diff options
| -rw-r--r-- | src/ChangeLog | 4 | ||||
| -rw-r--r-- | src/algebra/syntax.spad.pamphlet | 5 | ||||
| -rw-r--r-- | src/interp/sys-utility.boot | 1 | ||||
| -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 | 1321 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8896 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 29986 |
8 files changed, 21037 insertions, 21028 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 983ebcb7..65af902d 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,9 @@ 2009-04-24 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/syntax.spad.pamphlet (new$Identifier): New. + +2009-04-24 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/strap/ULSCAT.lsp: Remove. 2009-04-24 Gabriel Dos Reis <gdr@cs.tamu.edu> diff --git a/src/algebra/syntax.spad.pamphlet b/src/algebra/syntax.spad.pamphlet index 359942fd..acbf8892 100644 --- a/src/algebra/syntax.spad.pamphlet +++ b/src/algebra/syntax.spad.pamphlet @@ -562,8 +562,11 @@ Literal(T: SetCategory): Public == Private where ++ )abbrev domain IDENT Identifier Identifier(): Public == Private where - Public == Join(SetCategory, CoercibleTo Symbol) + Public == Join(SetCategory, CoercibleTo Symbol) with + new: () -> % ++ returns a new identifier, different from + ++ any other identifier in the running system Private == add + new() == GENSYM()$Foreign(Builtin) x = y == EQ(x,y)$Lisp coerce(x: %): Symbol == x : Symbol coerce(x: %): OutputForm == x : OutputForm diff --git a/src/interp/sys-utility.boot b/src/interp/sys-utility.boot index 5192ded1..8cc18dc5 100644 --- a/src/interp/sys-utility.boot +++ b/src/interp/sys-utility.boot @@ -70,6 +70,7 @@ getVMType d == STRINGP d => "%Thing" -- literal flag parameter case (d' := devaluate d) of Void => "%Void" + Identiifier => "%Symbol" Boolean => "%Boolean" Byte => "%Byte" Character => "%Char" diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 84cf1c25..f71153ac 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2283252 . 3449460961) +(2283354 . 3449600530) (-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 -3446) +(-32 R -3378) ((|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 -1035) (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 -3446 UP UPUP -1869) +(-40 -3378 UP UPUP -4022) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4005 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4005 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4005 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4005 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -3446) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4002 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4002 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4002 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -3378) ((|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 (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (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."))) ((-4411 . T) (-4412 . T)) -((-4005 (-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|))))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|))))))) +((-4002 (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|))))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3446) +(-54 |Base| R -3378) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|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}"))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-61 -4346) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-61 -4363) ((|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 -4346) +(-62 -4363) ((|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 -4346) +(-63 -4363) ((|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 -4346) +(-64 -4363) ((|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 -4346) +(-65 -4363) ((|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 -4346) +(-66 -4363) ((|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 -4346) +(-67 -4363) ((|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 -4346) +(-68 -4363) ((|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 -4346) +(-69 -4363) ((|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 -4346) +(-70 -4363) ((|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 -4346) +(-71 -4363) ((|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 -4346) +(-72 -4363) ((|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 -4346) +(-73 -4363) ((|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 -4346) +(-74 -4363) ((|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 -4346) +(-77 -4363) ((|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 -4346) +(-78 -4363) ((|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 -4346) +(-79 -4363) ((|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 -4346) +(-80 -4363) ((|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 -4346) +(-81 -4363) ((|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 -4346) +(-82 -4363) ((|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 -4346) +(-83 -4363) ((|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 -4346) +(-84 -4363) ((|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 -4346) +(-85 -4363) ((|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 -4346) +(-86 -4363) ((|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 -4346) +(-87 -4363) ((|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 -4346) +(-88 -4363) ((|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 -4346) +(-89 -4363) ((|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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4005 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|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| (((|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!| (($ $ (|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.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|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}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -3446 UP) +(-115 -3378 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}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4005 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (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 (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-906))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1019))) (|HasCategory| (-116 |#1|) (QUOTE (-817))) (-4002 (|HasCategory| (-116 |#1|) (QUOTE (-817))) (|HasCategory| (-116 |#1|) (QUOTE (-847)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -897) (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 (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-906)))) (|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"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4005 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-4002 (-12 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-4002 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-859)))) (-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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4413 "*") . T)) NIL -(-135 |minix| -2879 S T$) +(-135 |minix| -2592 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2879 R) +(-136 |minix| -2592 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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}."))) ((-4411 . T) (-4401 . T) (-4412 . T)) -((-4005 (-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 (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4002 (-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 (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-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."))) ((-4408 . T)) NIL -(-148 -3446 UP UPUP) +(-148 -3378 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 -3446) +(-158 R -3378) ((|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 (-906))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-999))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1055))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4407)) (|HasAttribute| |#2| (QUOTE -4410)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-847)))) (-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})"))) -((-4404 -4005 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2471 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4404 -4002 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2305 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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}."))) -((-4404 -4005 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4407 |has| |#1| (-6 -4407)) (-4410 |has| |#1| (-6 -4410)) (-2471 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| 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(QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (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 (-825))) (|HasCategory| |#1| (QUOTE (-1055))) (-12 (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasAttribute| |#1| (QUOTE -4407)) (|HasAttribute| |#1| (QUOTE -4410)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-906)))) (|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| $) (|Symbol|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -3446) +(-188 R -3378) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -3446 UP UPUP R) +(-215 -3378 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 -3446 FP) +(-216 -3378 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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4005 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|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|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -3446) +(-219 R -3378) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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}."))) ((-4408 . T)) NIL -(-224 R -3446) +(-224 R -3378) ((|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}."))) -((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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 -2879 R) +(-237 S -2592 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 (-790))) (|HasCategory| |#3| (QUOTE (-845))) (|HasAttribute| |#3| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-723))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -2879 R) +(-238 -2592 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"))) ((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . T)) NIL -(-239 -2879 A B) +(-239 -2592 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 -2879 R) +(-240 -2592 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."))) ((-4405 |has| |#2| (-1046)) (-4406 |has| |#2| (-1046)) (-4408 |has| |#2| (-6 -4408)) ((-4413 "*") |has| |#2| (-172)) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-723))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-790))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST 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(|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -911,7 +911,7 @@ NIL (-245 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}"))) ((-4412 . T) (-4411 . 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(|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL @@ -919,7 +919,7 @@ NIL (-247 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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(|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}.")) (|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Create: October 18,{} 2007. Date Last Updated: December 20,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall") (((|DomainConstructor|) $) "\\spad{constructor(d)} returns the domain constructor that is instantiated to the domain object \\spad{`d'}."))) 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(QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-4002 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (|HasCategory| |#3| (QUOTE (-723))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-4002 (|HasCategory| |#3| (QUOTE (-1046))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-4002 (|HasAttribute| |#3| (QUOTE -4408)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859)))) (-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"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|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 -3446) +(-276 R -3378) ((|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 -3446) +(-277 R -3378) ((|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| -3560 -1445 |exactQuo|) +(-289 S R |Mod| -3753 -4012 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-296) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-297 -3446 S) +(-297 -3378 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 -3446) +(-298 E -3378) ((|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 -3446) +(-310 -3378) ((|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))}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (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 (-1019))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (-4005 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (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 -897) (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 (-847))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-4005 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (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 (-1019))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (-4002 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-817))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-847)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -889) (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 -897) (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 (-847))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|HasCategory| $ (QUOTE (-145)))) (-4002 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-906))) (|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."))) -((-4408 -4005 (-4260 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-4005 (-4260 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1046)) (|has| |#1| (-473)))) (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 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(QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4005 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) -(-317 R -3446) +((-4408 -4002 (-4266 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-4002 (-4266 (|has| |#1| (-1046)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1046)) (|has| |#1| (-473)))) (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) 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(-4002 (|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 (-1046)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4002 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4002 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-4002 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-4002 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1046)))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1046))) (|HasCategory| $ (LIST (QUOTE -1035) (QUOTE (-564))))) +(-317 R -3378) ((|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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4005 (|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 -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|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 -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -3446) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -3378) ((|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 -3446) +(-329 -3378) ((|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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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 -3446 UP UPUP R) +(-334 S -3378 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 -3446 UP UPUP R) +(-335 -3378 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 -3446 UP UPUP R) +(-336 -3378 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 -3446 UP UPUP) +(-341 S -3378 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 -3446 UP UPUP) +(-342 -3378 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."))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4002 (|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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4002 (|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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-350 R UP -3446) +(-350 R UP -3378) ((|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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4002 (|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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4002 (|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}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#1|) (QUOTE (-145)))) +((-4002 (|HasCategory| (-907 |#1|) (QUOTE (-145))) (|HasCategory| (-907 |#1|) (QUOTE (-368)))) (|HasCategory| (-907 |#1|) (QUOTE (-147))) (|HasCategory| (-907 |#1|) (QUOTE (-368))) (|HasCategory| (-907 |#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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -3446 GF) +((-4002 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -3378 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 -3446 FP FPP) +(-358 -3378 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}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-4002 (|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}."))) -((-4394 . T) (-4402 . T) (-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-4394 . T) (-4402 . T) (-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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 -3446 UP UPUP R) +(-392 -3378 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 -4346 |returnType| -2829 |symbols|) +(-398 -4363 |returnType| -4229 |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 -3446 UP) +(-399 -3378 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| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4394)) (|HasAttribute| |#1| (QUOTE -4402))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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."))) ((-4398 -12 (|has| |#1| (-6 -4409)) (|has| |#1| (-452)) (|has| |#1| (-6 -4398))) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4005 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (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 (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4398)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (QUOTE (-817))) (-4002 (|HasCategory| |#1| (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-847)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-825))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (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 (-825)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4409)) (|HasAttribute| |#1| (QUOTE -4398)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|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| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -3446 UP A) +(-413 R -3378 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) ((-4408 . T)) NIL -(-414 R -3446 UP A |ibasis|) +(-414 R -3378 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 -1035) (|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."))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (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 -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1019))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (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 -897) (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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4411 . T) (-4401 . T) (-4412 . T)) NIL -(-426 R -3446) +(-426 R -3378) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) ((-4398 -12 (|has| |#1| (-6 -4398)) (|has| |#2| (-6 -4398))) (-4405 . T) (-4406 . T) (-4408 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4398)) (|HasAttribute| |#2| (QUOTE -4398)))) -(-428 R -3446) +(-428 R -3378) ((|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 -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1046))) (|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}."))) -((-4408 -4005 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-556)) (-4403 |has| |#1| (-556))) +((-4408 -4002 (|has| |#1| (-1046)) (|has| |#1| (-473))) (-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-556)) (-4403 |has| |#1| (-556))) NIL -(-431 R -3446) +(-431 R -3378) ((|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 -3446) +(-432 R -3378) ((|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 -3446) +(-433 R -3378) ((|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 -3446 UP) +(-435 R -3378 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 -1035) (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 -3446) +(-443 R UP -3378) ((|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"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|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| -3446 R) +(-471 |lv| -3378 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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4005 (|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 -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|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 -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-475 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094)))) (-476 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{TriangularSetCategory}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members but they are displayed in reverse order.\\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}"))) ((-4412 . T) (-4411 . 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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-480) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -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.