(((*1 *2 *3) + (-12 (-4 *4 (-1045)) (-4 *3 (-1235 *4)) (-4 *2 (-1250 *4)) + (-5 *1 (-1253 *4 *3 *5 *2)) (-4 *5 (-652 *3))))) (((*1 *2 *3 *4) (-12 (-5 *4 (-641 (-48))) (-5 *2 (-418 *3)) (-5 *1 (-39 *3)) (-4 *3 (-1235 (-48))))) @@ -11549,8 +11168,8 @@ (-12 (-4 *4 (-13 (-846) - (-10 -8 (-15 -3172 ((-1170) $)) - (-15 -3256 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -3193 ((-1170) $)) + (-15 -3282 ((-3 $ "failed") (-1170)))))) (-4 *5 (-789)) (-4 *7 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-456 *4 *5 *6 *7 *3)) (-4 *6 (-556)) (-4 *3 (-945 *7 *5 *4)))) @@ -11599,13 +11218,13 @@ (-12 (-4 *4 (-789)) (-4 *5 (-13 (-846) - (-10 -8 (-15 -3172 ((-1170) $)) - (-15 -3256 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -3193 ((-1170) $)) + (-15 -3282 ((-3 $ "failed") (-1170)))))) (-4 *6 (-307)) (-5 *2 (-418 *3)) (-5 *1 (-726 *4 *5 *6 *3)) (-4 *3 (-945 (-948 *6) *4 *5)))) ((*1 *2 *3) (-12 (-4 *4 (-789)) - (-4 *5 (-13 (-846) (-10 -8 (-15 -3172 ((-1170) $))))) (-4 *6 (-556)) + (-4 *5 (-13 (-846) (-10 -8 (-15 -3193 ((-1170) $))))) (-4 *6 (-556)) (-5 *2 (-418 *3)) (-5 *1 (-728 *4 *5 *6 *3)) (-4 *3 (-945 (-407 (-948 *6)) *4 *5)))) ((*1 *2 *3) @@ -11641,147 +11260,160 @@ ((*1 *2 *1) (-12 (-5 *2 (-418 *1)) (-4 *1 (-1213)))) ((*1 *2 *3) (-12 (-5 *2 (-418 *3)) (-5 *1 (-1224 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) +(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-561)))) + ((*1 *2 *3) + (-12 (-5 *2 (-1166 (-407 (-564)))) (-5 *1 (-938)) (-5 *3 (-564))))) (((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-641 *5) *6)) - (-4 *5 (-13 (-363) (-147) (-1034 (-407 (-564))))) (-4 *6 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+(((*1 *2 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) + ((*1 *2 *2 *2) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-431 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *1 *1 *1) (-4 *1 (-1133)))) (((*1 *2 *3) - (-12 (-4 *4 (-13 (-363) (-10 -8 (-15 ** ($ $ (-407 (-564))))))) - (-5 *2 (-641 *4)) (-5 *1 (-1122 *3 *4)) (-4 *3 (-1235 *4)))) - ((*1 *2 *3 *3 *3 *3 *3) - (-12 (-4 *3 (-13 (-363) (-10 -8 (-15 ** ($ $ (-407 (-564))))))) - (-5 *2 (-641 *3)) (-5 *1 (-1122 *4 *3)) (-4 *4 (-1235 *3))))) + (-12 (-4 *4 (-1235 (-407 *2))) (-5 *2 (-564)) (-5 *1 (-909 *4 *3)) + (-4 *3 (-1235 (-407 *4)))))) +(((*1 *2 *1) + (|partial| -12 (-4 *3 (-452)) (-4 *4 (-846)) (-4 *5 (-789)) + (-5 *2 (-112)) (-5 *1 (-983 *3 *4 *5 *6)) + (-4 *6 (-945 *3 *5 *4)))) + ((*1 *2 *1) + (-12 (-5 *2 (-112)) (-5 *1 (-1134 *3 *4)) (-4 *3 (-13 (-1094) (-34))) + (-4 *4 (-13 (-1094) (-34)))))) (((*1 *1 *2) (-12 (-5 *2 (-641 *3)) (-4 *3 (-1209)) (-4 *1 (-151 *3)))) ((*1 *1 *2) (-12 - (-5 *2 (-641 (-2 (|:| -3866 (-767)) (|:| -2965 *4) (|:| |num| *4)))) + (-5 *2 (-641 (-2 (|:| -1469 (-767)) (|:| -2350 *4) (|:| |num| *4)))) (-4 *4 (-1235 *3)) (-4 *3 (-13 (-363) (-147))) (-5 *1 (-399 *3 *4)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3734 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3761 "void"))) (-5 *3 (-641 (-948 (-564)))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *1 *2 *3 *4) - (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3734 "void"))) + (-12 (-5 *2 (-3 (|:| |fst| (-434)) (|:| -3761 "void"))) (-5 *3 (-641 (-1170))) (-5 *4 (-112)) (-5 *1 (-437)))) ((*1 *2 *1) (-12 (-5 *2 (-1150 *3)) (-5 *1 (-599 *3)) (-4 *3 (-1209)))) @@ -11860,24 +11511,24 @@ ((*1 *1 *2 *3) (-12 (-5 *1 (-709 *2 *3 *4)) (-4 *2 (-846)) (-4 *3 (-1094)) (-14 *4 - (-1 (-112) (-2 (|:| -1998 *2) (|:| -3866 *3)) - (-2 (|:| -1998 *2) (|:| -3866 *3)))))) + (-1 (-112) (-2 (|:| -2017 *2) (|:| -1469 *3)) + (-2 (|:| -2017 *2) (|:| -1469 *3)))))) ((*1 *1 *2 *3) (-12 (-5 *2 (-506)) (-5 *3 (-1112)) (-5 *1 (-834)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-869 *2 *3)) (-4 *2 (-1209)) (-4 *3 (-1209)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -3076 (-1170)) (|:| -2511 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -3090 (-1170)) (|:| -2538 *4)))) (-4 *4 (-1094)) (-5 *1 (-885 *3 *4)) (-4 *3 (-1094)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-641 *5)) (-4 *5 (-13 (-1094) (-34))) (-5 *2 (-641 (-1134 *3 *5))) (-5 *1 (-1134 *3 *5)) (-4 *3 (-13 (-1094) (-34))))) ((*1 *2 *3) - (-12 (-5 *3 (-641 (-2 (|:| |val| *4) (|:| -2244 *5)))) + (-12 (-5 *3 (-641 (-2 (|:| |val| *4) (|:| -2266 *5)))) (-4 *4 (-13 (-1094) (-34))) (-4 *5 (-13 (-1094) (-34))) (-5 *2 (-641 (-1134 *4 *5))) (-5 *1 (-1134 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2244 *4))) + (-12 (-5 *2 (-2 (|:| |val| *3) (|:| -2266 *4))) (-4 *3 (-13 (-1094) (-34))) (-4 *4 (-13 (-1094) (-34))) (-5 *1 (-1134 *3 *4)))) ((*1 *1 *2 *3) @@ -11900,105 +11551,140 @@ (-4 *4 (-13 (-1094) (-34))) (-5 *1 (-1135 *3 *4)))) ((*1 *1 *2 *3) (-12 (-5 *1 (-1159 *2 *3)) (-4 *2 (-1094)) (-4 *3 (-1094))))) -(((*1 *1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-529)))) - ((*1 *1 *2) (-12 (-5 *2 (-388)) (-5 *1 (-529))))) -(((*1 *2 *3 *4 *2) - (-12 (-5 *2 (-641 (-2 (|:| |totdeg| (-767)) (|:| -3429 *3)))) - (-5 *4 (-767)) (-4 *3 (-945 *5 *6 *7)) (-4 *5 (-452)) (-4 *6 (-789)) - (-4 *7 (-846)) (-5 *1 (-449 *5 *6 *7 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-888 *3)) (-4 *3 (-1094))))) +(((*1 *1 *2 *3) + (-12 (-5 *3 (-641 (-506))) (-5 *2 (-506)) (-5 *1 (-483))))) (((*1 *2 *1) - (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-4 *3 (-556)) - (-5 *2 (-1166 *3))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-431 *3 *2)) - (-4 *2 (-430 *3))))) + (-12 + (-5 *2 + (-641 + (-2 + (|:| -3090 + (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) + (|:| -3533 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| |relerr| (-225)))) + (|:| -2538 + (-2 + (|:| |endPointContinuity| + (-3 (|:| |continuous| "Continuous at the end points") + (|:| |lowerSingular| + "There is a singularity at the lower end point") + (|:| |upperSingular| + "There is a singularity at the upper end point") + (|:| |bothSingular| + "There are singularities at both end points") + (|:| |notEvaluated| + "End point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1150 (-225))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -3533 + (-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 (-559)))) + ((*1 *2 *1) + (-12 (-4 *1 (-602 *3 *4)) (-4 *3 (-1094)) (-4 *4 (-1209)) + (-5 *2 (-641 *4))))) (((*1 *1 *1) (-4 *1 (-123))) ((*1 *1 *1) (-5 *1 (-858))) ((*1 *1 *1) (-4 *1 (-963))) ((*1 *1 *1) (-5 *1 (-1114)))) -(((*1 *2 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172)) (-4 *2 (-1194)))) - ((*1 *2 *1) (-12 (-5 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(-2355) (-695)))) (-5 *1 (-84 *3)) (-14 *3 (-1170)))) ((*1 *1 *2) - (-12 (-5 *2 (-1259 (-339 (-2335 'X) (-2335) (-695)))) + (-12 (-5 *2 (-1259 (-339 (-2355 'X) (-2355) (-695)))) (-5 *1 (-85 *3)) (-14 *3 (-1170)))) ((*1 *1 *2) - (-12 (-5 *2 (-1259 (-339 (-2335 'X) (-2335 '-2266) (-695)))) + (-12 (-5 *2 (-1259 (-339 (-2355 'X) (-2355 '-2288) (-695)))) (-5 *1 (-86 *3)) (-14 *3 (-1170)))) ((*1 *1 *2) - (-12 (-5 *2 (-685 (-339 (-2335 'XL 'XR 'ELAM) (-2335) (-695)))) + (-12 (-5 *2 (-685 (-339 (-2355 'XL 'XR 'ELAM) (-2355) (-695)))) (-5 *1 (-87 *3)) (-14 *3 (-1170)))) ((*1 *1 *2) - (-12 (-5 *2 (-339 (-2335 'X) (-2335 '-2266) (-695))) (-5 *1 (-89 *3)) + (-12 (-5 *2 (-339 (-2355 'X) (-2355 '-2288) (-695))) (-5 *1 (-89 *3)) (-14 *3 (-1170)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-136 *3 *4 *5))) (-5 *1 (-136 *3 *4 *5)) @@ -12049,85 +11735,85 @@ ((*1 *1 *2) (-12 (-4 *1 (-374 *2 *3)) (-4 *2 (-846)) (-4 *3 (-172)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3080 (-641 (-330))))) + 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|localSymbols| (-1174)) (|:| -3080 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3093 (-641 (-330))))) (-5 *1 (-398 *3 *4 *5 *6)) (-14 *3 (-1170)) - (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3734 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3761 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-5 *1 (-398 *3 *4 *5 *6)) - (-14 *3 (-1170)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3734 "void"))) + (-14 *3 (-1170)) (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3761 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-5 *1 (-398 *3 *4 *5 *6)) (-14 *3 (-1170)) - (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3734 "void"))) + (-14 *4 (-3 (|:| |fst| (-434)) (|:| -3761 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-331 *4)) (-4 *4 (-13 (-846) (-21))) @@ -12154,14 +11840,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-434)) (-5 *1 (-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3080 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3093 (-641 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1259 (-695))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3080 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3093 (-641 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-441)))) @@ -12230,7 +11916,7 @@ (-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 (-641 (-2 (|:| -3139 *3) (|:| -1955 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -3154 *3) (|:| -1970 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-759)))) ((*1 *1 *2) @@ -12239,25 +11925,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -4195 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3533 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -4195 (-641 (-1088 (-839 (-225))))) + (|:| -3533 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -4195 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) + (|:| -3533 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -4195 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -3533 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *2 *3) (-12 (-5 *2 (-770)) (-5 *1 (-769 *3)) (-4 *3 (-1209)))) @@ -12275,23 +11961,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -3346 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -2760 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -3346 (-641 (-225))))))) + (|:| -2760 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3346 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -2760 (-641 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -3346 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -2760 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (-5 *1 (-837)))) @@ -12392,74 +12078,136 @@ ((*1 *1 *2) (-12 (-5 *2 (-660 *3 *4)) (-4 *3 (-846)) (-4 *4 (-172)) (-5 *1 (-1279 *3 *4))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-529)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-577)))) + ((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-857))))) (((*1 *2 *1) - (-12 (-5 *2 (-687 (-869 (-962 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