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-790))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-845))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-847))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1046)))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4002 (|HasCategory| |#2| (QUOTE (-1046))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) -(-485 -3446 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +(-485 -3378 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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4005 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|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 -3446 UP |AlExt| |AlPol|) +(-494 -3378 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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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 -3446) +(-499 R UP -3378) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -3446 |Expon| |VarSet| |DPoly|) +(-504 -3378 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#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}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1953,7 +1953,7 @@ NIL NIL NIL (-506) -((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline"))) +((|constructor| (NIL "This domain represents identifer AST. This domain differs from Symbol in that it does not support any form of scripting. A value of this domain is a plain old identifier. \\blankline")) (|new| (($) "returns a new identifier,{} different from any other identifier in the running system"))) NIL NIL (-507 A S) @@ -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}"))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((-4005 (|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)))) +((-4002 (|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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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 -3446 |Par|) +(-532 K -3378 |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 -3446 |Par|) +(-538 K -3378 |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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) -(-551 R -3446) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +(-551 R -3378) ((|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 -3446 UP UPUP R) +(-552 R0 -3378 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."))) -((-2460 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2299 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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."))) ((-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-557 R -3446) +(-557 R -3378) ((|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 -3446 L) +(-560 R -3378 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 -3446 UP UPUP R) +(-562 -3378 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 -3446 UP) +(-563 -3378 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 -3446 L) +(-566 R -3378 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 -3446) +(-567 R -3378) ((|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 -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -3446 UP) +(-568 -3378 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 -3446) +(-570 -3378) ((|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."))) -((-2460 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2299 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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 -3446) +(-573 R -3378) ((|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 -889) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -3446 UP) +(-574 -3378 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 -3446) +(-575 R -3378) ((|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 -3446) +(-583 R -3378) ((|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 -3446) +(-584 E -3378) ((|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 -3446) +(-585 -3378) ((|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}."))) ((-4406 . T) (-4405 . T)) ((|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (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"))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4005 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4002 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-4002 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4005 (|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 -897) (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 -3708) (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))) (-4002 (|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 -897) (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 -1765) (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.}"))) ((-4406 |has| |#1| (-556)) (-4405 |has| |#1| (-556)) ((-4413 "*") |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4408 . 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 -3446 FG) +(-598 R -3378 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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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)."))) -((-4408 -4005 (-4260 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4005 (|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|)))) (-4005 (-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|)))) +((-4408 -4002 (-4266 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) +((-4002 (|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|)))) (-4002 (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#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 (-847))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#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 (-847))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -3446 UP) +(-613 -3378 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-845)))) -(-620 R -3446) +(-620 R -3378) ((|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 -3446) +(-628 R -3378) ((|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| -3446) +(-629 |lv| -3378) ((|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."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 (-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)."))) -((-4408 -4005 (-4260 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) -((-4005 (|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|)))) (-4005 (-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|)))) +((-4408 -4002 (-4266 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4406 . T) (-4405 . T)) +((-4002 (|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|)))) (-4002 (-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 -((-4248 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-4254 (|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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4408 . T)) @@ -2495,7 +2495,7 @@ NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-825))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#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 -3446 L) +(-648 R -3378 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}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-653 -3446 UP) +(-653 -3378 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 -2933) +(-654 A -3691) ((|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}}"))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (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}."))) ((-4412 . T) (-4411 . T)) NIL -(-663 -3446) +(-663 -3378) ((|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 -3446 |Row| |Col| M) +(-664 -3378 |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."))) ((-4408 . T) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4005 (-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 -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4005 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (-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 -897) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-4002 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-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 -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (QUOTE (-1046))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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."))) ((-4411 . T) (-4412 . T)) -((-4005 (-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))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-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))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4413 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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 -3446 FLAF FLAS) +(-688 S -3378 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"))) -((-4404 . T) (-4409 |has| (-695) (-363)) (-4403 |has| (-695) (-363)) (-2471 . T) (-4410 |has| (-695) (-6 -4410)) (-4407 |has| (-695) (-6 -4407)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-4005 (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-4005 (|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 -883) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4005 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1019))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-999))) (|HasCategory| (-695) (QUOTE (-1194)))) (-4005 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (-4005 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906))) (-4005 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363)))) (-4005 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-847))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4410)) (|HasAttribute| (-695) (QUOTE -4407)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-145)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4404 . T) (-4409 |has| (-695) (-363)) (-4403 |has| (-695) (-363)) (-2305 . T) (-4410 |has| (-695) (-6 -4410)) (-4407 |has| (-695) (-6 -4407)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-4002 (|HasCategory| (-695) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-4002 (|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 -883) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (-4002 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1019))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-999))) (|HasCategory| (-695) (QUOTE (-1194)))) (-4002 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (-4002 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-906)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-906))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1055))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906))) (-4002 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-363)))) (-4002 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-847))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4410)) (|HasAttribute| (-695) (QUOTE -4407)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|HasCategory| (-695) (QUOTE (-145)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-906)))) (|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}."))) ((-4412 . 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 -3446 PG) +(-694 OV E -3378 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}"))) -((-2460 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) +((-2299 . T) (-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . 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."))) @@ -2740,7 +2740,7 @@ 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 -(-703 S -2265 I) +(-703 S -3190 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 @@ -2760,14 +2760,14 @@ 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 -(-708 R |Mod| -3560 -1445 |exactQuo|) +(-708 R |Mod| -3753 -4012 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-709 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-710 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2776,7 +2776,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#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| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4406 |has| |#1| (-172)) (-4405 |has| |#1| (-172)) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-712 R |Mod| -3560 -1445 |exactQuo|) +(-712 R |Mod| -3753 -4012 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4408 . T)) NIL @@ -2788,7 +2788,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4406 . T) (-4405 . T)) NIL -(-715 -3446) +(-715 -3378) ((|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]]}."))) ((-4408 . T)) NIL @@ -2824,7 +2824,7 @@ 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 -(-724 -3446 UP) +(-724 -3378 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 @@ -2843,7 +2843,7 @@ NIL (-728 |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."))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-861 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-729 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 @@ -2976,11 +2976,11 @@ 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 -(-762 -3446) +(-762 -3378) ((|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 -(-763 P -3446) +(-763 P -3378) ((|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 @@ -2988,7 +2988,7 @@ NIL NIL NIL NIL -(-765 UP -3446) +(-765 UP -3378) ((|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 @@ -3004,7 +3004,7 @@ 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."))) (((-4413 "*") . T)) NIL -(-769 R -3446) +(-769 R -3378) ((|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 @@ -3024,7 +3024,7 @@ 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 -(-774 -3446 |ExtF| |SUEx| |ExtP| |n|) +(-774 -3378 |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 @@ -3039,7 +3039,7 @@ NIL (-777 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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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\\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 @@ -3047,7 +3047,7 @@ NIL (-779 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| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4407 |has| |#1| (-363)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . 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(|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3108,23 +3108,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) NIL -(-795 -4005 R OS S) +(-795 -4002 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-796 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|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|))) (-4005 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-847))) (|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|))) (-4002 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-996 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (-797) ((|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 -(-798 R -3446 L) +(-798 R -3378 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 -(-799 R -3446) +(-799 R -3378) ((|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 @@ -3132,7 +3132,7 @@ 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 -(-801 R -3446) +(-801 R -3378) ((|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 @@ -3140,11 +3140,11 @@ 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 -(-803 -3446 UP UPUP R) +(-803 -3378 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 -(-804 -3446 UP L LQ) +(-804 -3378 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 @@ -3152,38 +3152,38 @@ 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 -(-806 -3446 UP L LQ) +(-806 -3378 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 -(-807 -3446 UP) +(-807 -3378 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 -(-808 -3446 L UP A LO) +(-808 -3378 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 -(-809 -3446 UP) +(-809 -3378 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)))) -(-810 -3446 LO) +(-810 -3378 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") (((|Record| (|:| A (|Matrix| |#1|)) (|:| |eqs| (|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)) (|:| |eq| |#2|) (|:| |rh| |#1|))))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{triangulate(M,{}v)} returns \\spad{A,{}[[C_1,{}g_1,{}L_1,{}h_1],{}...,{}[C_k,{}g_k,{}L_k,{}h_k]]} such that under the change of variable \\spad{y = A z},{} the first order linear system \\spad{D y = M y + v} is uncoupled as \\spad{D z_i = C_i z_i + g_i} and each \\spad{C_i} is a companion matrix corresponding to the scalar equation \\spad{L_i z_j = h_i}."))) NIL NIL -(-811 -3446 LODO) +(-811 -3378 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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|#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4408)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-813 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-815 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) (-814 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4413 "*") |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4409 |has| |#2| (-363)) (-4403 |has| |#2| (-363)) (-4408 . T) (-4406 . T) (-4405 . T)) @@ -3251,7 +3251,7 @@ NIL (-830 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."))) ((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4005 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4005 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-845))) (-4002 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-831 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 @@ -3291,12 +3291,12 @@ NIL (-840 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| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4408 |has| |#1| (-845))) -((|HasCategory| |#1| (QUOTE (-845))) (-4005 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4005 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-845))) (-4002 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-845)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#1| (QUOTE (-845))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-841) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-842 -2879 S) +(-842 -2592 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 @@ -3332,11 +3332,11 @@ 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)))) -(-851 R |sigma| -2759) +(-851 R |sigma| -2689) ((|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."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-852 |x| R |sigma| -2759) +(-852 |x| R |sigma| -2689) ((|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}."))) ((-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3403,15 +3403,15 @@ NIL (-868 |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)."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4005 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) +((|HasCategory| (-867 |#1|) (QUOTE (-906))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-147))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-867 |#1|) (QUOTE (-1019))) (|HasCategory| (-867 |#1|) (QUOTE (-817))) (-4002 (|HasCategory| (-867 |#1|) (QUOTE (-817))) (|HasCategory| (-867 |#1|) (QUOTE (-847)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-1145))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-867 |#1|) (QUOTE (-233))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -867) (|devaluate| |#1|)) (LIST (QUOTE -867) (|devaluate| |#1|)))) (|HasCategory| (-867 |#1|) (QUOTE (-307))) (|HasCategory| (-867 |#1|) (QUOTE (-545))) (|HasCategory| (-867 |#1|) (QUOTE (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-867 |#1|) (QUOTE (-906)))) (|HasCategory| (-867 |#1|) (QUOTE (-145))))) (-869 |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)}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4005 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (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 (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1019))) (|HasCategory| |#2| (QUOTE (-817))) (-4002 (|HasCategory| |#2| (QUOTE (-817))) (|HasCategory| |#2| (QUOTE (-847)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -897) (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 (-847))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) (-870 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)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))))) (-871) ((|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 @@ -3467,7 +3467,7 @@ NIL (-884 |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 (-4248 (|HasCategory| |#2| (QUOTE (-1046)))) (-4248 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4248 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) +((-12 (-4254 (|HasCategory| |#2| (QUOTE (-1046)))) (-4254 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1046))) (-4254 (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-1170))))) (-885 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 @@ -3476,7 +3476,7 @@ 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 -(-887 R -2265) +(-887 R -3190) ((|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 @@ -3500,7 +3500,7 @@ 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 -(-893 UP -3446) +(-893 UP -3378) ((|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 @@ -3523,7 +3523,7 @@ NIL (-898 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))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-899 |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 @@ -3539,7 +3539,7 @@ NIL (-902 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."))) ((-4408 . T)) -((-4005 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) +((-4002 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-847)))) (-903 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 @@ -3560,7 +3560,7 @@ 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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-908 R0 -3446 UP UPUP R) +(-908 R0 -3378 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 @@ -3588,7 +3588,7 @@ 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 -(-915 -3446) +(-915 -3378) ((|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 @@ -3604,11 +3604,11 @@ 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}."))) (((-4413 "*") . T)) NIL -(-919 -3446 P) +(-919 -3378 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-920 |xx| -3446) +(-920 |xx| -3378) ((|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 @@ -3632,7 +3632,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-926 R -3446) +(-926 R -3378) ((|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 @@ -3644,7 +3644,7 @@ 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 -(-929 S R -3446) +(-929 S R -3378) ((|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 @@ -3664,11 +3664,11 @@ 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 -883) (|devaluate| |#1|)))) -(-934 R -3446 -2265) +(-934 R -3378 -3190) ((|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 -(-935 -2265) +(-935 -3190) ((|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 @@ -3691,7 +3691,7 @@ NIL (-940 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-941 |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 @@ -3716,7 +3716,7 @@ 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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) NIL -(-947 E V R P -3446) +(-947 E V R P -3378) ((|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 @@ -3727,8 +3727,8 @@ NIL (-949 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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-950 E V R P -3446) +((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-950 E V R P -3378) ((|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| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3751,12 +3751,12 @@ NIL (-955 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-956) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|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 -(-957 -3446) +(-957 -3378) ((|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 @@ -3771,11 +3771,11 @@ NIL (-960 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}"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4409))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4409))) (-961 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"))) ((-4408 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4005 (-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 (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-4005 (-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 (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-4002 (-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 (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-4002 (-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 (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-790))) (|HasCategory| |#2| (QUOTE (-790))))) (-12 (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#2| (QUOTE (-723)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-847))))) (-962) ((|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 @@ -3856,7 +3856,7 @@ 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 -(-982 K R UP -3446) +(-982 K R UP -3378) ((|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 @@ -3915,11 +3915,11 @@ NIL (-996 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.}"))) ((-4404 |has| |#1| (-290)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4005 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -897) (QUOTE (-1170)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -897) (QUOTE (-1170)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1055))) (|HasCategory| |#1| (QUOTE (-545)))) (-997 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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-998 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3928,14 +3928,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-1000 -3446 UP UPUP |radicnd| |n|) +(-1000 -3378 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4404 |has| (-407 |#2|) (-363)) (-4409 |has| (-407 |#2|) (-363)) (-4403 |has| (-407 |#2|) (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-4005 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4005 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4005 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4005 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-4002 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-4002 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1001 |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."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4005 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-906))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1019))) (|HasCategory| (-564) (QUOTE (-817))) (-4002 (|HasCategory| (-564) (QUOTE (-817))) (|HasCategory| (-564) (QUOTE (-847)))) (|HasCategory| (-564) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -897) (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 (-847))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-906)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1002) ((|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 @@ -3968,19 +3968,19 @@ 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}}"))) ((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) NIL -(-1010 R -3446) +(-1010 R -3378) ((|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 -(-1011 R -3446) +(-1011 R -3378) ((|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 -(-1012 -3446 UP) +(-1012 -3378 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 -(-1013 -3446 UP) +(-1013 -3378 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 @@ -4015,8 +4015,8 @@ NIL (-1021 |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"))) ((-4404 . T) (-4409 . T) (-4403 . T) (-4406 . T) (-4405 . T) ((-4413 "*") . T) (-4408 . T)) -((-4005 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) -(-1022 -3446 L) +((-4002 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1035) (QUOTE (-564))))) +(-1022 -3378 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 @@ -4052,14 +4052,14 @@ 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 -(-1031 -3446 |Expon| |VarSet| |FPol| |LFPol|) +(-1031 -3378 |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"))) (((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL (-1032) ((|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.}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1033) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4116,7 +4116,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4408 . T)) NIL -(-1047 |xx| -3446) +(-1047 |xx| -3378) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4131,7 +4131,7 @@ NIL (-1050 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4411 . T) (-4406 . T) (-4405 . T)) -((-4005 (-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)))) (-4005 (|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 (-859))))) +((-4002 (-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)))) (-4002 (|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 (-859))))) (-1051 |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 @@ -4163,7 +4163,7 @@ NIL (-1058) ((|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}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2577) (QUOTE (-52))))))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -1327) (QUOTE (-52))))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-847))) (|HasCategory| (-52) (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (LIST (QUOTE -611) (QUOTE (-859))))) (-1059 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 -3446) +(-1070 |Base| R -3378) ((|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 -3446) +(-1071 |Base| R -3378) ((|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."))) ((-4404 |has| |#1| (-363)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4005 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-4002 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -897) (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"))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|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)}}"))) ((-4411 . T) (-4401 . T) (-4412 . T)) -((-4005 (-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 (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-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 (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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 (-790))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-845))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-847))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1046)))) (-12 (|HasCategory| |#3| (QUOTE (-1046))) (|HasCategory| |#3| (LIST (QUOTE -897) (QUOTE (-1170))))) (-4002 (|HasCategory| |#3| (QUOTE (-1046))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1035) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4408)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-859)))) (-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 -3446) +(-1110 R -3378) ((|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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-906))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-906))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-906)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4409)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-906)))) (|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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4005 (|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))) (-4002 (|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}"))) ((-4412 . T) (-4411 . T)) NIL -(-1122 UP -3446) +(-1122 UP -3378) ((|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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4005 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-4002 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-859))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|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}."))) ((-4408 . T) (-4400 |has| |#2| (-6 (-4413 "*"))) (-4411 . T) (-4405 . T) (-4406 . T)) -((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4005 (-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 -897) (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))) (-4005 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (QUOTE (-564)))) (-4002 (-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 -897) (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))) (-4002 (|HasAttribute| |#2| (QUOTE (-4413 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (-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}."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) ((-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-847))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#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."))) ((-4412 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4412 . T) (-4411 . T)) @@ -4539,11 +4539,11 @@ NIL (-1152) NIL ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|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 (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-4002 (-12 (|HasCategory| (-144) (QUOTE (-847))) (|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 (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-859)))) (-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."))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#1|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#1|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-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."))) -(((-4413 "*") -4005 (-4260 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-817))) (|has| |#1| (-172)) (-4260 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-906)))) (-4404 -4005 (-4260 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-817))) (|has| |#1| (-556)) (-4260 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-906)))) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . 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the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4005 (|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 -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|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 -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1168 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4005 (|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 -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|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 -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1169) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4005 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4409))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-4002 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-968) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4409))) (-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}"))) ((-4411 . T) (-4412 . T)) -((-12 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1353) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2577) (|devaluate| |#2|)))))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4005 (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2351) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1327) (|devaluate| |#2|)))))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#2| (QUOTE (-1094))) (-4002 (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-859)))) (|HasCategory| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (LIST (QUOTE -611) (QUOTE (-859))))) (-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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4412 . T) (-4411 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -3446) +(-1198 R -3378) ((|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 -3446) +(-1200 R -3378) ((|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 -889) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -883) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -883) (|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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-4005 (|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))) (-4002 (|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 (-859))))) -(-1207 -3446) +(-1207 -3378) ((|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 -1035) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-817))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-906))) (|HasCategory| |#1| (QUOTE (-363)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-906))) (|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}"))) (((-4413 "*") |has| |#2| (-172)) (-4404 |has| |#2| (-556)) (-4407 |has| |#2| (-363)) (-4409 |has| |#2| (-6 -4409)) (-4406 . T) (-4405 . T) (-4408 . T)) -((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4005 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4005 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4005 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-906))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -883) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -883) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -889) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-847))) (|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 -1035) (QUOTE (-564)))) (-4002 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (-4002 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-906)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -897) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4409)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (-4002 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-906)))) (|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 -897) (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 -3708) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -897) (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 -1765) (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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . 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)}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4005 (|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 -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|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 -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4409 |has| |#1| (-363)) (-4403 |has| |#1| (-363)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4005 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4005 (|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 -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -897) (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))) (-4002 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-4002 (|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 -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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))}."))) (((-4413 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4404 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4405 . T) (-4406 . T) (-4408 . 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))) (-4005 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (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))) (-4002 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1035) (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 (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4276) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3359) (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 (-956))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -4170) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3591) (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."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . 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}."))) (((-4413 "*") |has| |#1| (-172)) (-4404 |has| |#1| (-556)) (-4405 . T) (-4406 . T) (-4408 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4005 (|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 -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -3708) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4005 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3359) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4276) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-4002 (|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 -897) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-768)) (|devaluate| |#1|)))) (|HasCategory| (-768) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasSignature| |#1| (LIST (QUOTE -1765) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-768))))) (|HasCategory| |#1| (QUOTE (-363))) (-4002 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-956))) (|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 -3591) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -4170) (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 -3446 UP L UTS) +(-1253 -3378 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."))) ((-4412 . T) (-4411 . T)) -((-4005 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4005 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4005 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-4002 (-12 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-4002 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-4002 (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-847))) (|HasCategory| (-564) (QUOTE (-847))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-723))) (|HasCategory| |#1| (QUOTE (-1046))) (-12 (|HasCategory| |#1| (QUOTE (-999))) (|HasCategory| |#1| (QUOTE (-1046)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-859)))) (-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 -3446) +(-1268 K R UP -3378) ((|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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4404 |has| |#2| (-6 -4404)) (-4406 . T) (-4405 . T) (-4408 . T)) NIL -(-1277 S -3446) +(-1277 S -3378) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -3446) +(-1278 -3378) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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}."))) ((-4403 . T) (-4409 . T) (-4404 . T) ((-4413 "*") . T) (-4405 . T) (-4406 . T) (-4408 . T)) NIL @@ -5096,4 +5096,4 @@ NIL NIL NIL NIL -((-3 NIL 2283232 2283237 2283242 2283247) (-2 NIL 2283212 2283217 2283222 2283227) (-1 NIL 2283192 2283197 2283202 2283207) (0 NIL 2283172 2283177 2283182 2283187) (-1287 "ZMOD.spad" 2282981 2282994 2283110 2283167) (-1286 "ZLINDEP.spad" 2282025 2282036 2282971 2282976) (-1285 "ZDSOLVE.spad" 2271874 2271896 2282015 2282020) (-1284 "YSTREAM.spad" 2271367 2271378 2271864 2271869) (-1283 "XRPOLY.spad" 2270587 2270607 2271223 2271292) (-1282 "XPR.spad" 2268378 2268391 2270305 2270404) (-1281 "XPOLY.spad" 2267933 2267944 2268234 2268303) (-1280 "XPOLYC.spad" 2267250 2267266 2267859 2267928) (-1279 "XPBWPOLY.spad" 2265687 2265707 2267030 2267099) (-1278 "XF.spad" 2264148 2264163 2265589 2265682) (-1277 "XF.spad" 2262589 2262606 2264032 2264037) (-1276 "XFALG.spad" 2259613 2259629 2262515 2262584) (-1275 "XEXPPKG.spad" 2258864 2258890 2259603 2259608) (-1274 "XDPOLY.spad" 2258478 2258494 2258720 2258789) (-1273 "XALG.spad" 2258138 2258149 2258434 2258473) (-1272 "WUTSET.spad" 2253977 2253994 2257784 2257811) (-1271 "WP.spad" 2253176 2253220 2253835 2253902) (-1270 "WHILEAST.spad" 2252974 2252983 2253166 2253171) (-1269 "WHEREAST.spad" 2252645 2252654 2252964 2252969) (-1268 "WFFINTBS.spad" 2250208 2250230 2252635 2252640) (-1267 "WEIER.spad" 2248422 2248433 2250198 2250203) (-1266 "VSPACE.spad" 2248095 2248106 2248390 2248417) (-1265 "VSPACE.spad" 2247788 2247801 2248085 2248090) (-1264 "VOID.spad" 2247465 2247474 2247778 2247783) (-1263 "VIEW.spad" 2245087 2245096 2247455 2247460) (-1262 "VIEWDEF.spad" 2240284 2240293 2245077 2245082) (-1261 "VIEW3D.spad" 2224119 2224128 2240274 2240279) (-1260 "VIEW2D.spad" 2211856 2211865 2224109 2224114) (-1259 "VECTOR.spad" 2210531 2210542 2210782 2210809) (-1258 "VECTOR2.spad" 2209158 2209171 2210521 2210526) (-1257 "VECTCAT.spad" 2207058 2207069 2209126 2209153) (-1256 "VECTCAT.spad" 2204766 2204779 2206836 2206841) (-1255 "VARIABLE.spad" 2204546 2204561 2204756 2204761) (-1254 "UTYPE.spad" 2204190 2204199 2204536 2204541) (-1253 "UTSODETL.spad" 2203483 2203507 2204146 2204151) (-1252 "UTSODE.spad" 2201671 2201691 2203473 2203478) (-1251 "UTS.spad" 2196460 2196488 2200138 2200235) (-1250 "UTSCAT.spad" 2193911 2193927 2196358 2196455) (-1249 "UTSCAT.spad" 2191006 2191024 2193455 2193460) (-1248 "UTS2.spad" 2190599 2190634 2190996 2191001) (-1247 "URAGG.spad" 2185231 2185242 2190589 2190594) (-1246 "URAGG.spad" 2179827 2179840 2185187 2185192) (-1245 "UPXSSING.spad" 2177470 2177496 2178908 2179041) (-1244 "UPXS.spad" 2174618 2174646 2175602 2175751) (-1243 "UPXSCONS.spad" 2172375 2172395 2172750 2172899) (-1242 "UPXSCCA.spad" 2170940 2170960 2172221 2172370) (-1241 "UPXSCCA.spad" 2169647 2169669 2170930 2170935) (-1240 "UPXSCAT.spad" 2168228 2168244 2169493 2169642) (-1239 "UPXS2.spad" 2167769 2167822 2168218 2168223) (-1238 "UPSQFREE.spad" 2166181 2166195 2167759 2167764) (-1237 "UPSCAT.spad" 2163774 2163798 2166079 2166176) (-1236 "UPSCAT.spad" 2161073 2161099 2163380 2163385) (-1235 "UPOLYC.spad" 2156051 2156062 2160915 2161068) (-1234 "UPOLYC.spad" 2150921 2150934 2155787 2155792) (-1233 "UPOLYC2.spad" 2150390 2150409 2150911 2150916) (-1232 "UP.spad" 2147547 2147562 2147940 2148093) (-1231 "UPMP.spad" 2146437 2146450 2147537 2147542) (-1230 "UPDIVP.spad" 2146000 2146014 2146427 2146432) (-1229 "UPDECOMP.spad" 2144237 2144251 2145990 2145995) (-1228 "UPCDEN.spad" 2143444 2143460 2144227 2144232) (-1227 "UP2.spad" 2142806 2142827 2143434 2143439) (-1226 "UNISEG.spad" 2142159 2142170 2142725 2142730) (-1225 "UNISEG2.spad" 2141652 2141665 2142115 2142120) (-1224 "UNIFACT.spad" 2140753 2140765 2141642 2141647) (-1223 "ULS.spad" 2131305 2131333 2132398 2132827) (-1222 "ULSCONS.spad" 2123699 2123719 2124071 2124220) (-1221 "ULSCCAT.spad" 2121428 2121448 2123545 2123694) (-1220 "ULSCCAT.spad" 2119265 2119287 2121384 2121389) (-1219 "ULSCAT.spad" 2117481 2117497 2119111 2119260) (-1218 "ULS2.spad" 2116993 2117046 2117471 2117476) (-1217 "UINT8.spad" 2116870 2116879 2116983 2116988) (-1216 "UINT64.spad" 2116746 2116755 2116860 2116865) (-1215 "UINT32.spad" 2116622 2116631 2116736 2116741) (-1214 "UINT16.spad" 2116498 2116507 2116612 2116617) (-1213 "UFD.spad" 2115563 2115572 2116424 2116493) (-1212 "UFD.spad" 2114690 2114701 2115553 2115558) (-1211 "UDVO.spad" 2113537 2113546 2114680 2114685) (-1210 "UDPO.spad" 2110964 2110975 2113493 2113498) (-1209 "TYPE.spad" 2110896 2110905 2110954 2110959) (-1208 "TYPEAST.spad" 2110815 2110824 2110886 2110891) (-1207 "TWOFACT.spad" 2109465 2109480 2110805 2110810) (-1206 "TUPLE.spad" 2108949 2108960 2109364 2109369) (-1205 "TUBETOOL.spad" 2105786 2105795 2108939 2108944) (-1204 "TUBE.spad" 2104427 2104444 2105776 2105781) (-1203 "TS.spad" 2103016 2103032 2103992 2104089) (-1202 "TSETCAT.spad" 2090143 2090160 2102984 2103011) (-1201 "TSETCAT.spad" 2077256 2077275 2090099 2090104) (-1200 "TRMANIP.spad" 2071622 2071639 2076962 2076967) (-1199 "TRIMAT.spad" 2070581 2070606 2071612 2071617) (-1198 "TRIGMNIP.spad" 2069098 2069115 2070571 2070576) (-1197 "TRIGCAT.spad" 2068610 2068619 2069088 2069093) (-1196 "TRIGCAT.spad" 2068120 2068131 2068600 2068605) (-1195 "TREE.spad" 2066691 2066702 2067727 2067754) (-1194 "TRANFUN.spad" 2066522 2066531 2066681 2066686) (-1193 "TRANFUN.spad" 2066351 2066362 2066512 2066517) (-1192 "TOPSP.spad" 2066025 2066034 2066341 2066346) (-1191 "TOOLSIGN.spad" 2065688 2065699 2066015 2066020) (-1190 "TEXTFILE.spad" 2064245 2064254 2065678 2065683) (-1189 "TEX.spad" 2061377 2061386 2064235 2064240) (-1188 "TEX1.spad" 2060933 2060944 2061367 2061372) (-1187 "TEMUTL.spad" 2060488 2060497 2060923 2060928) (-1186 "TBCMPPK.spad" 2058581 2058604 2060478 2060483) (-1185 "TBAGG.spad" 2057617 2057640 2058561 2058576) (-1184 "TBAGG.spad" 2056661 2056686 2057607 2057612) (-1183 "TANEXP.spad" 2056037 2056048 2056651 2056656) (-1182 "TABLE.spad" 2054448 2054471 2054718 2054745) (-1181 "TABLEAU.spad" 2053929 2053940 2054438 2054443) (-1180 "TABLBUMP.spad" 2050712 2050723 2053919 2053924) (-1179 "SYSTEM.spad" 2049940 2049949 2050702 2050707) (-1178 "SYSSOLP.spad" 2047413 2047424 2049930 2049935) (-1177 "SYSNNI.spad" 2046593 2046604 2047403 2047408) (-1176 "SYSINT.spad" 2045997 2046008 2046583 2046588) (-1175 "SYNTAX.spad" 2042191 2042200 2045987 2045992) (-1174 "SYMTAB.spad" 2040247 2040256 2042181 2042186) (-1173 "SYMS.spad" 2036232 2036241 2040237 2040242) (-1172 "SYMPOLY.spad" 2035239 2035250 2035321 2035448) (-1171 "SYMFUNC.spad" 2034714 2034725 2035229 2035234) (-1170 "SYMBOL.spad" 2032141 2032150 2034704 2034709) (-1169 "SWITCH.spad" 2028898 2028907 2032131 2032136) (-1168 "SUTS.spad" 2025797 2025825 2027365 2027462) (-1167 "SUPXS.spad" 2022932 2022960 2023929 2024078) (-1166 "SUP.spad" 2019701 2019712 2020482 2020635) (-1165 "SUPFRACF.spad" 2018806 2018824 2019691 2019696) (-1164 "SUP2.spad" 2018196 2018209 2018796 2018801) (-1163 "SUMRF.spad" 2017162 2017173 2018186 2018191) (-1162 "SUMFS.spad" 2016795 2016812 2017152 2017157) (-1161 "SULS.spad" 2007334 2007362 2008440 2008869) (-1160 "SUCHTAST.spad" 2007103 2007112 2007324 2007329) (-1159 "SUCH.spad" 2006783 2006798 2007093 2007098) (-1158 "SUBSPACE.spad" 1998790 1998805 2006773 2006778) (-1157 "SUBRESP.spad" 1997950 1997964 1998746 1998751) (-1156 "STTF.spad" 1994049 1994065 1997940 1997945) (-1155 "STTFNC.spad" 1990517 1990533 1994039 1994044) (-1154 "STTAYLOR.spad" 1982915 1982926 1990398 1990403) (-1153 "STRTBL.spad" 1981420 1981437 1981569 1981596) (-1152 "STRING.spad" 1980829 1980838 1980843 1980870) (-1151 "STRICAT.spad" 1980617 1980626 1980797 1980824) (-1150 "STREAM.spad" 1977475 1977486 1980142 1980157) (-1149 "STREAM3.spad" 1977020 1977035 1977465 1977470) (-1148 "STREAM2.spad" 1976088 1976101 1977010 1977015) (-1147 "STREAM1.spad" 1975792 1975803 1976078 1976083) (-1146 "STINPROD.spad" 1974698 1974714 1975782 1975787) (-1145 "STEP.spad" 1973899 1973908 1974688 1974693) (-1144 "STBL.spad" 1972425 1972453 1972592 1972607) (-1143 "STAGG.spad" 1971500 1971511 1972415 1972420) (-1142 "STAGG.spad" 1970573 1970586 1971490 1971495) (-1141 "STACK.spad" 1969924 1969935 1970180 1970207) (-1140 "SREGSET.spad" 1967628 1967645 1969570 1969597) (-1139 "SRDCMPK.spad" 1966173 1966193 1967618 1967623) (-1138 "SRAGG.spad" 1961270 1961279 1966141 1966168) (-1137 "SRAGG.spad" 1956387 1956398 1961260 1961265) (-1136 "SQMATRIX.spad" 1954003 1954021 1954919 1955006) (-1135 "SPLTREE.spad" 1948555 1948568 1953439 1953466) (-1134 "SPLNODE.spad" 1945143 1945156 1948545 1948550) (-1133 "SPFCAT.spad" 1943920 1943929 1945133 1945138) (-1132 "SPECOUT.spad" 1942470 1942479 1943910 1943915) (-1131 "SPADXPT.spad" 1934609 1934618 1942460 1942465) (-1130 "spad-parser.spad" 1934074 1934083 1934599 1934604) (-1129 "SPADAST.spad" 1933775 1933784 1934064 1934069) (-1128 "SPACEC.spad" 1917788 1917799 1933765 1933770) (-1127 "SPACE3.spad" 1917564 1917575 1917778 1917783) (-1126 "SORTPAK.spad" 1917109 1917122 1917520 1917525) (-1125 "SOLVETRA.spad" 1914866 1914877 1917099 1917104) (-1124 "SOLVESER.spad" 1913386 1913397 1914856 1914861) (-1123 "SOLVERAD.spad" 1909396 1909407 1913376 1913381) (-1122 "SOLVEFOR.spad" 1907816 1907834 1909386 1909391) (-1121 "SNTSCAT.spad" 1907416 1907433 1907784 1907811) (-1120 "SMTS.spad" 1905676 1905702 1906981 1907078) (-1119 "SMP.spad" 1903115 1903135 1903505 1903632) (-1118 "SMITH.spad" 1901958 1901983 1903105 1903110) (-1117 "SMATCAT.spad" 1900068 1900098 1901902 1901953) (-1116 "SMATCAT.spad" 1898110 1898142 1899946 1899951) (-1115 "SKAGG.spad" 1897071 1897082 1898078 1898105) (-1114 "SINT.spad" 1895897 1895906 1896937 1897066) (-1113 "SIMPAN.spad" 1895625 1895634 1895887 1895892) (-1112 "SIG.spad" 1894953 1894962 1895615 1895620) (-1111 "SIGNRF.spad" 1894061 1894072 1894943 1894948) (-1110 "SIGNEF.spad" 1893330 1893347 1894051 1894056) (-1109 "SIGAST.spad" 1892711 1892720 1893320 1893325) (-1108 "SHP.spad" 1890629 1890644 1892667 1892672) (-1107 "SHDP.spad" 1880340 1880367 1880849 1880980) (-1106 "SGROUP.spad" 1879948 1879957 1880330 1880335) (-1105 "SGROUP.spad" 1879554 1879565 1879938 1879943) (-1104 "SGCF.spad" 1872435 1872444 1879544 1879549) (-1103 "SFRTCAT.spad" 1871363 1871380 1872403 1872430) (-1102 "SFRGCD.spad" 1870426 1870446 1871353 1871358) (-1101 "SFQCMPK.spad" 1865063 1865083 1870416 1870421) (-1100 "SFORT.spad" 1864498 1864512 1865053 1865058) (-1099 "SEXOF.spad" 1864341 1864381 1864488 1864493) (-1098 "SEX.spad" 1864233 1864242 1864331 1864336) (-1097 "SEXCAT.spad" 1861784 1861824 1864223 1864228) (-1096 "SET.spad" 1860084 1860095 1861205 1861244) (-1095 "SETMN.spad" 1858518 1858535 1860074 1860079) (-1094 "SETCAT.spad" 1858003 1858012 1858508 1858513) (-1093 "SETCAT.spad" 1857486 1857497 1857993 1857998) (-1092 "SETAGG.spad" 1854007 1854018 1857466 1857481) (-1091 "SETAGG.spad" 1850536 1850549 1853997 1854002) (-1090 "SEQAST.spad" 1850239 1850248 1850526 1850531) (-1089 "SEGXCAT.spad" 1849361 1849374 1850229 1850234) (-1088 "SEG.spad" 1849174 1849185 1849280 1849285) (-1087 "SEGCAT.spad" 1848081 1848092 1849164 1849169) (-1086 "SEGBIND.spad" 1847153 1847164 1848036 1848041) (-1085 "SEGBIND2.spad" 1846849 1846862 1847143 1847148) (-1084 "SEGAST.spad" 1846563 1846572 1846839 1846844) (-1083 "SEG2.spad" 1845988 1846001 1846519 1846524) (-1082 "SDVAR.spad" 1845264 1845275 1845978 1845983) (-1081 "SDPOL.spad" 1842654 1842665 1842945 1843072) (-1080 "SCPKG.spad" 1840733 1840744 1842644 1842649) (-1079 "SCOPE.spad" 1839886 1839895 1840723 1840728) (-1078 "SCACHE.spad" 1838568 1838579 1839876 1839881) (-1077 "SASTCAT.spad" 1838477 1838486 1838558 1838563) (-1076 "SAOS.spad" 1838349 1838358 1838467 1838472) (-1075 "SAERFFC.spad" 1838062 1838082 1838339 1838344) (-1074 "SAE.spad" 1836237 1836253 1836848 1836983) (-1073 "SAEFACT.spad" 1835938 1835958 1836227 1836232) (-1072 "RURPK.spad" 1833579 1833595 1835928 1835933) (-1071 "RULESET.spad" 1833020 1833044 1833569 1833574) (-1070 "RULE.spad" 1831224 1831248 1833010 1833015) (-1069 "RULECOLD.spad" 1831076 1831089 1831214 1831219) (-1068 "RSTRCAST.spad" 1830793 1830802 1831066 1831071) (-1067 "RSETGCD.spad" 1827171 1827191 1830783 1830788) (-1066 "RSETCAT.spad" 1816955 1816972 1827139 1827166) (-1065 "RSETCAT.spad" 1806759 1806778 1816945 1816950) (-1064 "RSDCMPK.spad" 1805211 1805231 1806749 1806754) (-1063 "RRCC.spad" 1803595 1803625 1805201 1805206) (-1062 "RRCC.spad" 1801977 1802009 1803585 1803590) (-1061 "RPTAST.spad" 1801679 1801688 1801967 1801972) (-1060 "RPOLCAT.spad" 1781039 1781054 1801547 1801674) (-1059 "RPOLCAT.spad" 1760113 1760130 1780623 1780628) (-1058 "ROUTINE.spad" 1755976 1755985 1758760 1758787) (-1057 "ROMAN.spad" 1755304 1755313 1755842 1755971) (-1056 "ROIRC.spad" 1754384 1754416 1755294 1755299) (-1055 "RNS.spad" 1753287 1753296 1754286 1754379) (-1054 "RNS.spad" 1752276 1752287 1753277 1753282) (-1053 "RNG.spad" 1752011 1752020 1752266 1752271) (-1052 "RMODULE.spad" 1751649 1751660 1752001 1752006) (-1051 "RMCAT2.spad" 1751057 1751114 1751639 1751644) (-1050 "RMATRIX.spad" 1749881 1749900 1750224 1750263) (-1049 "RMATCAT.spad" 1745414 1745445 1749837 1749876) (-1048 "RMATCAT.spad" 1740837 1740870 1745262 1745267) (-1047 "RINTERP.spad" 1740725 1740745 1740827 1740832) (-1046 "RING.spad" 1740195 1740204 1740705 1740720) (-1045 "RING.spad" 1739673 1739684 1740185 1740190) (-1044 "RIDIST.spad" 1739057 1739066 1739663 1739668) (-1043 "RGCHAIN.spad" 1737636 1737652 1738542 1738569) (-1042 "RGBCSPC.spad" 1737417 1737429 1737626 1737631) (-1041 "RGBCMDL.spad" 1736947 1736959 1737407 1737412) (-1040 "RF.spad" 1734561 1734572 1736937 1736942) (-1039 "RFFACTOR.spad" 1734023 1734034 1734551 1734556) (-1038 "RFFACT.spad" 1733758 1733770 1734013 1734018) (-1037 "RFDIST.spad" 1732746 1732755 1733748 1733753) (-1036 "RETSOL.spad" 1732163 1732176 1732736 1732741) (-1035 "RETRACT.spad" 1731591 1731602 1732153 1732158) (-1034 "RETRACT.spad" 1731017 1731030 1731581 1731586) (-1033 "RETAST.spad" 1730829 1730838 1731007 1731012) (-1032 "RESULT.spad" 1728889 1728898 1729476 1729503) (-1031 "RESRING.spad" 1728236 1728283 1728827 1728884) (-1030 "RESLATC.spad" 1727560 1727571 1728226 1728231) (-1029 "REPSQ.spad" 1727289 1727300 1727550 1727555) (-1028 "REP.spad" 1724841 1724850 1727279 1727284) (-1027 "REPDB.spad" 1724546 1724557 1724831 1724836) (-1026 "REP2.spad" 1714118 1714129 1724388 1724393) (-1025 "REP1.spad" 1708108 1708119 1714068 1714073) (-1024 "REGSET.spad" 1705905 1705922 1707754 1707781) (-1023 "REF.spad" 1705234 1705245 1705860 1705865) (-1022 "REDORDER.spad" 1704410 1704427 1705224 1705229) (-1021 "RECLOS.spad" 1703193 1703213 1703897 1703990) (-1020 "REALSOLV.spad" 1702325 1702334 1703183 1703188) (-1019 "REAL.spad" 1702197 1702206 1702315 1702320) (-1018 "REAL0Q.spad" 1699479 1699494 1702187 1702192) (-1017 "REAL0.spad" 1696307 1696322 1699469 1699474) (-1016 "RDUCEAST.spad" 1696028 1696037 1696297 1696302) (-1015 "RDIV.spad" 1695679 1695704 1696018 1696023) (-1014 "RDIST.spad" 1695242 1695253 1695669 1695674) (-1013 "RDETRS.spad" 1694038 1694056 1695232 1695237) (-1012 "RDETR.spad" 1692145 1692163 1694028 1694033) (-1011 "RDEEFS.spad" 1691218 1691235 1692135 1692140) (-1010 "RDEEF.spad" 1690214 1690231 1691208 1691213) (-1009 "RCFIELD.spad" 1687400 1687409 1690116 1690209) (-1008 "RCFIELD.spad" 1684672 1684683 1687390 1687395) (-1007 "RCAGG.spad" 1682584 1682595 1684662 1684667) (-1006 "RCAGG.spad" 1680423 1680436 1682503 1682508) (-1005 "RATRET.spad" 1679783 1679794 1680413 1680418) (-1004 "RATFACT.spad" 1679475 1679487 1679773 1679778) (-1003 "RANDSRC.spad" 1678794 1678803 1679465 1679470) (-1002 "RADUTIL.spad" 1678548 1678557 1678784 1678789) (-1001 "RADIX.spad" 1675449 1675463 1677015 1677108) (-1000 "RADFF.spad" 1673862 1673899 1673981 1674137) (-999 "RADCAT.spad" 1673456 1673464 1673852 1673857) (-998 "RADCAT.spad" 1673048 1673058 1673446 1673451) (-997 "QUEUE.spad" 1672391 1672401 1672655 1672682) (-996 "QUAT.spad" 1670973 1670983 1671315 1671380) (-995 "QUATCT2.spad" 1670592 1670610 1670963 1670968) (-994 "QUATCAT.spad" 1668757 1668767 1670522 1670587) (-993 "QUATCAT.spad" 1666673 1666685 1668440 1668445) (-992 "QUAGG.spad" 1665499 1665509 1666641 1666668) (-991 "QQUTAST.spad" 1665268 1665276 1665489 1665494) (-990 "QFORM.spad" 1664731 1664745 1665258 1665263) (-989 "QFCAT.spad" 1663434 1663444 1664633 1664726) (-988 "QFCAT.spad" 1661728 1661740 1662929 1662934) (-987 "QFCAT2.spad" 1661419 1661435 1661718 1661723) (-986 "QEQUAT.spad" 1660976 1660984 1661409 1661414) (-985 "QCMPACK.spad" 1655723 1655742 1660966 1660971) (-984 "QALGSET.spad" 1651798 1651830 1655637 1655642) (-983 "QALGSET2.spad" 1649794 1649812 1651788 1651793) (-982 "PWFFINTB.spad" 1647104 1647125 1649784 1649789) (-981 "PUSHVAR.spad" 1646433 1646452 1647094 1647099) (-980 "PTRANFN.spad" 1642559 1642569 1646423 1646428) (-979 "PTPACK.spad" 1639647 1639657 1642549 1642554) (-978 "PTFUNC2.spad" 1639468 1639482 1639637 1639642) (-977 "PTCAT.spad" 1638717 1638727 1639436 1639463) (-976 "PSQFR.spad" 1638024 1638048 1638707 1638712) (-975 "PSEUDLIN.spad" 1636882 1636892 1638014 1638019) (-974 "PSETPK.spad" 1622315 1622331 1636760 1636765) (-973 "PSETCAT.spad" 1616235 1616258 1622295 1622310) (-972 "PSETCAT.spad" 1610129 1610154 1616191 1616196) (-971 "PSCURVE.spad" 1609112 1609120 1610119 1610124) (-970 "PSCAT.spad" 1607879 1607908 1609010 1609107) (-969 "PSCAT.spad" 1606736 1606767 1607869 1607874) (-968 "PRTITION.spad" 1605681 1605689 1606726 1606731) (-967 "PRTDAST.spad" 1605400 1605408 1605671 1605676) (-966 "PRS.spad" 1594962 1594979 1605356 1605361) (-965 "PRQAGG.spad" 1594393 1594403 1594930 1594957) (-964 "PROPLOG.spad" 1593796 1593804 1594383 1594388) (-963 "PROPFRML.spad" 1591714 1591725 1593786 1593791) (-962 "PROPERTY.spad" 1591208 1591216 1591704 1591709) (-961 "PRODUCT.spad" 1588888 1588900 1589174 1589229) (-960 "PR.spad" 1587274 1587286 1587979 1588106) (-959 "PRINT.spad" 1587026 1587034 1587264 1587269) (-958 "PRIMES.spad" 1585277 1585287 1587016 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(-845 "ORDRING.spad" 1396769 1396777 1397359 1397374) (-844 "ORDRING.spad" 1396167 1396177 1396759 1396764) (-843 "ORDMON.spad" 1396022 1396030 1396157 1396162) (-842 "ORDFUNS.spad" 1395148 1395164 1396012 1396017) (-841 "ORDFIN.spad" 1394968 1394976 1395138 1395143) (-840 "ORDCOMP.spad" 1393433 1393443 1394515 1394544) (-839 "ORDCOMP2.spad" 1392718 1392730 1393423 1393428) (-838 "OPTPROB.spad" 1391356 1391364 1392708 1392713) (-837 "OPTPACK.spad" 1383741 1383749 1391346 1391351) (-836 "OPTCAT.spad" 1381416 1381424 1383731 1383736) (-835 "OPSIG.spad" 1381068 1381076 1381406 1381411) (-834 "OPQUERY.spad" 1380617 1380625 1381058 1381063) (-833 "OP.spad" 1380359 1380369 1380439 1380506) (-832 "OPERCAT.spad" 1379947 1379957 1380349 1380354) (-831 "OPERCAT.spad" 1379533 1379545 1379937 1379942) (-830 "ONECOMP.spad" 1378278 1378288 1379080 1379109) (-829 "ONECOMP2.spad" 1377696 1377708 1378268 1378273) (-828 "OMSERVER.spad" 1376698 1376706 1377686 1377691) (-827 "OMSAGG.spad" 1376486 1376496 1376654 1376693) (-826 "OMPKG.spad" 1375098 1375106 1376476 1376481) (-825 "OM.spad" 1374063 1374071 1375088 1375093) (-824 "OMLO.spad" 1373488 1373500 1373949 1373988) (-823 "OMEXPR.spad" 1373322 1373332 1373478 1373483) (-822 "OMERR.spad" 1372865 1372873 1373312 1373317) (-821 "OMERRK.spad" 1371899 1371907 1372855 1372860) (-820 "OMENC.spad" 1371243 1371251 1371889 1371894) (-819 "OMDEV.spad" 1365532 1365540 1371233 1371238) (-818 "OMCONN.spad" 1364941 1364949 1365522 1365527) (-817 "OINTDOM.spad" 1364704 1364712 1364867 1364936) (-816 "OFMONOID.spad" 1360891 1360901 1364694 1364699) (-815 "ODVAR.spad" 1360152 1360162 1360881 1360886) (-814 "ODR.spad" 1359796 1359822 1359964 1360113) (-813 "ODPOL.spad" 1357142 1357152 1357482 1357609) (-812 "ODP.spad" 1346989 1347009 1347362 1347493) (-811 "ODETOOLS.spad" 1345572 1345591 1346979 1346984) (-810 "ODESYS.spad" 1343222 1343239 1345562 1345567) (-809 "ODERTRIC.spad" 1339163 1339180 1343179 1343184) (-808 "ODERED.spad" 1338550 1338574 1339153 1339158) (-807 "ODERAT.spad" 1336101 1336118 1338540 1338545) (-806 "ODEPRRIC.spad" 1332992 1333014 1336091 1336096) (-805 "ODEPROB.spad" 1332249 1332257 1332982 1332987) (-804 "ODEPRIM.spad" 1329523 1329545 1332239 1332244) (-803 "ODEPAL.spad" 1328899 1328923 1329513 1329518) (-802 "ODEPACK.spad" 1315501 1315509 1328889 1328894) (-801 "ODEINT.spad" 1314932 1314948 1315491 1315496) (-800 "ODEIFTBL.spad" 1312327 1312335 1314922 1314927) (-799 "ODEEF.spad" 1307694 1307710 1312317 1312322) (-798 "ODECONST.spad" 1307213 1307231 1307684 1307689) (-797 "ODECAT.spad" 1305809 1305817 1307203 1307208) (-796 "OCT.spad" 1303947 1303957 1304663 1304702) (-795 "OCTCT2.spad" 1303591 1303612 1303937 1303942) (-794 "OC.spad" 1301365 1301375 1303547 1303586) (-793 "OC.spad" 1298864 1298876 1301048 1301053) (-792 "OCAMON.spad" 1298712 1298720 1298854 1298859) (-791 "OASGP.spad" 1298527 1298535 1298702 1298707) (-790 "OAMONS.spad" 1298047 1298055 1298517 1298522) (-789 "OAMON.spad" 1297908 1297916 1298037 1298042) (-788 "OAGROUP.spad" 1297770 1297778 1297898 1297903) (-787 "NUMTUBE.spad" 1297357 1297373 1297760 1297765) (-786 "NUMQUAD.spad" 1285219 1285227 1297347 1297352) (-785 "NUMODE.spad" 1276355 1276363 1285209 1285214) (-784 "NUMINT.spad" 1273913 1273921 1276345 1276350) (-783 "NUMFMT.spad" 1272753 1272761 1273903 1273908) (-782 "NUMERIC.spad" 1264825 1264835 1272558 1272563) (-781 "NTSCAT.spad" 1263327 1263343 1264793 1264820) (-780 "NTPOLFN.spad" 1262872 1262882 1263244 1263249) (-779 "NSUP.spad" 1255882 1255892 1260422 1260575) (-778 "NSUP2.spad" 1255274 1255286 1255872 1255877) (-777 "NSMP.spad" 1251469 1251488 1251777 1251904) (-776 "NREP.spad" 1249841 1249855 1251459 1251464) (-775 "NPCOEF.spad" 1249087 1249107 1249831 1249836) (-774 "NORMRETR.spad" 1248685 1248724 1249077 1249082) (-773 "NORMPK.spad" 1246587 1246606 1248675 1248680) (-772 "NORMMA.spad" 1246275 1246301 1246577 1246582) (-771 "NONE.spad" 1246016 1246024 1246265 1246270) (-770 "NONE1.spad" 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1151410) (-732 "MRING.spad" 1148231 1148243 1150968 1151035) (-731 "MRF2.spad" 1147799 1147813 1148221 1148226) (-730 "MRATFAC.spad" 1147345 1147362 1147789 1147794) (-729 "MPRFF.spad" 1145375 1145394 1147335 1147340) (-728 "MPOLY.spad" 1142810 1142825 1143169 1143296) (-727 "MPCPF.spad" 1142074 1142093 1142800 1142805) (-726 "MPC3.spad" 1141889 1141929 1142064 1142069) (-725 "MPC2.spad" 1141531 1141564 1141879 1141884) (-724 "MONOTOOL.spad" 1139866 1139883 1141521 1141526) (-723 "MONOID.spad" 1139185 1139193 1139856 1139861) (-722 "MONOID.spad" 1138502 1138512 1139175 1139180) (-721 "MONOGEN.spad" 1137248 1137261 1138362 1138497) (-720 "MONOGEN.spad" 1136016 1136031 1137132 1137137) (-719 "MONADWU.spad" 1134030 1134038 1136006 1136011) (-718 "MONADWU.spad" 1132042 1132052 1134020 1134025) (-717 "MONAD.spad" 1131186 1131194 1132032 1132037) (-716 "MONAD.spad" 1130328 1130338 1131176 1131181) (-715 "MOEBIUS.spad" 1129014 1129028 1130308 1130323) (-714 "MODULE.spad" 1128884 1128894 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(-394 "FORMULA.spad" 645230 645238 647756 647761) (-393 "FORMULA1.spad" 644709 644719 645220 645225) (-392 "FORDER.spad" 644400 644424 644699 644704) (-391 "FOP.spad" 643601 643609 644390 644395) (-390 "FNLA.spad" 643025 643047 643569 643596) (-389 "FNCAT.spad" 641612 641620 643015 643020) (-388 "FNAME.spad" 641504 641512 641602 641607) (-387 "FMTC.spad" 641302 641310 641430 641499) (-386 "FMONOID.spad" 638357 638367 641258 641263) (-385 "FM.spad" 638052 638064 638291 638318) (-384 "FMFUN.spad" 635082 635090 638042 638047) (-383 "FMC.spad" 634134 634142 635072 635077) (-382 "FMCAT.spad" 631788 631806 634102 634129) (-381 "FM1.spad" 631145 631157 631722 631749) (-380 "FLOATRP.spad" 628866 628880 631135 631140) (-379 "FLOAT.spad" 622154 622162 628732 628861) (-378 "FLOATCP.spad" 619571 619585 622144 622149) (-377 "FLINEXP.spad" 619283 619293 619551 619566) (-376 "FLINEXP.spad" 618949 618961 619219 619224) (-375 "FLASORT.spad" 618269 618281 618939 618944) (-374 "FLALG.spad" 615915 615934 618195 618264) (-373 "FLAGG.spad" 612933 612943 615895 615910) (-372 "FLAGG.spad" 609852 609864 612816 612821) (-371 "FLAGG2.spad" 608533 608549 609842 609847) (-370 "FINRALG.spad" 606562 606575 608489 608528) (-369 "FINRALG.spad" 604517 604532 606446 606451) (-368 "FINITE.spad" 603669 603677 604507 604512) (-367 "FINAALG.spad" 592650 592660 603611 603664) (-366 "FINAALG.spad" 581643 581655 592606 592611) (-365 "FILE.spad" 581226 581236 581633 581638) (-364 "FILECAT.spad" 579744 579761 581216 581221) (-363 "FIELD.spad" 579150 579158 579646 579739) (-362 "FIELD.spad" 578642 578652 579140 579145) (-361 "FGROUP.spad" 577251 577261 578622 578637) (-360 "FGLMICPK.spad" 576038 576053 577241 577246) (-359 "FFX.spad" 575413 575428 575754 575847) (-358 "FFSLPE.spad" 574902 574923 575403 575408) (-357 "FFPOLY.spad" 566154 566165 574892 574897) (-356 "FFPOLY2.spad" 565214 565231 566144 566149) (-355 "FFP.spad" 564611 564631 564930 565023) (-354 "FF.spad" 564059 564075 564292 564385) (-353 "FFNBX.spad" 562571 562591 563775 563868) (-352 "FFNBP.spad" 561084 561101 562287 562380) (-351 "FFNB.spad" 559549 559570 560765 560858) (-350 "FFINTBAS.spad" 556963 556982 559539 559544) (-349 "FFIELDC.spad" 554538 554546 556865 556958) (-348 "FFIELDC.spad" 552199 552209 554528 554533) (-347 "FFHOM.spad" 550947 550964 552189 552194) (-346 "FFF.spad" 548382 548393 550937 550942) (-345 "FFCGX.spad" 547229 547249 548098 548191) (-344 "FFCGP.spad" 546118 546138 546945 547038) (-343 "FFCG.spad" 544910 544931 545799 545892) (-342 "FFCAT.spad" 537937 537959 544749 544905) (-341 "FFCAT.spad" 531043 531067 537857 537862) (-340 "FFCAT2.spad" 530788 530828 531033 531038) (-339 "FEXPR.spad" 522497 522543 530544 530583) (-338 "FEVALAB.spad" 522203 522213 522487 522492) (-337 "FEVALAB.spad" 521694 521706 521980 521985) (-336 "FDIV.spad" 521136 521160 521684 521689) (-335 "FDIVCAT.spad" 519178 519202 521126 521131) (-334 "FDIVCAT.spad" 517218 517244 519168 519173) (-333 "FDIV2.spad" 516872 516912 517208 517213) (-332 "FCPAK1.spad" 515425 515433 516862 516867) (-331 "FCOMP.spad" 514804 514814 515415 515420) (-330 "FC.spad" 504719 504727 514794 514799) (-329 "FAXF.spad" 497654 497668 504621 504714) (-328 "FAXF.spad" 490641 490657 497610 497615) (-327 "FARRAY.spad" 488787 488797 489824 489851) (-326 "FAMR.spad" 486907 486919 488685 488782) (-325 "FAMR.spad" 485011 485025 486791 486796) (-324 "FAMONOID.spad" 484661 484671 484965 484970) (-323 "FAMONC.spad" 482883 482895 484651 484656) (-322 "FAGROUP.spad" 482489 482499 482779 482806) (-321 "FACUTIL.spad" 480685 480702 482479 482484) (-320 "FACTFUNC.spad" 479861 479871 480675 480680) (-319 "EXPUPXS.spad" 476694 476717 477993 478142) (-318 "EXPRTUBE.spad" 473922 473930 476684 476689) (-317 "EXPRODE.spad" 470794 470810 473912 473917) (-316 "EXPR.spad" 466069 466079 466783 467190) (-315 "EXPR2UPS.spad" 462161 462174 466059 466064) (-314 "EXPR2.spad" 461864 461876 462151 462156) (-313 "EXPEXPAN.spad" 458802 458827 459436 459529) (-312 "EXIT.spad" 458473 458481 458792 458797) (-311 "EXITAST.spad" 458209 458217 458463 458468) (-310 "EVALCYC.spad" 457667 457681 458199 458204) (-309 "EVALAB.spad" 457231 457241 457657 457662) (-308 "EVALAB.spad" 456793 456805 457221 457226) (-307 "EUCDOM.spad" 454335 454343 456719 456788) (-306 "EUCDOM.spad" 451939 451949 454325 454330) (-305 "ESTOOLS.spad" 443779 443787 451929 451934) (-304 "ESTOOLS2.spad" 443380 443394 443769 443774) (-303 "ESTOOLS1.spad" 443065 443076 443370 443375) (-302 "ES.spad" 435612 435620 443055 443060) (-301 "ES.spad" 428065 428075 435510 435515) (-300 "ESCONT.spad" 424838 424846 428055 428060) (-299 "ESCONT1.spad" 424587 424599 424828 424833) (-298 "ES2.spad" 424082 424098 424577 424582) (-297 "ES1.spad" 423648 423664 424072 424077) (-296 "ERROR.spad" 420969 420977 423638 423643) (-295 "EQTBL.spad" 419441 419463 419650 419677) (-294 "EQ.spad" 414315 414325 417114 417226) (-293 "EQ2.spad" 414031 414043 414305 414310) (-292 "EP.spad" 410345 410355 414021 414026) (-291 "ENV.spad" 409021 409029 410335 410340) (-290 "ENTIRER.spad" 408689 408697 408965 409016) (-289 "EMR.spad" 407890 407931 408615 408684) (-288 "ELTAGG.spad" 406130 406149 407880 407885) (-287 "ELTAGG.spad" 404334 404355 406086 406091) (-286 "ELTAB.spad" 403781 403799 404324 404329) (-285 "ELFUTS.spad" 403160 403179 403771 403776) (-284 "ELEMFUN.spad" 402849 402857 403150 403155) (-283 "ELEMFUN.spad" 402536 402546 402839 402844) (-282 "ELAGG.spad" 400479 400489 402516 402531) (-281 "ELAGG.spad" 398359 398371 400398 400403) (-280 "ELABEXPR.spad" 397282 397290 398349 398354) (-279 "EFUPXS.spad" 394058 394088 397238 397243) (-278 "EFULS.spad" 390894 390917 394014 394019) (-277 "EFSTRUC.spad" 388849 388865 390884 390889) (-276 "EF.spad" 383615 383631 388839 388844) (-275 "EAB.spad" 381891 381899 383605 383610) (-274 "E04UCFA.spad" 381427 381435 381881 381886) (-273 "E04NAFA.spad" 381004 381012 381417 381422) (-272 "E04MBFA.spad" 380584 380592 380994 380999) (-271 "E04JAFA.spad" 380120 380128 380574 380579) (-270 "E04GCFA.spad" 379656 379664 380110 380115) (-269 "E04FDFA.spad" 379192 379200 379646 379651) (-268 "E04DGFA.spad" 378728 378736 379182 379187) (-267 "E04AGNT.spad" 374570 374578 378718 378723) (-266 "DVARCAT.spad" 371255 371265 374560 374565) (-265 "DVARCAT.spad" 367938 367950 371245 371250) (-264 "DSMP.spad" 365369 365383 365674 365801) (-263 "DROPT.spad" 359314 359322 365359 365364) (-262 "DROPT1.spad" 358977 358987 359304 359309) (-261 "DROPT0.spad" 353804 353812 358967 358972) (-260 "DRAWPT.spad" 351959 351967 353794 353799) (-259 "DRAW.spad" 344559 344572 351949 351954) (-258 "DRAWHACK.spad" 343867 343877 344549 344554) (-257 "DRAWCX.spad" 341309 341317 343857 343862) (-256 "DRAWCURV.spad" 340846 340861 341299 341304) (-255 "DRAWCFUN.spad" 330018 330026 340836 340841) (-254 "DQAGG.spad" 328186 328196 329986 330013) (-253 "DPOLCAT.spad" 323527 323543 328054 328181) (-252 "DPOLCAT.spad" 318954 318972 323483 323488) (-251 "DPMO.spad" 311180 311196 311318 311619) (-250 "DPMM.spad" 303419 303437 303544 303845) (-249 "DOMCTOR.spad" 303311 303319 303409 303414) (-248 "DOMAIN.spad" 302442 302450 303301 303306) (-247 "DMP.spad" 299664 299679 300236 300363) (-246 "DLP.spad" 299012 299022 299654 299659) (-245 "DLIST.spad" 297591 297601 298195 298222) (-244 "DLAGG.spad" 296002 296012 297581 297586) (-243 "DIVRING.spad" 295544 295552 295946 295997) (-242 "DIVRING.spad" 295130 295140 295534 295539) (-241 "DISPLAY.spad" 293310 293318 295120 295125) (-240 "DIRPROD.spad" 282890 282906 283530 283661) (-239 "DIRPROD2.spad" 281698 281716 282880 282885) (-238 "DIRPCAT.spad" 280640 280656 281562 281693) (-237 "DIRPCAT.spad" 279311 279329 280235 280240) (-236 "DIOSP.spad" 278136 278144 279301 279306) (-235 "DIOPS.spad" 277120 277130 278116 278131) (-234 "DIOPS.spad" 276078 276090 277076 277081) (-233 "DIFRING.spad" 275370 275378 276058 276073) (-232 "DIFRING.spad" 274670 274680 275360 275365) (-231 "DIFEXT.spad" 273829 273839 274650 274665) (-230 "DIFEXT.spad" 272905 272917 273728 273733) (-229 "DIAGG.spad" 272535 272545 272885 272900) (-228 "DIAGG.spad" 272173 272185 272525 272530) (-227 "DHMATRIX.spad" 270477 270487 271630 271657) (-226 "DFSFUN.spad" 263885 263893 270467 270472) (-225 "DFLOAT.spad" 260606 260614 263775 263880) (-224 "DFINTTLS.spad" 258815 258831 260596 260601) (-223 "DERHAM.spad" 256725 256757 258795 258810) (-222 "DEQUEUE.spad" 256043 256053 256332 256359) (-221 "DEGRED.spad" 255658 255672 256033 256038) (-220 "DEFINTRF.spad" 253183 253193 255648 255653) (-219 "DEFINTEF.spad" 251679 251695 253173 253178) (-218 "DEFAST.spad" 251047 251055 251669 251674) (-217 "DECIMAL.spad" 249153 249161 249514 249607) (-216 "DDFACT.spad" 246952 246969 249143 249148) (-215 "DBLRESP.spad" 246550 246574 246942 246947) (-214 "DBASE.spad" 245204 245214 246540 246545) (-213 "DATAARY.spad" 244666 244679 245194 245199) (-212 "D03FAFA.spad" 244494 244502 244656 244661) (-211 "D03EEFA.spad" 244314 244322 244484 244489) (-210 "D03AGNT.spad" 243394 243402 244304 244309) (-209 "D02EJFA.spad" 242856 242864 243384 243389) (-208 "D02CJFA.spad" 242334 242342 242846 242851) (-207 "D02BHFA.spad" 241824 241832 242324 242329) (-206 "D02BBFA.spad" 241314 241322 241814 241819) (-205 "D02AGNT.spad" 236118 236126 241304 241309) (-204 "D01WGTS.spad" 234437 234445 236108 236113) (-203 "D01TRNS.spad" 234414 234422 234427 234432) (-202 "D01GBFA.spad" 233936 233944 234404 234409) (-201 "D01FCFA.spad" 233458 233466 233926 233931) (-200 "D01ASFA.spad" 232926 232934 233448 233453) (-199 "D01AQFA.spad" 232372 232380 232916 232921) (-198 "D01APFA.spad" 231796 231804 232362 232367) (-197 "D01ANFA.spad" 231290 231298 231786 231791) (-196 "D01AMFA.spad" 230800 230808 231280 231285) (-195 "D01ALFA.spad" 230340 230348 230790 230795) (-194 "D01AKFA.spad" 229866 229874 230330 230335) (-193 "D01AJFA.spad" 229389 229397 229856 229861) (-192 "D01AGNT.spad" 225448 225456 229379 229384) (-191 "CYCLOTOM.spad" 224954 224962 225438 225443) (-190 "CYCLES.spad" 221786 221794 224944 224949) (-189 "CVMP.spad" 221203 221213 221776 221781) (-188 "CTRIGMNP.spad" 219693 219709 221193 221198) (-187 "CTOR.spad" 219388 219396 219683 219688) (-186 "CTORKIND.spad" 218991 218999 219378 219383) (-185 "CTORCAT.spad" 218240 218248 218981 218986) (-184 "CTORCAT.spad" 217487 217497 218230 218235) (-183 "CTORCALL.spad" 217067 217075 217477 217482) (-182 "CSTTOOLS.spad" 216310 216323 217057 217062) (-181 "CRFP.spad" 210014 210027 216300 216305) (-180 "CRCEAST.spad" 209734 209742 210004 210009) (-179 "CRAPACK.spad" 208777 208787 209724 209729) (-178 "CPMATCH.spad" 208277 208292 208702 208707) (-177 "CPIMA.spad" 207982 208001 208267 208272) (-176 "COORDSYS.spad" 202875 202885 207972 207977) (-175 "CONTOUR.spad" 202286 202294 202865 202870) (-174 "CONTFRAC.spad" 197898 197908 202188 202281) (-173 "CONDUIT.spad" 197656 197664 197888 197893) (-172 "COMRING.spad" 197330 197338 197594 197651) (-171 "COMPPROP.spad" 196844 196852 197320 197325) (-170 "COMPLPAT.spad" 196611 196626 196834 196839) (-169 "COMPLEX.spad" 190635 190645 190879 191140) (-168 "COMPLEX2.spad" 190348 190360 190625 190630) (-167 "COMPFACT.spad" 189950 189964 190338 190343) (-166 "COMPCAT.spad" 188018 188028 189684 189945) (-165 "COMPCAT.spad" 185779 185791 187447 187452) (-164 "COMMUPC.spad" 185525 185543 185769 185774) (-163 "COMMONOP.spad" 185058 185066 185515 185520) (-162 "COMM.spad" 184867 184875 185048 185053) (-161 "COMMAAST.spad" 184630 184638 184857 184862) (-160 "COMBOPC.spad" 183535 183543 184620 184625) (-159 "COMBINAT.spad" 182280 182290 183525 183530) (-158 "COMBF.spad" 179648 179664 182270 182275) (-157 "COLOR.spad" 178485 178493 179638 179643) (-156 "COLONAST.spad" 178151 178159 178475 178480) (-155 "CMPLXRT.spad" 177860 177877 178141 178146) (-154 "CLLCTAST.spad" 177522 177530 177850 177855) (-153 "CLIP.spad" 173614 173622 177512 177517) (-152 "CLIF.spad" 172253 172269 173570 173609) (-151 "CLAGG.spad" 168738 168748 172243 172248) (-150 "CLAGG.spad" 165094 165106 168601 168606) (-149 "CINTSLPE.spad" 164419 164432 165084 165089) (-148 "CHVAR.spad" 162497 162519 164409 164414) (-147 "CHARZ.spad" 162412 162420 162477 162492) (-146 "CHARPOL.spad" 161920 161930 162402 162407) (-145 "CHARNZ.spad" 161673 161681 161900 161915) (-144 "CHAR.spad" 159541 159549 161663 161668) (-143 "CFCAT.spad" 158857 158865 159531 159536) (-142 "CDEN.spad" 158015 158029 158847 158852) (-141 "CCLASS.spad" 156164 156172 157426 157465) (-140 "CATEGORY.spad" 155254 155262 156154 156159) (-139 "CATCTOR.spad" 155145 155153 155244 155249) (-138 "CATAST.spad" 154763 154771 155135 155140) (-137 "CASEAST.spad" 154477 154485 154753 154758) (-136 "CARTEN.spad" 149580 149604 154467 154472) (-135 "CARTEN2.spad" 148966 148993 149570 149575) (-134 "CARD.spad" 146255 146263 148940 148961) (-133 "CAPSLAST.spad" 146029 146037 146245 146250) (-132 "CACHSET.spad" 145651 145659 146019 146024) (-131 "CABMON.spad" 145204 145212 145641 145646) (-130 "BYTEORD.spad" 144879 144887 145194 145199) (-129 "BYTE.spad" 144304 144312 144869 144874) (-128 "BYTEBUF.spad" 142161 142169 143473 143500) (-127 "BTREE.spad" 141230 141240 141768 141795) (-126 "BTOURN.spad" 140233 140243 140837 140864) (-125 "BTCAT.spad" 139621 139631 140201 140228) (-124 "BTCAT.spad" 139029 139041 139611 139616) (-123 "BTAGG.spad" 138151 138159 138997 139024) (-122 "BTAGG.spad" 137293 137303 138141 138146) (-121 "BSTREE.spad" 136028 136038 136900 136927) (-120 "BRILL.spad" 134223 134234 136018 136023) (-119 "BRAGG.spad" 133147 133157 134213 134218) (-118 "BRAGG.spad" 132035 132047 133103 133108) (-117 "BPADICRT.spad" 130016 130028 130271 130364) (-116 "BPADIC.spad" 129680 129692 129942 130011) (-115 "BOUNDZRO.spad" 129336 129353 129670 129675) (-114 "BOP.spad" 124800 124808 129326 129331) (-113 "BOP1.spad" 122186 122196 124756 124761) (-112 "BOOLEAN.spad" 121510 121518 122176 122181) (-111 "BMODULE.spad" 121222 121234 121478 121505) (-110 "BITS.spad" 120641 120649 120858 120885) (-109 "BINDING.spad" 120060 120068 120631 120636) (-108 "BINARY.spad" 118171 118179 118527 118620) (-107 "BGAGG.spad" 117368 117378 118151 118166) (-106 "BGAGG.spad" 116573 116585 117358 117363) (-105 "BFUNCT.spad" 116137 116145 116553 116568) (-104 "BEZOUT.spad" 115271 115298 116087 116092) (-103 "BBTREE.spad" 112090 112100 114878 114905) (-102 "BASTYPE.spad" 111762 111770 112080 112085) (-101 "BASTYPE.spad" 111432 111442 111752 111757) (-100 "BALFACT.spad" 110871 110884 111422 111427) (-99 "AUTOMOR.spad" 110318 110327 110851 110866) (-98 "ATTREG.spad" 107037 107044 110070 110313) (-97 "ATTRBUT.spad" 103060 103067 107017 107032) (-96 "ATTRAST.spad" 102777 102784 103050 103055) (-95 "ATRIG.spad" 102247 102254 102767 102772) (-94 "ATRIG.spad" 101715 101724 102237 102242) (-93 "ASTCAT.spad" 101619 101626 101705 101710) (-92 "ASTCAT.spad" 101521 101530 101609 101614) (-91 "ASTACK.spad" 100854 100863 101128 101155) (-90 "ASSOCEQ.spad" 99654 99665 100810 100815) (-89 "ASP9.spad" 98735 98748 99644 99649) (-88 "ASP8.spad" 97778 97791 98725 98730) (-87 "ASP80.spad" 97100 97113 97768 97773) (-86 "ASP7.spad" 96260 96273 97090 97095) (-85 "ASP78.spad" 95711 95724 96250 96255) (-84 "ASP77.spad" 95080 95093 95701 95706) (-83 "ASP74.spad" 94172 94185 95070 95075) (-82 "ASP73.spad" 93443 93456 94162 94167) (-81 "ASP6.spad" 92310 92323 93433 93438) (-80 "ASP55.spad" 90819 90832 92300 92305) (-79 "ASP50.spad" 88636 88649 90809 90814) (-78 "ASP4.spad" 87931 87944 88626 88631) (-77 "ASP49.spad" 86930 86943 87921 87926) (-76 "ASP42.spad" 85337 85376 86920 86925) (-75 "ASP41.spad" 83916 83955 85327 85332) (-74 "ASP35.spad" 82904 82917 83906 83911) (-73 "ASP34.spad" 82205 82218 82894 82899) (-72 "ASP33.spad" 81765 81778 82195 82200) (-71 "ASP31.spad" 80905 80918 81755 81760) (-70 "ASP30.spad" 79797 79810 80895 80900) (-69 "ASP29.spad" 79263 79276 79787 79792) (-68 "ASP28.spad" 70536 70549 79253 79258) (-67 "ASP27.spad" 69433 69446 70526 70531) (-66 "ASP24.spad" 68520 68533 69423 69428) (-65 "ASP20.spad" 67984 67997 68510 68515) (-64 "ASP1.spad" 67365 67378 67974 67979) (-63 "ASP19.spad" 62051 62064 67355 67360) (-62 "ASP12.spad" 61465 61478 62041 62046) (-61 "ASP10.spad" 60736 60749 61455 61460) (-60 "ARRAY2.spad" 60096 60105 60343 60370) (-59 "ARRAY1.spad" 58931 58940 59279 59306) (-58 "ARRAY12.spad" 57600 57611 58921 58926) (-57 "ARR2CAT.spad" 53262 53283 57568 57595) (-56 "ARR2CAT.spad" 48944 48967 53252 53257) (-55 "ARITY.spad" 48512 48519 48934 48939) (-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 2283334 2283339 2283344 2283349) (-2 NIL 2283314 2283319 2283324 2283329) (-1 NIL 2283294 2283299 2283304 2283309) (0 NIL 2283274 2283279 2283284 2283289) (-1287 "ZMOD.spad" 2283083 2283096 2283212 2283269) (-1286 "ZLINDEP.spad" 2282127 2282138 2283073 2283078) (-1285 "ZDSOLVE.spad" 2271976 2271998 2282117 2282122) (-1284 "YSTREAM.spad" 2271469 2271480 2271966 2271971) (-1283 "XRPOLY.spad" 2270689 2270709 2271325 2271394) (-1282 "XPR.spad" 2268480 2268493 2270407 2270506) (-1281 "XPOLY.spad" 2268035 2268046 2268336 2268405) (-1280 "XPOLYC.spad" 2267352 2267368 2267961 2268030) (-1279 "XPBWPOLY.spad" 2265789 2265809 2267132 2267201) (-1278 "XF.spad" 2264250 2264265 2265691 2265784) (-1277 "XF.spad" 2262691 2262708 2264134 2264139) (-1276 "XFALG.spad" 2259715 2259731 2262617 2262686) (-1275 "XEXPPKG.spad" 2258966 2258992 2259705 2259710) (-1274 "XDPOLY.spad" 2258580 2258596 2258822 2258891) (-1273 "XALG.spad" 2258240 2258251 2258536 2258575) (-1272 "WUTSET.spad" 2254079 2254096 2257886 2257913) (-1271 "WP.spad" 2253278 2253322 2253937 2254004) (-1270 "WHILEAST.spad" 2253076 2253085 2253268 2253273) (-1269 "WHEREAST.spad" 2252747 2252756 2253066 2253071) (-1268 "WFFINTBS.spad" 2250310 2250332 2252737 2252742) (-1267 "WEIER.spad" 2248524 2248535 2250300 2250305) (-1266 "VSPACE.spad" 2248197 2248208 2248492 2248519) (-1265 "VSPACE.spad" 2247890 2247903 2248187 2248192) (-1264 "VOID.spad" 2247567 2247576 2247880 2247885) (-1263 "VIEW.spad" 2245189 2245198 2247557 2247562) (-1262 "VIEWDEF.spad" 2240386 2240395 2245179 2245184) (-1261 "VIEW3D.spad" 2224221 2224230 2240376 2240381) (-1260 "VIEW2D.spad" 2211958 2211967 2224211 2224216) (-1259 "VECTOR.spad" 2210633 2210644 2210884 2210911) (-1258 "VECTOR2.spad" 2209260 2209273 2210623 2210628) (-1257 "VECTCAT.spad" 2207160 2207171 2209228 2209255) (-1256 "VECTCAT.spad" 2204868 2204881 2206938 2206943) (-1255 "VARIABLE.spad" 2204648 2204663 2204858 2204863) (-1254 "UTYPE.spad" 2204292 2204301 2204638 2204643) (-1253 "UTSODETL.spad" 2203585 2203609 2204248 2204253) (-1252 "UTSODE.spad" 2201773 2201793 2203575 2203580) (-1251 "UTS.spad" 2196562 2196590 2200240 2200337) (-1250 "UTSCAT.spad" 2194013 2194029 2196460 2196557) (-1249 "UTSCAT.spad" 2191108 2191126 2193557 2193562) (-1248 "UTS2.spad" 2190701 2190736 2191098 2191103) (-1247 "URAGG.spad" 2185333 2185344 2190691 2190696) (-1246 "URAGG.spad" 2179929 2179942 2185289 2185294) (-1245 "UPXSSING.spad" 2177572 2177598 2179010 2179143) (-1244 "UPXS.spad" 2174720 2174748 2175704 2175853) (-1243 "UPXSCONS.spad" 2172477 2172497 2172852 2173001) (-1242 "UPXSCCA.spad" 2171042 2171062 2172323 2172472) (-1241 "UPXSCCA.spad" 2169749 2169771 2171032 2171037) (-1240 "UPXSCAT.spad" 2168330 2168346 2169595 2169744) (-1239 "UPXS2.spad" 2167871 2167924 2168320 2168325) (-1238 "UPSQFREE.spad" 2166283 2166297 2167861 2167866) (-1237 "UPSCAT.spad" 2163876 2163900 2166181 2166278) (-1236 "UPSCAT.spad" 2161175 2161201 2163482 2163487) (-1235 "UPOLYC.spad" 2156153 2156164 2161017 2161170) (-1234 "UPOLYC.spad" 2151023 2151036 2155889 2155894) (-1233 "UPOLYC2.spad" 2150492 2150511 2151013 2151018) (-1232 "UP.spad" 2147649 2147664 2148042 2148195) (-1231 "UPMP.spad" 2146539 2146552 2147639 2147644) (-1230 "UPDIVP.spad" 2146102 2146116 2146529 2146534) (-1229 "UPDECOMP.spad" 2144339 2144353 2146092 2146097) (-1228 "UPCDEN.spad" 2143546 2143562 2144329 2144334) (-1227 "UP2.spad" 2142908 2142929 2143536 2143541) (-1226 "UNISEG.spad" 2142261 2142272 2142827 2142832) (-1225 "UNISEG2.spad" 2141754 2141767 2142217 2142222) (-1224 "UNIFACT.spad" 2140855 2140867 2141744 2141749) (-1223 "ULS.spad" 2131407 2131435 2132500 2132929) (-1222 "ULSCONS.spad" 2123801 2123821 2124173 2124322) (-1221 "ULSCCAT.spad" 2121530 2121550 2123647 2123796) (-1220 "ULSCCAT.spad" 2119367 2119389 2121486 2121491) (-1219 "ULSCAT.spad" 2117583 2117599 2119213 2119362) (-1218 "ULS2.spad" 2117095 2117148 2117573 2117578) (-1217 "UINT8.spad" 2116972 2116981 2117085 2117090) (-1216 "UINT64.spad" 2116848 2116857 2116962 2116967) (-1215 "UINT32.spad" 2116724 2116733 2116838 2116843) (-1214 "UINT16.spad" 2116600 2116609 2116714 2116719) (-1213 "UFD.spad" 2115665 2115674 2116526 2116595) (-1212 "UFD.spad" 2114792 2114803 2115655 2115660) (-1211 "UDVO.spad" 2113639 2113648 2114782 2114787) (-1210 "UDPO.spad" 2111066 2111077 2113595 2113600) (-1209 "TYPE.spad" 2110998 2111007 2111056 2111061) (-1208 "TYPEAST.spad" 2110917 2110926 2110988 2110993) (-1207 "TWOFACT.spad" 2109567 2109582 2110907 2110912) (-1206 "TUPLE.spad" 2109051 2109062 2109466 2109471) (-1205 "TUBETOOL.spad" 2105888 2105897 2109041 2109046) (-1204 "TUBE.spad" 2104529 2104546 2105878 2105883) (-1203 "TS.spad" 2103118 2103134 2104094 2104191) (-1202 "TSETCAT.spad" 2090245 2090262 2103086 2103113) (-1201 "TSETCAT.spad" 2077358 2077377 2090201 2090206) (-1200 "TRMANIP.spad" 2071724 2071741 2077064 2077069) (-1199 "TRIMAT.spad" 2070683 2070708 2071714 2071719) (-1198 "TRIGMNIP.spad" 2069200 2069217 2070673 2070678) (-1197 "TRIGCAT.spad" 2068712 2068721 2069190 2069195) (-1196 "TRIGCAT.spad" 2068222 2068233 2068702 2068707) (-1195 "TREE.spad" 2066793 2066804 2067829 2067856) (-1194 "TRANFUN.spad" 2066624 2066633 2066783 2066788) (-1193 "TRANFUN.spad" 2066453 2066464 2066614 2066619) (-1192 "TOPSP.spad" 2066127 2066136 2066443 2066448) (-1191 "TOOLSIGN.spad" 2065790 2065801 2066117 2066122) (-1190 "TEXTFILE.spad" 2064347 2064356 2065780 2065785) (-1189 "TEX.spad" 2061479 2061488 2064337 2064342) (-1188 "TEX1.spad" 2061035 2061046 2061469 2061474) (-1187 "TEMUTL.spad" 2060590 2060599 2061025 2061030) (-1186 "TBCMPPK.spad" 2058683 2058706 2060580 2060585) (-1185 "TBAGG.spad" 2057719 2057742 2058663 2058678) (-1184 "TBAGG.spad" 2056763 2056788 2057709 2057714) (-1183 "TANEXP.spad" 2056139 2056150 2056753 2056758) (-1182 "TABLE.spad" 2054550 2054573 2054820 2054847) (-1181 "TABLEAU.spad" 2054031 2054042 2054540 2054545) (-1180 "TABLBUMP.spad" 2050814 2050825 2054021 2054026) (-1179 "SYSTEM.spad" 2050042 2050051 2050804 2050809) (-1178 "SYSSOLP.spad" 2047515 2047526 2050032 2050037) (-1177 "SYSNNI.spad" 2046695 2046706 2047505 2047510) (-1176 "SYSINT.spad" 2046099 2046110 2046685 2046690) (-1175 "SYNTAX.spad" 2042293 2042302 2046089 2046094) (-1174 "SYMTAB.spad" 2040349 2040358 2042283 2042288) (-1173 "SYMS.spad" 2036334 2036343 2040339 2040344) (-1172 "SYMPOLY.spad" 2035341 2035352 2035423 2035550) (-1171 "SYMFUNC.spad" 2034816 2034827 2035331 2035336) (-1170 "SYMBOL.spad" 2032243 2032252 2034806 2034811) (-1169 "SWITCH.spad" 2029000 2029009 2032233 2032238) (-1168 "SUTS.spad" 2025899 2025927 2027467 2027564) (-1167 "SUPXS.spad" 2023034 2023062 2024031 2024180) (-1166 "SUP.spad" 2019803 2019814 2020584 2020737) (-1165 "SUPFRACF.spad" 2018908 2018926 2019793 2019798) (-1164 "SUP2.spad" 2018298 2018311 2018898 2018903) (-1163 "SUMRF.spad" 2017264 2017275 2018288 2018293) (-1162 "SUMFS.spad" 2016897 2016914 2017254 2017259) (-1161 "SULS.spad" 2007436 2007464 2008542 2008971) (-1160 "SUCHTAST.spad" 2007205 2007214 2007426 2007431) (-1159 "SUCH.spad" 2006885 2006900 2007195 2007200) (-1158 "SUBSPACE.spad" 1998892 1998907 2006875 2006880) (-1157 "SUBRESP.spad" 1998052 1998066 1998848 1998853) (-1156 "STTF.spad" 1994151 1994167 1998042 1998047) (-1155 "STTFNC.spad" 1990619 1990635 1994141 1994146) (-1154 "STTAYLOR.spad" 1983017 1983028 1990500 1990505) (-1153 "STRTBL.spad" 1981522 1981539 1981671 1981698) (-1152 "STRING.spad" 1980931 1980940 1980945 1980972) (-1151 "STRICAT.spad" 1980719 1980728 1980899 1980926) (-1150 "STREAM.spad" 1977577 1977588 1980244 1980259) (-1149 "STREAM3.spad" 1977122 1977137 1977567 1977572) (-1148 "STREAM2.spad" 1976190 1976203 1977112 1977117) (-1147 "STREAM1.spad" 1975894 1975905 1976180 1976185) (-1146 "STINPROD.spad" 1974800 1974816 1975884 1975889) (-1145 "STEP.spad" 1974001 1974010 1974790 1974795) (-1144 "STBL.spad" 1972527 1972555 1972694 1972709) (-1143 "STAGG.spad" 1971602 1971613 1972517 1972522) (-1142 "STAGG.spad" 1970675 1970688 1971592 1971597) (-1141 "STACK.spad" 1970026 1970037 1970282 1970309) (-1140 "SREGSET.spad" 1967730 1967747 1969672 1969699) (-1139 "SRDCMPK.spad" 1966275 1966295 1967720 1967725) (-1138 "SRAGG.spad" 1961372 1961381 1966243 1966270) (-1137 "SRAGG.spad" 1956489 1956500 1961362 1961367) (-1136 "SQMATRIX.spad" 1954105 1954123 1955021 1955108) (-1135 "SPLTREE.spad" 1948657 1948670 1953541 1953568) (-1134 "SPLNODE.spad" 1945245 1945258 1948647 1948652) (-1133 "SPFCAT.spad" 1944022 1944031 1945235 1945240) (-1132 "SPECOUT.spad" 1942572 1942581 1944012 1944017) (-1131 "SPADXPT.spad" 1934711 1934720 1942562 1942567) (-1130 "spad-parser.spad" 1934176 1934185 1934701 1934706) (-1129 "SPADAST.spad" 1933877 1933886 1934166 1934171) (-1128 "SPACEC.spad" 1917890 1917901 1933867 1933872) (-1127 "SPACE3.spad" 1917666 1917677 1917880 1917885) (-1126 "SORTPAK.spad" 1917211 1917224 1917622 1917627) (-1125 "SOLVETRA.spad" 1914968 1914979 1917201 1917206) (-1124 "SOLVESER.spad" 1913488 1913499 1914958 1914963) (-1123 "SOLVERAD.spad" 1909498 1909509 1913478 1913483) (-1122 "SOLVEFOR.spad" 1907918 1907936 1909488 1909493) (-1121 "SNTSCAT.spad" 1907518 1907535 1907886 1907913) (-1120 "SMTS.spad" 1905778 1905804 1907083 1907180) (-1119 "SMP.spad" 1903217 1903237 1903607 1903734) (-1118 "SMITH.spad" 1902060 1902085 1903207 1903212) (-1117 "SMATCAT.spad" 1900170 1900200 1902004 1902055) (-1116 "SMATCAT.spad" 1898212 1898244 1900048 1900053) (-1115 "SKAGG.spad" 1897173 1897184 1898180 1898207) (-1114 "SINT.spad" 1895999 1896008 1897039 1897168) (-1113 "SIMPAN.spad" 1895727 1895736 1895989 1895994) (-1112 "SIG.spad" 1895055 1895064 1895717 1895722) (-1111 "SIGNRF.spad" 1894163 1894174 1895045 1895050) (-1110 "SIGNEF.spad" 1893432 1893449 1894153 1894158) (-1109 "SIGAST.spad" 1892813 1892822 1893422 1893427) (-1108 "SHP.spad" 1890731 1890746 1892769 1892774) (-1107 "SHDP.spad" 1880442 1880469 1880951 1881082) (-1106 "SGROUP.spad" 1880050 1880059 1880432 1880437) (-1105 "SGROUP.spad" 1879656 1879667 1880040 1880045) (-1104 "SGCF.spad" 1872537 1872546 1879646 1879651) (-1103 "SFRTCAT.spad" 1871465 1871482 1872505 1872532) (-1102 "SFRGCD.spad" 1870528 1870548 1871455 1871460) (-1101 "SFQCMPK.spad" 1865165 1865185 1870518 1870523) (-1100 "SFORT.spad" 1864600 1864614 1865155 1865160) (-1099 "SEXOF.spad" 1864443 1864483 1864590 1864595) (-1098 "SEX.spad" 1864335 1864344 1864433 1864438) (-1097 "SEXCAT.spad" 1861886 1861926 1864325 1864330) (-1096 "SET.spad" 1860186 1860197 1861307 1861346) (-1095 "SETMN.spad" 1858620 1858637 1860176 1860181) (-1094 "SETCAT.spad" 1858105 1858114 1858610 1858615) (-1093 "SETCAT.spad" 1857588 1857599 1858095 1858100) (-1092 "SETAGG.spad" 1854109 1854120 1857568 1857583) (-1091 "SETAGG.spad" 1850638 1850651 1854099 1854104) (-1090 "SEQAST.spad" 1850341 1850350 1850628 1850633) (-1089 "SEGXCAT.spad" 1849463 1849476 1850331 1850336) (-1088 "SEG.spad" 1849276 1849287 1849382 1849387) (-1087 "SEGCAT.spad" 1848183 1848194 1849266 1849271) (-1086 "SEGBIND.spad" 1847255 1847266 1848138 1848143) (-1085 "SEGBIND2.spad" 1846951 1846964 1847245 1847250) (-1084 "SEGAST.spad" 1846665 1846674 1846941 1846946) (-1083 "SEG2.spad" 1846090 1846103 1846621 1846626) (-1082 "SDVAR.spad" 1845366 1845377 1846080 1846085) (-1081 "SDPOL.spad" 1842756 1842767 1843047 1843174) (-1080 "SCPKG.spad" 1840835 1840846 1842746 1842751) (-1079 "SCOPE.spad" 1839988 1839997 1840825 1840830) (-1078 "SCACHE.spad" 1838670 1838681 1839978 1839983) (-1077 "SASTCAT.spad" 1838579 1838588 1838660 1838665) (-1076 "SAOS.spad" 1838451 1838460 1838569 1838574) (-1075 "SAERFFC.spad" 1838164 1838184 1838441 1838446) (-1074 "SAE.spad" 1836339 1836355 1836950 1837085) (-1073 "SAEFACT.spad" 1836040 1836060 1836329 1836334) (-1072 "RURPK.spad" 1833681 1833697 1836030 1836035) (-1071 "RULESET.spad" 1833122 1833146 1833671 1833676) (-1070 "RULE.spad" 1831326 1831350 1833112 1833117) (-1069 "RULECOLD.spad" 1831178 1831191 1831316 1831321) (-1068 "RSTRCAST.spad" 1830895 1830904 1831168 1831173) (-1067 "RSETGCD.spad" 1827273 1827293 1830885 1830890) (-1066 "RSETCAT.spad" 1817057 1817074 1827241 1827268) (-1065 "RSETCAT.spad" 1806861 1806880 1817047 1817052) (-1064 "RSDCMPK.spad" 1805313 1805333 1806851 1806856) (-1063 "RRCC.spad" 1803697 1803727 1805303 1805308) (-1062 "RRCC.spad" 1802079 1802111 1803687 1803692) (-1061 "RPTAST.spad" 1801781 1801790 1802069 1802074) (-1060 "RPOLCAT.spad" 1781141 1781156 1801649 1801776) (-1059 "RPOLCAT.spad" 1760215 1760232 1780725 1780730) (-1058 "ROUTINE.spad" 1756078 1756087 1758862 1758889) (-1057 "ROMAN.spad" 1755406 1755415 1755944 1756073) (-1056 "ROIRC.spad" 1754486 1754518 1755396 1755401) (-1055 "RNS.spad" 1753389 1753398 1754388 1754481) (-1054 "RNS.spad" 1752378 1752389 1753379 1753384) (-1053 "RNG.spad" 1752113 1752122 1752368 1752373) (-1052 "RMODULE.spad" 1751751 1751762 1752103 1752108) (-1051 "RMCAT2.spad" 1751159 1751216 1751741 1751746) (-1050 "RMATRIX.spad" 1749983 1750002 1750326 1750365) (-1049 "RMATCAT.spad" 1745516 1745547 1749939 1749978) (-1048 "RMATCAT.spad" 1740939 1740972 1745364 1745369) (-1047 "RINTERP.spad" 1740827 1740847 1740929 1740934) (-1046 "RING.spad" 1740297 1740306 1740807 1740822) (-1045 "RING.spad" 1739775 1739786 1740287 1740292) (-1044 "RIDIST.spad" 1739159 1739168 1739765 1739770) (-1043 "RGCHAIN.spad" 1737738 1737754 1738644 1738671) (-1042 "RGBCSPC.spad" 1737519 1737531 1737728 1737733) (-1041 "RGBCMDL.spad" 1737049 1737061 1737509 1737514) (-1040 "RF.spad" 1734663 1734674 1737039 1737044) (-1039 "RFFACTOR.spad" 1734125 1734136 1734653 1734658) (-1038 "RFFACT.spad" 1733860 1733872 1734115 1734120) (-1037 "RFDIST.spad" 1732848 1732857 1733850 1733855) (-1036 "RETSOL.spad" 1732265 1732278 1732838 1732843) (-1035 "RETRACT.spad" 1731693 1731704 1732255 1732260) (-1034 "RETRACT.spad" 1731119 1731132 1731683 1731688) (-1033 "RETAST.spad" 1730931 1730940 1731109 1731114) (-1032 "RESULT.spad" 1728991 1729000 1729578 1729605) (-1031 "RESRING.spad" 1728338 1728385 1728929 1728986) (-1030 "RESLATC.spad" 1727662 1727673 1728328 1728333) (-1029 "REPSQ.spad" 1727391 1727402 1727652 1727657) (-1028 "REP.spad" 1724943 1724952 1727381 1727386) (-1027 "REPDB.spad" 1724648 1724659 1724933 1724938) (-1026 "REP2.spad" 1714220 1714231 1724490 1724495) (-1025 "REP1.spad" 1708210 1708221 1714170 1714175) (-1024 "REGSET.spad" 1706007 1706024 1707856 1707883) (-1023 "REF.spad" 1705336 1705347 1705962 1705967) (-1022 "REDORDER.spad" 1704512 1704529 1705326 1705331) (-1021 "RECLOS.spad" 1703295 1703315 1703999 1704092) (-1020 "REALSOLV.spad" 1702427 1702436 1703285 1703290) (-1019 "REAL.spad" 1702299 1702308 1702417 1702422) (-1018 "REAL0Q.spad" 1699581 1699596 1702289 1702294) (-1017 "REAL0.spad" 1696409 1696424 1699571 1699576) (-1016 "RDUCEAST.spad" 1696130 1696139 1696399 1696404) (-1015 "RDIV.spad" 1695781 1695806 1696120 1696125) (-1014 "RDIST.spad" 1695344 1695355 1695771 1695776) (-1013 "RDETRS.spad" 1694140 1694158 1695334 1695339) (-1012 "RDETR.spad" 1692247 1692265 1694130 1694135) (-1011 "RDEEFS.spad" 1691320 1691337 1692237 1692242) (-1010 "RDEEF.spad" 1690316 1690333 1691310 1691315) (-1009 "RCFIELD.spad" 1687502 1687511 1690218 1690311) (-1008 "RCFIELD.spad" 1684774 1684785 1687492 1687497) (-1007 "RCAGG.spad" 1682686 1682697 1684764 1684769) (-1006 "RCAGG.spad" 1680525 1680538 1682605 1682610) (-1005 "RATRET.spad" 1679885 1679896 1680515 1680520) (-1004 "RATFACT.spad" 1679577 1679589 1679875 1679880) (-1003 "RANDSRC.spad" 1678896 1678905 1679567 1679572) (-1002 "RADUTIL.spad" 1678650 1678659 1678886 1678891) (-1001 "RADIX.spad" 1675551 1675565 1677117 1677210) (-1000 "RADFF.spad" 1673964 1674001 1674083 1674239) (-999 "RADCAT.spad" 1673558 1673566 1673954 1673959) (-998 "RADCAT.spad" 1673150 1673160 1673548 1673553) (-997 "QUEUE.spad" 1672493 1672503 1672757 1672784) (-996 "QUAT.spad" 1671075 1671085 1671417 1671482) (-995 "QUATCT2.spad" 1670694 1670712 1671065 1671070) (-994 "QUATCAT.spad" 1668859 1668869 1670624 1670689) (-993 "QUATCAT.spad" 1666775 1666787 1668542 1668547) (-992 "QUAGG.spad" 1665601 1665611 1666743 1666770) (-991 "QQUTAST.spad" 1665370 1665378 1665591 1665596) (-990 "QFORM.spad" 1664833 1664847 1665360 1665365) (-989 "QFCAT.spad" 1663536 1663546 1664735 1664828) (-988 "QFCAT.spad" 1661830 1661842 1663031 1663036) (-987 "QFCAT2.spad" 1661521 1661537 1661820 1661825) (-986 "QEQUAT.spad" 1661078 1661086 1661511 1661516) (-985 "QCMPACK.spad" 1655825 1655844 1661068 1661073) (-984 "QALGSET.spad" 1651900 1651932 1655739 1655744) (-983 "QALGSET2.spad" 1649896 1649914 1651890 1651895) (-982 "PWFFINTB.spad" 1647206 1647227 1649886 1649891) (-981 "PUSHVAR.spad" 1646535 1646554 1647196 1647201) (-980 "PTRANFN.spad" 1642661 1642671 1646525 1646530) (-979 "PTPACK.spad" 1639749 1639759 1642651 1642656) (-978 "PTFUNC2.spad" 1639570 1639584 1639739 1639744) (-977 "PTCAT.spad" 1638819 1638829 1639538 1639565) (-976 "PSQFR.spad" 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"PRIMELT.spad" 1583360 1583374 1585369 1585374) (-956 "PRIMCAT.spad" 1582983 1582991 1583350 1583355) (-955 "PRIMARR.spad" 1581988 1581998 1582166 1582193) (-954 "PRIMARR2.spad" 1580711 1580723 1581978 1581983) (-953 "PREASSOC.spad" 1580083 1580095 1580701 1580706) (-952 "PPCURVE.spad" 1579220 1579228 1580073 1580078) (-951 "PORTNUM.spad" 1578995 1579003 1579210 1579215) (-950 "POLYROOT.spad" 1577824 1577846 1578951 1578956) (-949 "POLY.spad" 1575121 1575131 1575638 1575765) (-948 "POLYLIFT.spad" 1574382 1574405 1575111 1575116) (-947 "POLYCATQ.spad" 1572484 1572506 1574372 1574377) (-946 "POLYCAT.spad" 1565890 1565911 1572352 1572479) (-945 "POLYCAT.spad" 1558598 1558621 1565062 1565067) (-944 "POLY2UP.spad" 1558046 1558060 1558588 1558593) (-943 "POLY2.spad" 1557641 1557653 1558036 1558041) (-942 "POLUTIL.spad" 1556582 1556611 1557597 1557602) (-941 "POLTOPOL.spad" 1555330 1555345 1556572 1556577) (-940 "POINT.spad" 1554169 1554179 1554256 1554283) (-939 "PNTHEORY.spad" 1550835 1550843 1554159 1554164) (-938 "PMTOOLS.spad" 1549592 1549606 1550825 1550830) (-937 "PMSYM.spad" 1549137 1549147 1549582 1549587) (-936 "PMQFCAT.spad" 1548724 1548738 1549127 1549132) (-935 "PMPRED.spad" 1548193 1548207 1548714 1548719) (-934 "PMPREDFS.spad" 1547637 1547659 1548183 1548188) (-933 "PMPLCAT.spad" 1546707 1546725 1547569 1547574) (-932 "PMLSAGG.spad" 1546288 1546302 1546697 1546702) (-931 "PMKERNEL.spad" 1545855 1545867 1546278 1546283) (-930 "PMINS.spad" 1545431 1545441 1545845 1545850) (-929 "PMFS.spad" 1545004 1545022 1545421 1545426) (-928 "PMDOWN.spad" 1544290 1544304 1544994 1544999) (-927 "PMASS.spad" 1543302 1543310 1544280 1544285) (-926 "PMASSFS.spad" 1542271 1542287 1543292 1543297) (-925 "PLOTTOOL.spad" 1542051 1542059 1542261 1542266) (-924 "PLOT.spad" 1536882 1536890 1542041 1542046) (-923 "PLOT3D.spad" 1533302 1533310 1536872 1536877) (-922 "PLOT1.spad" 1532443 1532453 1533292 1533297) (-921 "PLEQN.spad" 1519659 1519686 1532433 1532438) (-920 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(-882 "PATLRES.spad" 1449638 1449652 1450544 1450549) (-881 "PATAB.spad" 1449402 1449412 1449628 1449633) (-880 "PARTPERM.spad" 1446764 1446772 1449392 1449397) (-879 "PARSURF.spad" 1446192 1446220 1446754 1446759) (-878 "PARSU2.spad" 1445987 1446003 1446182 1446187) (-877 "script-parser.spad" 1445507 1445515 1445977 1445982) (-876 "PARSCURV.spad" 1444935 1444963 1445497 1445502) (-875 "PARSC2.spad" 1444724 1444740 1444925 1444930) (-874 "PARPCURV.spad" 1444182 1444210 1444714 1444719) (-873 "PARPC2.spad" 1443971 1443987 1444172 1444177) (-872 "PAN2EXPR.spad" 1443383 1443391 1443961 1443966) (-871 "PALETTE.spad" 1442353 1442361 1443373 1443378) (-870 "PAIR.spad" 1441336 1441349 1441941 1441946) (-869 "PADICRC.spad" 1438666 1438684 1439841 1439934) (-868 "PADICRAT.spad" 1436681 1436693 1436902 1436995) (-867 "PADIC.spad" 1436376 1436388 1436607 1436676) (-866 "PADICCT.spad" 1434917 1434929 1436302 1436371) (-865 "PADEPAC.spad" 1433596 1433615 1434907 1434912) (-864 "PADE.spad" 1432336 1432352 1433586 1433591) (-863 "OWP.spad" 1431576 1431606 1432194 1432261) (-862 "OVERSET.spad" 1431149 1431157 1431566 1431571) (-861 "OVAR.spad" 1430930 1430953 1431139 1431144) (-860 "OUT.spad" 1430014 1430022 1430920 1430925) (-859 "OUTFORM.spad" 1419310 1419318 1430004 1430009) (-858 "OUTBFILE.spad" 1418728 1418736 1419300 1419305) (-857 "OUTBCON.spad" 1417726 1417734 1418718 1418723) (-856 "OUTBCON.spad" 1416722 1416732 1417716 1417721) (-855 "OSI.spad" 1416197 1416205 1416712 1416717) (-854 "OSGROUP.spad" 1416115 1416123 1416187 1416192) (-853 "ORTHPOL.spad" 1414576 1414586 1416032 1416037) (-852 "OREUP.spad" 1414029 1414057 1414256 1414295) (-851 "ORESUP.spad" 1413328 1413352 1413709 1413748) (-850 "OREPCTO.spad" 1411147 1411159 1413248 1413253) (-849 "OREPCAT.spad" 1405204 1405214 1411103 1411142) (-848 "OREPCAT.spad" 1399151 1399163 1405052 1405057) (-847 "ORDSET.spad" 1398317 1398325 1399141 1399146) (-846 "ORDSET.spad" 1397481 1397491 1398307 1398312) (-845 "ORDRING.spad" 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(-826 "OMPKG.spad" 1375200 1375208 1376578 1376583) (-825 "OM.spad" 1374165 1374173 1375190 1375195) (-824 "OMLO.spad" 1373590 1373602 1374051 1374090) (-823 "OMEXPR.spad" 1373424 1373434 1373580 1373585) (-822 "OMERR.spad" 1372967 1372975 1373414 1373419) (-821 "OMERRK.spad" 1372001 1372009 1372957 1372962) (-820 "OMENC.spad" 1371345 1371353 1371991 1371996) (-819 "OMDEV.spad" 1365634 1365642 1371335 1371340) (-818 "OMCONN.spad" 1365043 1365051 1365624 1365629) (-817 "OINTDOM.spad" 1364806 1364814 1364969 1365038) (-816 "OFMONOID.spad" 1360993 1361003 1364796 1364801) (-815 "ODVAR.spad" 1360254 1360264 1360983 1360988) (-814 "ODR.spad" 1359898 1359924 1360066 1360215) (-813 "ODPOL.spad" 1357244 1357254 1357584 1357711) (-812 "ODP.spad" 1347091 1347111 1347464 1347595) (-811 "ODETOOLS.spad" 1345674 1345693 1347081 1347086) (-810 "ODESYS.spad" 1343324 1343341 1345664 1345669) (-809 "ODERTRIC.spad" 1339265 1339282 1343281 1343286) (-808 "ODERED.spad" 1338652 1338676 1339255 1339260) (-807 "ODERAT.spad" 1336203 1336220 1338642 1338647) (-806 "ODEPRRIC.spad" 1333094 1333116 1336193 1336198) (-805 "ODEPROB.spad" 1332351 1332359 1333084 1333089) (-804 "ODEPRIM.spad" 1329625 1329647 1332341 1332346) (-803 "ODEPAL.spad" 1329001 1329025 1329615 1329620) (-802 "ODEPACK.spad" 1315603 1315611 1328991 1328996) (-801 "ODEINT.spad" 1315034 1315050 1315593 1315598) (-800 "ODEIFTBL.spad" 1312429 1312437 1315024 1315029) (-799 "ODEEF.spad" 1307796 1307812 1312419 1312424) (-798 "ODECONST.spad" 1307315 1307333 1307786 1307791) (-797 "ODECAT.spad" 1305911 1305919 1307305 1307310) (-796 "OCT.spad" 1304049 1304059 1304765 1304804) (-795 "OCTCT2.spad" 1303693 1303714 1304039 1304044) (-794 "OC.spad" 1301467 1301477 1303649 1303688) (-793 "OC.spad" 1298966 1298978 1301150 1301155) (-792 "OCAMON.spad" 1298814 1298822 1298956 1298961) (-791 "OASGP.spad" 1298629 1298637 1298804 1298809) (-790 "OAMONS.spad" 1298149 1298157 1298619 1298624) (-789 "OAMON.spad" 1298010 1298018 1298139 1298144) (-788 "OAGROUP.spad" 1297872 1297880 1298000 1298005) (-787 "NUMTUBE.spad" 1297459 1297475 1297862 1297867) (-786 "NUMQUAD.spad" 1285321 1285329 1297449 1297454) (-785 "NUMODE.spad" 1276457 1276465 1285311 1285316) (-784 "NUMINT.spad" 1274015 1274023 1276447 1276452) (-783 "NUMFMT.spad" 1272855 1272863 1274005 1274010) (-782 "NUMERIC.spad" 1264927 1264937 1272660 1272665) (-781 "NTSCAT.spad" 1263429 1263445 1264895 1264922) (-780 "NTPOLFN.spad" 1262974 1262984 1263346 1263351) (-779 "NSUP.spad" 1255984 1255994 1260524 1260677) (-778 "NSUP2.spad" 1255376 1255388 1255974 1255979) (-777 "NSMP.spad" 1251571 1251590 1251879 1252006) (-776 "NREP.spad" 1249943 1249957 1251561 1251566) (-775 "NPCOEF.spad" 1249189 1249209 1249933 1249938) (-774 "NORMRETR.spad" 1248787 1248826 1249179 1249184) (-773 "NORMPK.spad" 1246689 1246708 1248777 1248782) (-772 "NORMMA.spad" 1246377 1246403 1246679 1246684) (-771 "NONE.spad" 1246118 1246126 1246367 1246372) (-770 "NONE1.spad" 1245794 1245804 1246108 1246113) (-769 "NODE1.spad" 1245263 1245279 1245784 1245789) (-768 "NNI.spad" 1244150 1244158 1245237 1245258) (-767 "NLINSOL.spad" 1242772 1242782 1244140 1244145) (-766 "NIPROB.spad" 1241313 1241321 1242762 1242767) (-765 "NFINTBAS.spad" 1238773 1238790 1241303 1241308) (-764 "NETCLT.spad" 1238747 1238758 1238763 1238768) (-763 "NCODIV.spad" 1236945 1236961 1238737 1238742) (-762 "NCNTFRAC.spad" 1236587 1236601 1236935 1236940) (-761 "NCEP.spad" 1234747 1234761 1236577 1236582) (-760 "NASRING.spad" 1234343 1234351 1234737 1234742) (-759 "NASRING.spad" 1233937 1233947 1234333 1234338) (-758 "NARNG.spad" 1233281 1233289 1233927 1233932) (-757 "NARNG.spad" 1232623 1232633 1233271 1233276) (-756 "NAGSP.spad" 1231696 1231704 1232613 1232618) (-755 "NAGS.spad" 1221221 1221229 1231686 1231691) (-754 "NAGF07.spad" 1219614 1219622 1221211 1221216) (-753 "NAGF04.spad" 1213846 1213854 1219604 1219609) (-752 "NAGF02.spad" 1207655 1207663 1213836 1213841) (-751 "NAGF01.spad" 1203258 1203266 1207645 1207650) (-750 "NAGE04.spad" 1196718 1196726 1203248 1203253) (-749 "NAGE02.spad" 1187060 1187068 1196708 1196713) (-748 "NAGE01.spad" 1182944 1182952 1187050 1187055) (-747 "NAGD03.spad" 1180864 1180872 1182934 1182939) (-746 "NAGD02.spad" 1173395 1173403 1180854 1180859) (-745 "NAGD01.spad" 1167508 1167516 1173385 1173390) (-744 "NAGC06.spad" 1163295 1163303 1167498 1167503) (-743 "NAGC05.spad" 1161764 1161772 1163285 1163290) (-742 "NAGC02.spad" 1161019 1161027 1161754 1161759) (-741 "NAALG.spad" 1160554 1160564 1160987 1161014) (-740 "NAALG.spad" 1160109 1160121 1160544 1160549) (-739 "MULTSQFR.spad" 1157067 1157084 1160099 1160104) (-738 "MULTFACT.spad" 1156450 1156467 1157057 1157062) (-737 "MTSCAT.spad" 1154484 1154505 1156348 1156445) (-736 "MTHING.spad" 1154141 1154151 1154474 1154479) (-735 "MSYSCMD.spad" 1153575 1153583 1154131 1154136) (-734 "MSET.spad" 1151517 1151527 1153281 1153320) (-733 "MSETAGG.spad" 1151362 1151372 1151485 1151512) (-732 "MRING.spad" 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1017313 1020414 1020419) (-637 "LINEXP.spad" 1016733 1016743 1017281 1017296) (-636 "LINDEP.spad" 1015510 1015522 1016645 1016650) (-635 "LIMITRF.spad" 1013424 1013434 1015500 1015505) (-634 "LIMITPS.spad" 1012307 1012320 1013414 1013419) (-633 "LIE.spad" 1010321 1010333 1011597 1011742) (-632 "LIECAT.spad" 1009797 1009807 1010247 1010316) (-631 "LIECAT.spad" 1009301 1009313 1009753 1009758) (-630 "LIB.spad" 1007349 1007357 1007960 1007975) (-629 "LGROBP.spad" 1004702 1004721 1007339 1007344) (-628 "LF.spad" 1003621 1003637 1004692 1004697) (-627 "LFCAT.spad" 1002640 1002648 1003611 1003616) (-626 "LEXTRIPK.spad" 998143 998158 1002630 1002635) (-625 "LEXP.spad" 996146 996173 998123 998138) (-624 "LETAST.spad" 995845 995853 996136 996141) (-623 "LEADCDET.spad" 994229 994246 995835 995840) (-622 "LAZM3PK.spad" 992933 992955 994219 994224) (-621 "LAUPOL.spad" 991622 991635 992526 992595) (-620 "LAPLACE.spad" 991195 991211 991612 991617) (-619 "LA.spad" 990635 990649 991117 991156) (-618 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(-577 "IOBFILE.spad" 947253 947261 947882 947887) (-576 "IOBCON.spad" 947118 947126 947243 947248) (-575 "INVLAPLA.spad" 946763 946779 947108 947113) (-574 "INTTR.spad" 940009 940026 946753 946758) (-573 "INTTOOLS.spad" 937720 937736 939583 939588) (-572 "INTSLPE.spad" 937026 937034 937710 937715) (-571 "INTRVL.spad" 936592 936602 936940 937021) (-570 "INTRF.spad" 934956 934970 936582 936587) (-569 "INTRET.spad" 934388 934398 934946 934951) (-568 "INTRAT.spad" 933063 933080 934378 934383) (-567 "INTPM.spad" 931426 931442 932706 932711) (-566 "INTPAF.spad" 929194 929212 931358 931363) (-565 "INTPACK.spad" 919504 919512 929184 929189) (-564 "INT.spad" 918865 918873 919358 919499) (-563 "INTHERTR.spad" 918131 918148 918855 918860) (-562 "INTHERAL.spad" 917797 917821 918121 918126) (-561 "INTHEORY.spad" 914210 914218 917787 917792) (-560 "INTG0.spad" 907673 907691 914142 914147) (-559 "INTFTBL.spad" 901702 901710 907663 907668) (-558 "INTFACT.spad" 900761 900771 901692 901697) (-557 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"FORMULA.spad" 645230 645238 647756 647761) (-393 "FORMULA1.spad" 644709 644719 645220 645225) (-392 "FORDER.spad" 644400 644424 644699 644704) (-391 "FOP.spad" 643601 643609 644390 644395) (-390 "FNLA.spad" 643025 643047 643569 643596) (-389 "FNCAT.spad" 641612 641620 643015 643020) (-388 "FNAME.spad" 641504 641512 641602 641607) (-387 "FMTC.spad" 641302 641310 641430 641499) (-386 "FMONOID.spad" 638357 638367 641258 641263) (-385 "FM.spad" 638052 638064 638291 638318) (-384 "FMFUN.spad" 635082 635090 638042 638047) (-383 "FMC.spad" 634134 634142 635072 635077) (-382 "FMCAT.spad" 631788 631806 634102 634129) (-381 "FM1.spad" 631145 631157 631722 631749) (-380 "FLOATRP.spad" 628866 628880 631135 631140) (-379 "FLOAT.spad" 622154 622162 628732 628861) (-378 "FLOATCP.spad" 619571 619585 622144 622149) (-377 "FLINEXP.spad" 619283 619293 619551 619566) (-376 "FLINEXP.spad" 618949 618961 619219 619224) (-375 "FLASORT.spad" 618269 618281 618939 618944) (-374 "FLALG.spad" 615915 615934 618195 618264) (-373 "FLAGG.spad" 612933 612943 615895 615910) (-372 "FLAGG.spad" 609852 609864 612816 612821) (-371 "FLAGG2.spad" 608533 608549 609842 609847) (-370 "FINRALG.spad" 606562 606575 608489 608528) (-369 "FINRALG.spad" 604517 604532 606446 606451) (-368 "FINITE.spad" 603669 603677 604507 604512) (-367 "FINAALG.spad" 592650 592660 603611 603664) (-366 "FINAALG.spad" 581643 581655 592606 592611) (-365 "FILE.spad" 581226 581236 581633 581638) (-364 "FILECAT.spad" 579744 579761 581216 581221) (-363 "FIELD.spad" 579150 579158 579646 579739) (-362 "FIELD.spad" 578642 578652 579140 579145) (-361 "FGROUP.spad" 577251 577261 578622 578637) (-360 "FGLMICPK.spad" 576038 576053 577241 577246) (-359 "FFX.spad" 575413 575428 575754 575847) (-358 "FFSLPE.spad" 574902 574923 575403 575408) (-357 "FFPOLY.spad" 566154 566165 574892 574897) (-356 "FFPOLY2.spad" 565214 565231 566144 566149) (-355 "FFP.spad" 564611 564631 564930 565023) (-354 "FF.spad" 564059 564075 564292 564385) (-353 "FFNBX.spad" 562571 562591 563775 563868) (-352 "FFNBP.spad" 561084 561101 562287 562380) (-351 "FFNB.spad" 559549 559570 560765 560858) (-350 "FFINTBAS.spad" 556963 556982 559539 559544) (-349 "FFIELDC.spad" 554538 554546 556865 556958) (-348 "FFIELDC.spad" 552199 552209 554528 554533) (-347 "FFHOM.spad" 550947 550964 552189 552194) (-346 "FFF.spad" 548382 548393 550937 550942) (-345 "FFCGX.spad" 547229 547249 548098 548191) (-344 "FFCGP.spad" 546118 546138 546945 547038) (-343 "FFCG.spad" 544910 544931 545799 545892) (-342 "FFCAT.spad" 537937 537959 544749 544905) (-341 "FFCAT.spad" 531043 531067 537857 537862) (-340 "FFCAT2.spad" 530788 530828 531033 531038) (-339 "FEXPR.spad" 522497 522543 530544 530583) (-338 "FEVALAB.spad" 522203 522213 522487 522492) (-337 "FEVALAB.spad" 521694 521706 521980 521985) (-336 "FDIV.spad" 521136 521160 521684 521689) (-335 "FDIVCAT.spad" 519178 519202 521126 521131) (-334 "FDIVCAT.spad" 517218 517244 519168 519173) (-333 "FDIV2.spad" 516872 516912 517208 517213) (-332 "FCPAK1.spad" 515425 515433 516862 516867) (-331 "FCOMP.spad" 514804 514814 515415 515420) (-330 "FC.spad" 504719 504727 514794 514799) (-329 "FAXF.spad" 497654 497668 504621 504714) (-328 "FAXF.spad" 490641 490657 497610 497615) (-327 "FARRAY.spad" 488787 488797 489824 489851) (-326 "FAMR.spad" 486907 486919 488685 488782) (-325 "FAMR.spad" 485011 485025 486791 486796) (-324 "FAMONOID.spad" 484661 484671 484965 484970) (-323 "FAMONC.spad" 482883 482895 484651 484656) (-322 "FAGROUP.spad" 482489 482499 482779 482806) (-321 "FACUTIL.spad" 480685 480702 482479 482484) (-320 "FACTFUNC.spad" 479861 479871 480675 480680) (-319 "EXPUPXS.spad" 476694 476717 477993 478142) (-318 "EXPRTUBE.spad" 473922 473930 476684 476689) (-317 "EXPRODE.spad" 470794 470810 473912 473917) (-316 "EXPR.spad" 466069 466079 466783 467190) (-315 "EXPR2UPS.spad" 462161 462174 466059 466064) (-314 "EXPR2.spad" 461864 461876 462151 462156) (-313 "EXPEXPAN.spad" 458802 458827 459436 459529) (-312 "EXIT.spad" 458473 458481 458792 458797) (-311 "EXITAST.spad" 458209 458217 458463 458468) (-310 "EVALCYC.spad" 457667 457681 458199 458204) (-309 "EVALAB.spad" 457231 457241 457657 457662) (-308 "EVALAB.spad" 456793 456805 457221 457226) (-307 "EUCDOM.spad" 454335 454343 456719 456788) (-306 "EUCDOM.spad" 451939 451949 454325 454330) (-305 "ESTOOLS.spad" 443779 443787 451929 451934) (-304 "ESTOOLS2.spad" 443380 443394 443769 443774) (-303 "ESTOOLS1.spad" 443065 443076 443370 443375) (-302 "ES.spad" 435612 435620 443055 443060) (-301 "ES.spad" 428065 428075 435510 435515) (-300 "ESCONT.spad" 424838 424846 428055 428060) (-299 "ESCONT1.spad" 424587 424599 424828 424833) (-298 "ES2.spad" 424082 424098 424577 424582) (-297 "ES1.spad" 423648 423664 424072 424077) (-296 "ERROR.spad" 420969 420977 423638 423643) (-295 "EQTBL.spad" 419441 419463 419650 419677) (-294 "EQ.spad" 414315 414325 417114 417226) (-293 "EQ2.spad" 414031 414043 414305 414310) (-292 "EP.spad" 410345 410355 414021 414026) (-291 "ENV.spad" 409021 409029 410335 410340) (-290 "ENTIRER.spad" 408689 408697 408965 409016) (-289 "EMR.spad" 407890 407931 408615 408684) (-288 "ELTAGG.spad" 406130 406149 407880 407885) (-287 "ELTAGG.spad" 404334 404355 406086 406091) (-286 "ELTAB.spad" 403781 403799 404324 404329) (-285 "ELFUTS.spad" 403160 403179 403771 403776) (-284 "ELEMFUN.spad" 402849 402857 403150 403155) (-283 "ELEMFUN.spad" 402536 402546 402839 402844) (-282 "ELAGG.spad" 400479 400489 402516 402531) (-281 "ELAGG.spad" 398359 398371 400398 400403) (-280 "ELABEXPR.spad" 397282 397290 398349 398354) (-279 "EFUPXS.spad" 394058 394088 397238 397243) (-278 "EFULS.spad" 390894 390917 394014 394019) (-277 "EFSTRUC.spad" 388849 388865 390884 390889) (-276 "EF.spad" 383615 383631 388839 388844) (-275 "EAB.spad" 381891 381899 383605 383610) (-274 "E04UCFA.spad" 381427 381435 381881 381886) (-273 "E04NAFA.spad" 381004 381012 381417 381422) (-272 "E04MBFA.spad" 380584 380592 380994 380999) (-271 "E04JAFA.spad" 380120 380128 380574 380579) (-270 "E04GCFA.spad" 379656 379664 380110 380115) (-269 "E04FDFA.spad" 379192 379200 379646 379651) (-268 "E04DGFA.spad" 378728 378736 379182 379187) (-267 "E04AGNT.spad" 374570 374578 378718 378723) (-266 "DVARCAT.spad" 371255 371265 374560 374565) (-265 "DVARCAT.spad" 367938 367950 371245 371250) (-264 "DSMP.spad" 365369 365383 365674 365801) (-263 "DROPT.spad" 359314 359322 365359 365364) (-262 "DROPT1.spad" 358977 358987 359304 359309) (-261 "DROPT0.spad" 353804 353812 358967 358972) (-260 "DRAWPT.spad" 351959 351967 353794 353799) (-259 "DRAW.spad" 344559 344572 351949 351954) (-258 "DRAWHACK.spad" 343867 343877 344549 344554) (-257 "DRAWCX.spad" 341309 341317 343857 343862) (-256 "DRAWCURV.spad" 340846 340861 341299 341304) (-255 "DRAWCFUN.spad" 330018 330026 340836 340841) (-254 "DQAGG.spad" 328186 328196 329986 330013) (-253 "DPOLCAT.spad" 323527 323543 328054 328181) (-252 "DPOLCAT.spad" 318954 318972 323483 323488) (-251 "DPMO.spad" 311180 311196 311318 311619) (-250 "DPMM.spad" 303419 303437 303544 303845) (-249 "DOMCTOR.spad" 303311 303319 303409 303414) (-248 "DOMAIN.spad" 302442 302450 303301 303306) (-247 "DMP.spad" 299664 299679 300236 300363) (-246 "DLP.spad" 299012 299022 299654 299659) (-245 "DLIST.spad" 297591 297601 298195 298222) (-244 "DLAGG.spad" 296002 296012 297581 297586) (-243 "DIVRING.spad" 295544 295552 295946 295997) (-242 "DIVRING.spad" 295130 295140 295534 295539) (-241 "DISPLAY.spad" 293310 293318 295120 295125) (-240 "DIRPROD.spad" 282890 282906 283530 283661) (-239 "DIRPROD2.spad" 281698 281716 282880 282885) (-238 "DIRPCAT.spad" 280640 280656 281562 281693) (-237 "DIRPCAT.spad" 279311 279329 280235 280240) (-236 "DIOSP.spad" 278136 278144 279301 279306) (-235 "DIOPS.spad" 277120 277130 278116 278131) (-234 "DIOPS.spad" 276078 276090 277076 277081) (-233 "DIFRING.spad" 275370 275378 276058 276073) (-232 "DIFRING.spad" 274670 274680 275360 275365) (-231 "DIFEXT.spad" 273829 273839 274650 274665) (-230 "DIFEXT.spad" 272905 272917 273728 273733) (-229 "DIAGG.spad" 272535 272545 272885 272900) (-228 "DIAGG.spad" 272173 272185 272525 272530) (-227 "DHMATRIX.spad" 270477 270487 271630 271657) (-226 "DFSFUN.spad" 263885 263893 270467 270472) (-225 "DFLOAT.spad" 260606 260614 263775 263880) (-224 "DFINTTLS.spad" 258815 258831 260596 260601) (-223 "DERHAM.spad" 256725 256757 258795 258810) (-222 "DEQUEUE.spad" 256043 256053 256332 256359) (-221 "DEGRED.spad" 255658 255672 256033 256038) (-220 "DEFINTRF.spad" 253183 253193 255648 255653) (-219 "DEFINTEF.spad" 251679 251695 253173 253178) (-218 "DEFAST.spad" 251047 251055 251669 251674) (-217 "DECIMAL.spad" 249153 249161 249514 249607) (-216 "DDFACT.spad" 246952 246969 249143 249148) (-215 "DBLRESP.spad" 246550 246574 246942 246947) (-214 "DBASE.spad" 245204 245214 246540 246545) (-213 "DATAARY.spad" 244666 244679 245194 245199) (-212 "D03FAFA.spad" 244494 244502 244656 244661) (-211 "D03EEFA.spad" 244314 244322 244484 244489) (-210 "D03AGNT.spad" 243394 243402 244304 244309) (-209 "D02EJFA.spad" 242856 242864 243384 243389) (-208 "D02CJFA.spad" 242334 242342 242846 242851) (-207 "D02BHFA.spad" 241824 241832 242324 242329) (-206 "D02BBFA.spad" 241314 241322 241814 241819) (-205 "D02AGNT.spad" 236118 236126 241304 241309) (-204 "D01WGTS.spad" 234437 234445 236108 236113) (-203 "D01TRNS.spad" 234414 234422 234427 234432) (-202 "D01GBFA.spad" 233936 233944 234404 234409) (-201 "D01FCFA.spad" 233458 233466 233926 233931) (-200 "D01ASFA.spad" 232926 232934 233448 233453) (-199 "D01AQFA.spad" 232372 232380 232916 232921) (-198 "D01APFA.spad" 231796 231804 232362 232367) (-197 "D01ANFA.spad" 231290 231298 231786 231791) (-196 "D01AMFA.spad" 230800 230808 231280 231285) (-195 "D01ALFA.spad" 230340 230348 230790 230795) (-194 "D01AKFA.spad" 229866 229874 230330 230335) (-193 "D01AJFA.spad" 229389 229397 229856 229861) (-192 "D01AGNT.spad" 225448 225456 229379 229384) (-191 "CYCLOTOM.spad" 224954 224962 225438 225443) (-190 "CYCLES.spad" 221786 221794 224944 224949) (-189 "CVMP.spad" 221203 221213 221776 221781) (-188 "CTRIGMNP.spad" 219693 219709 221193 221198) (-187 "CTOR.spad" 219388 219396 219683 219688) (-186 "CTORKIND.spad" 218991 218999 219378 219383) (-185 "CTORCAT.spad" 218240 218248 218981 218986) (-184 "CTORCAT.spad" 217487 217497 218230 218235) (-183 "CTORCALL.spad" 217067 217075 217477 217482) (-182 "CSTTOOLS.spad" 216310 216323 217057 217062) (-181 "CRFP.spad" 210014 210027 216300 216305) (-180 "CRCEAST.spad" 209734 209742 210004 210009) (-179 "CRAPACK.spad" 208777 208787 209724 209729) (-178 "CPMATCH.spad" 208277 208292 208702 208707) (-177 "CPIMA.spad" 207982 208001 208267 208272) (-176 "COORDSYS.spad" 202875 202885 207972 207977) (-175 "CONTOUR.spad" 202286 202294 202865 202870) (-174 "CONTFRAC.spad" 197898 197908 202188 202281) (-173 "CONDUIT.spad" 197656 197664 197888 197893) (-172 "COMRING.spad" 197330 197338 197594 197651) (-171 "COMPPROP.spad" 196844 196852 197320 197325) (-170 "COMPLPAT.spad" 196611 196626 196834 196839) (-169 "COMPLEX.spad" 190635 190645 190879 191140) (-168 "COMPLEX2.spad" 190348 190360 190625 190630) (-167 "COMPFACT.spad" 189950 189964 190338 190343) (-166 "COMPCAT.spad" 188018 188028 189684 189945) (-165 "COMPCAT.spad" 185779 185791 187447 187452) (-164 "COMMUPC.spad" 185525 185543 185769 185774) (-163 "COMMONOP.spad" 185058 185066 185515 185520) (-162 "COMM.spad" 184867 184875 185048 185053) (-161 "COMMAAST.spad" 184630 184638 184857 184862) (-160 "COMBOPC.spad" 183535 183543 184620 184625) (-159 "COMBINAT.spad" 182280 182290 183525 183530) (-158 "COMBF.spad" 179648 179664 182270 182275) (-157 "COLOR.spad" 178485 178493 179638 179643) (-156 "COLONAST.spad" 178151 178159 178475 178480) (-155 "CMPLXRT.spad" 177860 177877 178141 178146) (-154 "CLLCTAST.spad" 177522 177530 177850 177855) (-153 "CLIP.spad" 173614 173622 177512 177517) (-152 "CLIF.spad" 172253 172269 173570 173609) (-151 "CLAGG.spad" 168738 168748 172243 172248) (-150 "CLAGG.spad" 165094 165106 168601 168606) (-149 "CINTSLPE.spad" 164419 164432 165084 165089) (-148 "CHVAR.spad" 162497 162519 164409 164414) (-147 "CHARZ.spad" 162412 162420 162477 162492) (-146 "CHARPOL.spad" 161920 161930 162402 162407) (-145 "CHARNZ.spad" 161673 161681 161900 161915) (-144 "CHAR.spad" 159541 159549 161663 161668) (-143 "CFCAT.spad" 158857 158865 159531 159536) (-142 "CDEN.spad" 158015 158029 158847 158852) (-141 "CCLASS.spad" 156164 156172 157426 157465) (-140 "CATEGORY.spad" 155254 155262 156154 156159) (-139 "CATCTOR.spad" 155145 155153 155244 155249) (-138 "CATAST.spad" 154763 154771 155135 155140) (-137 "CASEAST.spad" 154477 154485 154753 154758) (-136 "CARTEN.spad" 149580 149604 154467 154472) (-135 "CARTEN2.spad" 148966 148993 149570 149575) (-134 "CARD.spad" 146255 146263 148940 148961) (-133 "CAPSLAST.spad" 146029 146037 146245 146250) (-132 "CACHSET.spad" 145651 145659 146019 146024) (-131 "CABMON.spad" 145204 145212 145641 145646) (-130 "BYTEORD.spad" 144879 144887 145194 145199) (-129 "BYTE.spad" 144304 144312 144869 144874) (-128 "BYTEBUF.spad" 142161 142169 143473 143500) (-127 "BTREE.spad" 141230 141240 141768 141795) (-126 "BTOURN.spad" 140233 140243 140837 140864) (-125 "BTCAT.spad" 139621 139631 140201 140228) (-124 "BTCAT.spad" 139029 139041 139611 139616) (-123 "BTAGG.spad" 138151 138159 138997 139024) (-122 "BTAGG.spad" 137293 137303 138141 138146) (-121 "BSTREE.spad" 136028 136038 136900 136927) (-120 "BRILL.spad" 134223 134234 136018 136023) (-119 "BRAGG.spad" 133147 133157 134213 134218) (-118 "BRAGG.spad" 132035 132047 133103 133108) (-117 "BPADICRT.spad" 130016 130028 130271 130364) (-116 "BPADIC.spad" 129680 129692 129942 130011) (-115 "BOUNDZRO.spad" 129336 129353 129670 129675) (-114 "BOP.spad" 124800 124808 129326 129331) (-113 "BOP1.spad" 122186 122196 124756 124761) (-112 "BOOLEAN.spad" 121510 121518 122176 122181) (-111 "BMODULE.spad" 121222 121234 121478 121505) (-110 "BITS.spad" 120641 120649 120858 120885) (-109 "BINDING.spad" 120060 120068 120631 120636) (-108 "BINARY.spad" 118171 118179 118527 118620) (-107 "BGAGG.spad" 117368 117378 118151 118166) (-106 "BGAGG.spad" 116573 116585 117358 117363) (-105 "BFUNCT.spad" 116137 116145 116553 116568) (-104 "BEZOUT.spad" 115271 115298 116087 116092) (-103 "BBTREE.spad" 112090 112100 114878 114905) (-102 "BASTYPE.spad" 111762 111770 112080 112085) (-101 "BASTYPE.spad" 111432 111442 111752 111757) (-100 "BALFACT.spad" 110871 110884 111422 111427) (-99 "AUTOMOR.spad" 110318 110327 110851 110866) (-98 "ATTREG.spad" 107037 107044 110070 110313) (-97 "ATTRBUT.spad" 103060 103067 107017 107032) (-96 "ATTRAST.spad" 102777 102784 103050 103055) (-95 "ATRIG.spad" 102247 102254 102767 102772) (-94 "ATRIG.spad" 101715 101724 102237 102242) (-93 "ASTCAT.spad" 101619 101626 101705 101710) (-92 "ASTCAT.spad" 101521 101530 101609 101614) (-91 "ASTACK.spad" 100854 100863 101128 101155) (-90 "ASSOCEQ.spad" 99654 99665 100810 100815) (-89 "ASP9.spad" 98735 98748 99644 99649) (-88 "ASP8.spad" 97778 97791 98725 98730) (-87 "ASP80.spad" 97100 97113 97768 97773) (-86 "ASP7.spad" 96260 96273 97090 97095) (-85 "ASP78.spad" 95711 95724 96250 96255) (-84 "ASP77.spad" 95080 95093 95701 95706) (-83 "ASP74.spad" 94172 94185 95070 95075) (-82 "ASP73.spad" 93443 93456 94162 94167) (-81 "ASP6.spad" 92310 92323 93433 93438) (-80 "ASP55.spad" 90819 90832 92300 92305) (-79 "ASP50.spad" 88636 88649 90809 90814) (-78 "ASP4.spad" 87931 87944 88626 88631) (-77 "ASP49.spad" 86930 86943 87921 87926) (-76 "ASP42.spad" 85337 85376 86920 86925) (-75 "ASP41.spad" 83916 83955 85327 85332) (-74 "ASP35.spad" 82904 82917 83906 83911) (-73 "ASP34.spad" 82205 82218 82894 82899) (-72 "ASP33.spad" 81765 81778 82195 82200) (-71 "ASP31.spad" 80905 80918 81755 81760) (-70 "ASP30.spad" 79797 79810 80895 80900) (-69 "ASP29.spad" 79263 79276 79787 79792) (-68 "ASP28.spad" 70536 70549 79253 79258) (-67 "ASP27.spad" 69433 69446 70526 70531) (-66 "ASP24.spad" 68520 68533 69423 69428) (-65 "ASP20.spad" 67984 67997 68510 68515) (-64 "ASP1.spad" 67365 67378 67974 67979) (-63 "ASP19.spad" 62051 62064 67355 67360) (-62 "ASP12.spad" 61465 61478 62041 62046) (-61 "ASP10.spad" 60736 60749 61455 61460) (-60 "ARRAY2.spad" 60096 60105 60343 60370) (-59 "ARRAY1.spad" 58931 58940 59279 59306) (-58 "ARRAY12.spad" 57600 57611 58921 58926) (-57 "ARR2CAT.spad" 53262 53283 57568 57595) (-56 "ARR2CAT.spad" 48944 48967 53252 53257) (-55 "ARITY.spad" 48512 48519 48934 48939) (-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)) @@ -255,21 +255,21 @@ (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -474,10 +474,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -488,7 +488,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-388) (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . 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T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-859)) . T)) ((((-1175)) . T)) (|has| |#1| (-817)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-847)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-906)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-859)) . 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T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#) ((|#2|) . T) (((-564)) . T)) (((|#1| |#2| |#3|) . T)) -(-4005 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +(-4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -944,14 +944,14 @@ ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -962,7 +962,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-845)) -(((|#2| (-240 (-2781 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-240 (-2589 |#1|) (-768)) (-861 |#1|)) . T)) (|has| |#3| (-845)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -977,20 +977,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4005 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1046))) -(((|#2|) . T) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -(-4005 (|has| |#3| (-790)) (|has| |#3| (-845))) -(-4005 (|has| |#3| (-790)) (|has| |#3| (-845))) +(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1014,11 +1014,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-564)) -4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1046))) ((|#2|) -4005 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094)))) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-564)) -4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-1046))) ((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-1094))) (((-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094)))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($ $) . T) ((|#2| $) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1026,8 +1026,8 @@ ((((-859)) . T)) ((((-859)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) |has| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (-309 (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))))) ((((-859)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1038,10 +1038,10 @@ ((($ $) . T) ((#0=(-861 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1129,11 +1129,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-897 (-1170)))) -(-4005 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-4002 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-859)) . T)) ((((-859)) . T)) @@ -1141,8 +1141,8 @@ ((((-907 |#1|)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1151,16 +1151,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-867 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . T) (($) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1035 (-407 (-564))))) ((|#1|) . T)) +((((-564)) . T) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1035 (-407 (-564))))) ((|#1|) . T)) (((|#1| |#2|) . T)) -(-4005 (|has| |#2| (-790)) (|has| |#2| (-845))) -(-4005 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) (((|#1|) . T)) (-12 (|has| |#1| (-790)) (|has| |#2| (-790))) (-12 (|has| |#1| (-790)) (|has| |#2| (-790))) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1171,8 +1171,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -1187,14 +1187,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) -((($) . T) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . T) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) #0#) |has| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (-309 (-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))))) +(((#0=(-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))))) (|has| |#2| (-847)) ((($) . T)) (((|#2|) |has| |#2| (-1094))) -((((-859)) -4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +((((-859)) -4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) (|has| |#1| (-847)) (|has| |#1| (-847)) ((((-1152) (-52)) . T)) @@ -1203,10 +1203,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-859)) . T)) ((((-907 |#1|)) . T)) (|has| |#1| (-363)) @@ -1233,21 +1233,21 @@ ((((-859)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . T) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906)))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536))) (((-889 (-379))) |has| |#1| (-612 (-889 (-379)))) (((-889 (-564))) |has| |#1| (-612 (-889 (-564))))) ((((-859)) . T)) -(((|#2|) . T) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-506)) . T)) (|has| |#2| (-845)) ((((-506)) . T)) @@ -1255,39 +1255,39 @@ (|has| |#1| (-556)) ((((-1152) |#1|) . T)) (|has| |#1| (-1145)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-955 |#1|)) . T)) -(((#0=(-407 (-564)) #0#) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) +(((#0=(-407 (-564)) #0#) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-564))) (((-564)) |has| |#1| (-1035 (-564))) (((-1170)) |has| |#1| (-1035 (-1170))) ((|#1|) . T)) ((((-564) |#2|) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) ((((-564)) |has| |#1| (-883 (-564))) (((-379)) |has| |#1| (-883 (-379)))) -((((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1|) . T)) +((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1|) . T)) (((|#1|) . T)) ((((-641 |#4|)) . T) (((-859)) . T)) ((((-536)) |has| |#4| (-612 (-536)))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-859)) . T) (((-641 |#4|)) . 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T)) ((((-1170)) |has| (-407 |#2|) (-897 (-1170)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) #0#) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) #0#) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-859)) -4005 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-859))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) +((((-859)) -4002 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-859))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) -(((|#2| |#2|) -4005 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($ $) |has| |#2| (-172))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(((|#2| |#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-859)) . T)) ((((-859)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T) ((|#2|) . T)) ((((-859)) . T)) ((((-859)) . T)) ((((-1152) (-1170) (-564) (-225) (-859)) . T)) @@ -1322,8 +1322,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -(((|#2|) -4005 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1046))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-890 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) @@ -1335,11 +1335,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1376,7 +1376,7 @@ ((((-996 |#1|)) . T) ((|#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1384,9 +1384,9 @@ (|has| |#1| (-847)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1399,7 +1399,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) #0#) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) #0#) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1434,19 +1434,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) #0#) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) #0#) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-847)) (((|#2| (-768) (-1076)) . T)) (((|#1| |#2|) . T)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-788)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-4005 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-4005 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-4002 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-4002 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1460,10 +1460,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094))) (((-955 |#1|)) . T)) (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1477,8 +1477,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1353 (-1152)) (|:| -2577 #0#))) . T)) +((((-859)) -4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-859))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2351 (-1152)) (|:| -1327 #0#))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1486,7 +1486,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-4005 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4002 (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) (|has| |#1| (-363)) ((((-859)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1497,8 +1497,8 @@ (|has| |#1| (-845)) ((((-859)) . T)) (((|#2|) . T)) -((((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4005 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4005 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-816 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1507,7 +1507,7 @@ ((((-859)) . T)) ((((-859)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2781 |#1|) (-768)) (-861 |#1|)) . T)) +(((|#2| (-482 (-2589 |#1|) (-768)) (-861 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1527,16 +1527,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-907 |#1|)) . T)) -(((|#1|) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4005 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +(((|#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046))) (($) -4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) (|has| |#1| (-847)) (|has| |#1| (-847)) @@ -1555,11 +1555,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-847)) (|has| |#1| (-847)) -(((|#3|) -4005 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-4005 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) +(((|#3|) -4002 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-4002 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-906))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -4005 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1568,7 +1568,7 @@ (|has| |#1| (-817)) (|has| |#1| (-817)) (((|#1|) . T)) -(-4005 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-845)) (|has| |#1| (-845)) (|has| |#1| (-845)) @@ -1577,13 +1577,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-1170)) |has| |#1| (-897 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((#0=(-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) #0#) |has| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (-309 (-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))))) +(((#0=(-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-859)) . T) (((-1175)) . T)) @@ -1602,11 +1602,11 @@ (((|#1| (-768) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4005 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4002 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1629,32 +1629,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1663,7 +1663,7 @@ ((((-859)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1671,12 +1671,12 @@ ((((-859)) . T)) ((((-859)) . T)) (((|#2|) . T)) -(-4005 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1689,16 +1689,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-4005 (|has| |#2| (-817)) (|has| |#2| (-847))) +(-4002 (|has| |#2| (-817)) (|has| |#2| (-847))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-859)) . T)) ((((-564)) . T) (($) . T)) ((((-768)) . T)) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) ((($) . T) (((-564)) . T)) @@ -1706,30 +1706,30 @@ (|has| |#2| (-906)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-859)) . T)) (|has| |#1| (-906)) (|has| |#1| (-906)) (|has| |#1| (-906)) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-906))) ((($) . T) ((|#2|) . T)) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) ((((-859)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1751,7 +1751,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-768)) . T)) (((|#1|) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-859)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1771,18 +1771,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-859)) . T)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) (((|#3|) . T)) -(-4005 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4002 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-859)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-859)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4005 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) -4002 (-12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-768)) . T)) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4002 (|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| (-883 (-564))) (((-379)) |has| |#1| (-883 (-379)))) @@ -1790,7 +1790,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-859)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1798,7 +1798,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -4005 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -4002 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-817)) @@ -1808,8 +1808,8 @@ (|has| |#1| (-845)) (|has| |#1| (-845)) (((|#1| (-564) (-1076)) . T)) -(-4005 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +(-4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (|has| |#1| (-847)) @@ -1822,33 +1822,33 @@ (|has| |#1| (-1094)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -4005 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) +((((-564)) -4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) -((((-685 (-339 (-3720) (-3720 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +((((-685 (-339 (-1776) (-1776 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) ((((-859)) . T)) (|has| |#3| (-845)) ((((-859)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-859)) . T)) -(((|#1| |#1|) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) +(((|#1| |#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) +(((|#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1046)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-847)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) |has| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (-309 (-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-906))) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) |has| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-906))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-859)) . T)) ((((-859)) . T)) @@ -1879,25 +1879,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1035 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4005 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) -4002 (|has| |#1| (-845)) (|has| |#1| (-1035 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-859)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-1046))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1924,7 +1924,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-768) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -4005 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -4002 (|has| (-407 (-564)) (-1035 (-564))) (|has| |#1| (-1035 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1945,25 +1945,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-845)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1035 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-859)) -4005 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-859)) -4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) ((((-859)) . T)) ((((-564) |#1|) . T)) ((((-859)) . 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 (|:| -1353 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-949 |#1|))) . T)) (((|#2| |#2|) . T)) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-847)) @@ -1974,14 +1974,14 @@ (((|#3|) |has| |#3| (-1046))) ((((-1170)) |has| |#2| (-897 (-1170)))) ((((-859)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1046)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2002,11 +2002,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-847)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) |has| (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)) (-309 (-2 (|:| -1353 |#1|) (|:| -2577 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) |has| (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)) (-309 (-2 (|:| -2351 |#1|) (|:| -1327 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2024,11 +2024,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-889 (-564))) |has| |#1| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#1| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#1| (-1019))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-859)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -4005 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2039,11 +2039,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-859)) . T)) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-906))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-906))) (((|#1|) . T)) (|has| |#1| (-847)) (|has| |#1| (-847)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-768)) . T)) @@ -2054,13 +2054,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|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)) -(-4005 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4005 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4002 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4002 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2075,23 +2075,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-1035 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) ((((-859)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-949 |#1|)) . T) (((-859)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -4005 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -4002 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) ((((-949 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-897 (-1170)))) -(((|#1|) . T) (($) -4005 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -4002 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-859)) . T)) (((|#1|) . T)) @@ -2099,8 +2099,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-867 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4005 (|has| |#4| (-790)) (|has| |#4| (-845))) -(-4005 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4002 (|has| |#4| (-790)) (|has| |#4| (-845))) +(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) ((((-859)) . T)) ((((-859)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2116,17 +2116,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1035 (-407 (-564)))) (((-564)) |has| #0# (-1035 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-768)) . T)) (|has| |#1| (-847)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4005 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))) |has| (-2 (|:| -1353 (-1152)) (|:| -2577 (-52))) (-309 (-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))))) +((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-845)) (|has| |#1| (-38 (-407 (-564)))) @@ -2150,29 +2150,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-859)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) +(((|#2|) . T) (((-564)) . T) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) (((|#1| |#2|) . T)) ((((-144)) . T)) ((((-777 |#1| (-861 |#2|))) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (|has| |#1| (-1194)) ((((-859)) . T)) (((|#1|) . T)) -(-4005 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) +(-4002 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-723)) (|has| |#3| (-790)) (|has| |#3| (-845)) (|has| |#3| (-1046)) (|has| |#3| (-1094))) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) (((|#2|) . T)) -((($ $) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-907 |#1|)) . T)) ((($) . T)) ((((-407 (-949 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-859)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-845)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) |has| (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|)) (-309 (-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) |has| (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|)) (-309 (-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-847)) @@ -2181,16 +2181,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-4005 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-4005 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-4002 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-4002 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-845)) (((|#1| |#2|) . T)) @@ -2214,9 +2214,9 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -4002 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2238,13 +2238,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-4005 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-723)) (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1|) . T)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2260,7 +2260,7 @@ (((|#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| (-1035 (-564)))) (((-564)) -4005 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4005 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1035 (-564)))) (((-564)) -4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1035 (-564))) (|has| |#1| (-1046))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -4002 (|has| |#1| (-556)) (|has| |#1| (-1035 (-407 (-564))))) (((-407 (-949 |#1|))) |has| |#1| (-556)) (((-949 |#1|)) |has| |#1| (-1046)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1035 (-407 (-564)))) (((-564)) |has| |#2| (-1035 (-564))) ((|#2|) . T) (((-861 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) @@ -2273,12 +2273,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) (((-564)) |has| |#1| (-1035 (-564))) ((|#1|) . T)) ((((-859)) . T)) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-723)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2298,14 +2298,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-4005 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-768)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-906)) -(-4005 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-859)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-907 |#1|)) . T)) @@ -2314,14 +2314,14 @@ ((((-859)) . T)) ((($) . T)) ((($) . T)) -(-4005 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-4005 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4005 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) +(-4002 (-12 (|has| |#1| (-307)) (|has| |#1| (-906))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-897 (-1170))) (|has| |#1| (-1046))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-859)) . T)) @@ -2354,27 +2354,27 @@ (((|#1|) |has| |#1| (-172))) ((((-859)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -4005 (|has| |#2| (-6 (-4413 "*"))) (|has| |#2| (-172)))) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(((|#2|) -4002 (|has| |#2| (-6 (-4413 "*"))) (|has| |#2| (-172)))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#2| (-847)) (|has| |#2| (-906)) (|has| |#1| (-906)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-859)) . T)) ((((-859)) . T)) ((((-536)) . T) (((-564)) . T) (((-889 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) (((|#1|) . T)) ((((-859)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-4005 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-4002 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-845)) @@ -2390,7 +2390,7 @@ ((((-859)) . T)) ((((-859)) . T)) ((((-187)) . T) (((-859)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2403,7 +2403,7 @@ ((((-859)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) (|has| |#1| (-847)) ((((-859)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2415,16 +2415,16 @@ (((|#2|) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-4005 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4005 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4002 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4002 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-1170) (-52)) . T)) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (|has| |#1| (-906)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-906)) @@ -2441,12 +2441,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (|has| |#1| (-817)) (((#0=(-907 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-845)) -((((-1195 |#1|)) . T) (((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-907 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1046)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046)))) @@ -2457,11 +2457,11 @@ (((|#2|) . T)) ((((-859)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -1353 (-1170)) (|:| -2577 #0#))) . T)) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -2351 (-1170)) (|:| -1327 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-859)) . T)) @@ -2469,15 +2469,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-859)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -4005 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -4005 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4002 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -4002 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2500,7 +2500,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2538,7 +2538,7 @@ (|has| |#2| (-1019)) ((($) . T)) (|has| |#1| (-906)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2546,9 +2546,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-907 |#1|)) . T)) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-4005 (|has| |#1| (-368)) (|has| |#1| (-847))) +(-4002 (|has| |#1| (-368)) (|has| |#1| (-847))) (((|#1|) . T)) ((((-768)) . T)) ((((-859)) . T)) @@ -2559,16 +2559,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-768) |#1|) . T)) -(((|#2| (-240 (-2781 |#1|) (-768))) . T)) +(((|#2| (-240 (-2589 |#1|) (-768))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((((-1152)) . T) (((-859)) . T)) -(((#0=(-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) #0#) |has| (-2 (|:| -1353 (-1170)) (|:| -2577 (-52))) (-309 (-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))))) +(((#0=(-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) #0#) |has| (-2 (|:| -2351 (-1170)) (|:| -1327 (-52))) (-309 (-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-906)) (|has| |#2| (-363)) -(-4005 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) (((|#1|) . T)) @@ -2585,11 +2585,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-825))) ((((-859)) . T)) -((((-1170)) -4005 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) +((((-1170)) -4002 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-897 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-897 (-1170))))) (|has| |#1| (-363)) @@ -2600,7 +2600,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2625,9 +2625,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-883 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-883 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2636,22 +2636,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-4005 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#2|) . T)) (((|#2|) . T)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2659,7 +2659,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-4005 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-859)) . T)) ((($) . T)) @@ -2686,7 +2686,7 @@ ((((-859)) . T)) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2708,7 +2708,7 @@ ((((-564)) . T)) ((((-859)) . T)) ((((-564)) . T)) -(-4005 (|has| |#2| (-790)) (|has| |#2| (-845))) +(-4002 (|has| |#2| (-790)) (|has| |#2| (-845))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-859)) . T)) ((((-859)) . T)) @@ -2720,9 +2720,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2752,7 +2752,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-777 |#1| (-861 |#2|))) |has| (-777 |#1| (-861 |#2|)) (-309 (-777 |#1| (-861 |#2|))))) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2764,13 +2764,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 (-52)))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-859)) . T)) ((((-859)) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564)))))) +(-4002 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1046))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1035 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2800,7 +2800,7 @@ (((|#1|) . T)) ((((-859)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -4005 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -4002 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2808,21 +2808,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -4005 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -4005 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1| |#1|) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-906)) (|has| |#1| (-906)) -((($) -4005 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-859)) . T)) (((|#1|) . T)) -((((-2 (|:| -1353 (-1152)) (|:| -2577 |#1|))) . T)) +((((-2 (|:| -2351 (-1152)) (|:| -1327 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2837,10 +2837,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . T)) -(-4005 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) (((|#1|) . T)) (((|#1|) . T)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-536)) . T)) ((((-859)) . T)) @@ -2857,12 +2857,12 @@ ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-1170)) |has| |#1| (-897 (-1170)))) ((((-907 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) -((($) . T) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -4005 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((($) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -4002 (|has| |#1| (-172)) (|has| |#1| (-556)))) ((($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((|#2|) |has| |#2| (-1046)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -4005 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -4002 (|has| |#1| (-172)) (|has| |#1| (-556)))) (|has| |#1| (-556)) (((|#1|) |has| |#1| (-363))) ((((-564)) . T)) @@ -2881,8 +2881,8 @@ ((((-859)) . T)) (|has| |#2| (-817)) (|has| |#2| (-817)) -((((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -4005 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -4002 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T) (((-564)) |has| |#1| (-1035 (-564))) (((-407 (-564))) |has| |#1| (-1035 (-407 (-564))))) ((((-564)) |has| |#1| (-883 (-564))) (((-379)) |has| |#1| (-883 (-379)))) @@ -2908,12 +2908,12 @@ (((|#2| (-768)) . T)) ((((-1170)) . T)) ((((-867 |#1|)) . 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T)) -(-4005 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4005 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-790)) (|has| |#2| (-790)))) +(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-790)) (|has| |#2| (-790)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((($) . T) (((-867 |#1|)) . T) (((-407 (-564))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) @@ -3219,15 +3219,15 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-407 |#2|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3257,17 +3257,17 @@ ((((-129)) . T)) ((((-859)) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1098)) . T)) ((((-859)) . T)) -((($) -4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) ((($) . T)) -((($) -4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1251 |#1| |#2| |#3|)) . T) (((-1223 |#1| |#2| |#3|)) . T)) ((((-1170)) . T) (((-859)) . T)) (|has| |#2| (-906)) @@ -3277,7 +3277,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-695)) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3289,13 +3289,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-4005 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-768)) . T)) @@ -3310,16 +3310,16 @@ ((((-889 (-379))) . T) (((-889 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-859)) . T)) -(-4005 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) -(-4005 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-790)) (|has| |#2| (-790)))) +(-4002 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-790)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-790)) (|has| |#2| (-790)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-4005 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) +(-4002 (|has| |#2| (-172)) (|has| |#2| (-723)) (|has| |#2| (-845)) (|has| |#2| (-1046))) ((((-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046)))) -(-4005 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) +(-4002 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-723)) (|has| |#2| (-723)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3345,7 +3345,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-4005 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-4002 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3357,7 +3357,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-847)) (|has| |#1| (-1094)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-906)) (|has| |#1| (-906)) @@ -3368,14 +3368,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1175)) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-4005 (|has| |#1| (-21)) (|has| |#1| (-845))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-4002 (|has| |#1| (-21)) (|has| |#1| (-845))) (((|#2|) . T)) -(-4005 (|has| |#1| (-21)) (|has| |#1| (-845))) +(-4002 (|has| |#1| (-21)) (|has| |#1| (-845))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-859)) -4005 (-12 (|has| |#1| (-611 (-859))) (|has| |#2| (-611 (-859)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-859)) -4002 (-12 (|has| |#1| (-611 (-859))) (|has| |#2| (-611 (-859)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3387,19 +3387,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-4005 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) -(-4005 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) +(-4002 (|has| |#4| (-172)) (|has| |#4| (-723)) (|has| |#4| (-845)) (|has| |#4| (-1046))) +(-4002 (|has| |#3| (-172)) (|has| |#3| (-723)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((((-859)) . T) (((-1175)) . T)) (|has| |#4| (-790)) -(-4005 (|has| |#4| (-790)) (|has| |#4| (-845))) +(-4002 (|has| |#4| (-790)) (|has| |#4| (-845))) (|has| |#4| (-845)) (|has| |#3| (-790)) ((((-1175)) . T)) -(-4005 (|has| |#3| (-790)) (|has| |#3| (-845))) +(-4002 (|has| |#3| (-790)) (|has| |#3| (-845))) (|has| |#3| (-845)) ((((-564)) . T)) (((|#2|) . T)) -((((-1170)) -4005 (-12 (|has| (-1168 |#1| |#2| |#3|) (-897 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))))) +((((-1170)) -4002 (-12 (|has| (-1168 |#1| |#2| |#3|) (-897 (-1170))) (|has| |#1| (-363))) (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-897 (-1170)))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-897 (-1170))))) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-768) |#1|))) (|has| |#1| (-897 (-1170))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3414,11 +3414,11 @@ ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-1134 |#1| |#2|)) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1019)) -(((|#2|) . T) (((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) ((((-859)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-889 (-564))) |has| |#2| (-612 (-889 (-564)))) (((-889 (-379))) |has| |#2| (-612 (-889 (-379)))) (((-379)) . #0=(|has| |#2| (-1019))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3434,15 +3434,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-859)) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-564) |#1|) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-363)) -(((|#3|) . T) ((|#2|) . T) (($) -4005 (|has| |#4| (-172)) (|has| |#4| (-845)) (|has| |#4| (-1046))) ((|#4|) -4005 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1046)))) -(((|#2|) . T) (($) -4005 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((|#3|) -4005 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1046)))) +(((|#3|) . T) ((|#2|) . T) (($) -4002 (|has| |#4| (-172)) (|has| |#4| (-845)) (|has| |#4| (-1046))) ((|#4|) -4002 (|has| |#4| (-172)) (|has| |#4| (-363)) (|has| |#4| (-1046)))) +(((|#2|) . T) (($) -4002 (|has| |#3| (-172)) (|has| |#3| (-845)) (|has| |#3| (-1046))) ((|#3|) -4002 (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-1046)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-363)) @@ -3457,7 +3457,7 @@ ((((-187)) . T) (((-859)) . T)) ((((-859)) . T)) (((|#1|) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-859)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3466,13 +3466,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-4005 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) -(-4005 (|has| |#1| (-847)) (|has| |#1| (-1094))) +(-4002 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-906))) +(-4002 (|has| |#1| (-847)) (|has| |#1| (-1094))) ((((-859)) . T)) ((((-859)) . T)) ((((-859)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -1353 (-1170)) (|:| -2577 (-52)))) . T)) +((((-2 (|:| -2351 (-1170)) (|:| -1327 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3486,8 +3486,8 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) -(-4005 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) -(-4005 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) +(-4002 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-906))) +(-4002 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-906))) ((($) . T)) (((|#2| (-531 (-861 |#1|))) . T)) ((((-1175)) . T)) @@ -3502,13 +3502,13 @@ ((((-1175)) . T)) ((((-859)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-859)) -4005 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) +((((-859)) -4002 (|has| |#1| (-611 (-859))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-768)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -1353 |#1|) (|:| -2577 |#2|))) . T)) +((((-2 (|:| -2351 |#1|) (|:| -1327 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3517,14 +3517,14 @@ ((((-564)) . T) (($) . 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-131) T) ((-394 . -1094) T) ((-690 . -370) 144025) ((-867 . -1053) T) ((-223 . -618) 144002) ((-327 . -286) 143979) ((-474 . -111) 143800) ((-1243 . -1046) T) ((-1222 . -1046) T) ((-813 . -377) 143784) ((-169 . -723) T) ((-650 . -102) T) ((-1243 . -243) 143763) ((-1243 . -233) 143715) ((-1222 . -233) 143620) ((-1222 . -243) 143599) ((-1000 . -402) NIL) ((-666 . -637) 143547) ((-316 . -38) 143457) ((-313 . -38) 143386) ((-69 . -611) 143368) ((-319 . -493) 143334) ((-1182 . -288) 143313) ((-1217 . -847) T) ((-1107 . -1106) 143223) ((-83 . -1209) T) ((-61 . -611) 143205) ((-479 . -288) 143184) ((-1274 . -1035) 143161) ((-1158 . -1094) T) ((-1107 . -23) 143031) ((-813 . -897) 142967) ((-1232 . -723) T) ((-1096 . -1209) T) ((-474 . -614) 142793) ((-1081 . -290) 142724) ((-963 . -1094) T) ((-890 . -102) T) ((-779 . -290) 142635) ((-327 . -19) 142619) ((-59 . -288) 142596) ((-777 . -290) 142527) ((-852 . -723) T) ((-117 . -845) NIL) ((-516 . -288) 142504) ((-327 . -602) 142481) ((-496 . -288) 142458) ((-454 . -290) 142389) ((-1032 . -309) 142240) ((-677 . -490) 142221) ((-571 . -723) T) ((-672 . -490) 142202) ((-677 . -611) 142152) ((-672 . -611) 142118) ((-658 . -611) 142100) ((-478 . -490) 142081) ((-478 . -611) 142047) ((-245 . -612) 142008) ((-245 . -490) 141985) ((-138 . -490) 141966) ((-137 . -490) 141947) ((-133 . -490) 141928) ((-245 . -611) 141820) ((-213 . -102) T) ((-138 . -611) 141786) ((-137 . -611) 141752) ((-133 . -611) 141718) ((-1141 . -34) T) ((-940 . -1209) T) ((-343 . -714) 141663) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141644) ((-474 . -1046) T) ((-633 . -417) 141609) ((-605 . -417) 141574) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141553) ((-474 . -233) 141505) ((-474 . -243) 141484) ((-1223 . -307) 141463) ((-1223 . -1019) NIL) ((-1074 . -131) T) ((-869 . -792) 141442) ((-144 . -102) T) ((-40 . -1094) T) ((-869 . -789) 141421) ((-641 . -1007) 141405) ((-580 . -1053) T) ((-564 . -1053) T) ((-495 . -1053) T) 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137523) ((-955 . -34) T) ((-355 . -233) 137502) ((-355 . -243) T) ((-352 . -233) 137481) ((-352 . -243) T) ((-344 . -233) 137460) ((-344 . -243) T) ((-247 . -326) 137417) ((-264 . -326) 137389) ((-264 . -233) 137368) ((-1150 . -151) 137352) ((-251 . -897) 137284) ((-250 . -897) 137216) ((-1076 . -847) T) ((-414 . -1106) T) ((-1050 . -23) T) ((-907 . -1046) T) ((-322 . -644) 137198) ((-1021 . -845) T) ((-1203 . -999) 137164) ((-1167 . -917) 137143) ((-1161 . -917) 137122) ((-1161 . -817) NIL) ((-907 . -243) T) ((-814 . -363) 137101) ((-385 . -23) T) ((-127 . -1094) 137079) ((-121 . -1094) 137057) ((-907 . -233) T) ((-128 . -34) T) ((-379 . -644) 137022) ((-867 . -714) 137009) ((-1043 . -151) 136974) ((-40 . -172) T) ((-690 . -411) 136956) ((-709 . -309) 136943) ((-833 . -644) 136903) ((-824 . -644) 136877) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136856) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136833) ((-313 . -231) 136794) ((-1166 . -883) NIL) ((-55 . -1094) T) ((-1119 . -883) 136653) ((-129 . -847) T) ((-1166 . -1035) 136533) ((-1119 . -1035) 136416) ((-183 . -611) 136398) ((-851 . -1035) 136294) ((-779 . -286) 136221) ((-814 . -1106) T) ((-1031 . -723) T) ((-600 . -647) 136205) ((-1043 . -973) 136134) ((-996 . -102) T) ((-814 . -23) T) ((-709 . -1145) 136112) ((-690 . -1053) T) ((-600 . -373) 136096) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -723) T) ((-707 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136078) ((-1166 . -377) 136062) ((-1119 . -377) 136046) ((-1021 . -411) 136008) ((-141 . -229) 135990) ((-379 . -791) T) ((-379 . -788) T) ((-867 . -172) T) ((-379 . -723) T) ((-708 . -611) 135972) ((-709 . -38) 135801) ((-1259 . -1257) 135785) ((-351 . -402) T) ((-1259 . -1094) 135735) ((-580 . -714) 135722) ((-564 . -714) 135709) ((-495 . -714) 135674) ((-316 . -627) 135653) ((-833 . -723) T) ((-824 . -723) T) 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-614) 134872) ((-487 . -556) T) ((-478 . -614) 134853) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134830) ((-138 . -614) 134811) ((-137 . -614) 134792) ((-133 . -614) 134773) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1053) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134755) ((-734 . -733) 134739) ((-336 . -611) 134721) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134705) ((-1057 . -883) 134687) ((-949 . -883) 134612) ((-649 . -1106) T) ((-621 . -714) 134599) ((-481 . -883) NIL) ((-1140 . -102) T) ((-1088 . -616) 134583) ((-1057 . -1035) 134565) ((-97 . -611) 134547) ((-477 . -147) T) ((-949 . -1035) 134427) ((-117 . -714) 134372) ((-649 . -23) T) ((-481 . -1035) 134248) ((-1081 . -612) NIL) ((-1081 . -611) 134230) ((-779 . -612) NIL) ((-779 . -611) 134191) ((-777 . -612) 133825) ((-777 . -611) 133739) ((-1107 . -637) 133645) ((-461 . -611) 133627) ((-454 . -611) 133609) ((-454 . -612) 133470) ((-1032 . -229) 133416) ((-869 . -906) 133395) ((-126 . -34) T) ((-814 . -131) T) ((-645 . -611) 133377) ((-578 . -102) T) ((-355 . -1278) 133361) ((-352 . -1278) 133345) ((-344 . -1278) 133329) ((-127 . -514) 133262) ((-121 . -514) 133195) ((-511 . -789) T) ((-511 . -792) T) ((-510 . -791) T) ((-103 . -309) 133133) ((-222 . -102) 133111) ((-690 . -1094) T) ((-695 . -172) T) ((-869 . -644) 133063) ((-65 . -384) T) ((-275 . -611) 133045) ((-65 . -395) T) ((-949 . -377) 133029) ((-867 . -290) T) ((-50 . -611) 133011) ((-996 . -38) 132959) ((-581 . -611) 132941) ((-481 . -377) 132925) ((-581 . -612) 132907) ((-518 . -611) 132889) ((-907 . -1278) 132876) ((-868 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132842) ((-487 . -363) T) ((-355 . -368) 132821) ((-352 . -368) 132800) ((-344 . -368) 132779) ((-711 . -723) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132763) ((-868 . -881) 132740) ((-868 . -883) NIL) ((-961 . -847) 132639) ((-812 . -847) 132590) ((-1216 . -102) T) ((-650 . -652) 132574) ((-1195 . -34) T) ((-171 . -611) 132556) ((-1107 . -21) 132466) ((-1107 . -25) 132317) ((-868 . -1035) 132294) ((-949 . -897) 132275) ((-1232 . -47) 132252) ((-907 . -368) T) ((-59 . -647) 132236) ((-516 . -647) 132220) ((-481 . -897) 132197) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132181) ((-59 . -373) 132165) ((-621 . -172) T) ((-516 . -373) 132149) ((-496 . -373) 132133) ((-824 . -705) 132117) ((-1166 . -307) 132096) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132034) ((-169 . -1209) T) ((-633 . -741) 132018) ((-605 . -741) 132002) ((-1271 . -131) T) ((-1244 . -917) 131981) ((-1223 . -917) 131960) ((-1223 . -817) NIL) ((-690 . -714) 131910) ((-1222 . -906) 131863) ((-1021 . -1094) T) ((-868 . -377) 131840) ((-868 . -338) 131817) ((-902 . -1106) T) ((-169 . -881) 131801) ((-169 . -883) 131726) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1035) 131622) ((-319 . -847) T) ((-1259 . -514) 131555) ((-1243 . -644) 131452) ((-1222 . -644) 131322) ((-869 . -791) 131301) ((-869 . -788) 131280) ((-869 . -723) T) ((-487 . -23) T) ((-223 . -611) 131262) ((-174 . -452) T) ((-222 . -309) 131200) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131179) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1035) 131163) ((-495 . -290) T) ((-136 . -470) 131118) ((-48 . -1094) T) ((-709 . -231) 131102) ((-868 . -897) NIL) ((-1232 . -883) NIL) ((-886 . -102) T) ((-882 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131086) ((-169 . -338) 131070) ((-1232 . -1035) 130950) ((-852 . -1035) 130846) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130754) ((-658 . -789) 130733) ((-658 . -792) 130712) ((-571 . -1035) 130694) ((-294 . -1266) 130664) ((-863 . -102) T) ((-960 . -556) 130643) ((-1203 . -1052) 130526) ((-482 . -637) 130432) ((-901 . -1094) T) ((-1021 . -714) 130369) ((-708 . -1052) 130334) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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. -131) T) ((-654 . -644) 116275) ((-245 . -1007) 116259) ((-869 . -307) T) ((-1283 . -1273) 116243) ((-768 . -789) T) ((-768 . -792) T) ((-697 . -38) 116230) ((-564 . -233) T) ((-495 . -243) T) ((-495 . -233) T) ((-1144 . -235) 116180) ((-1081 . -906) 116159) ((-116 . -38) 116146) ((-209 . -797) T) ((-208 . -797) T) ((-207 . -797) T) ((-206 . -797) T) ((-869 . -1019) 116124) ((-1272 . -489) 116108) ((-779 . -906) 116087) ((-777 . -906) 116066) ((-1182 . -1209) T) ((-454 . -906) 116045) ((-734 . -489) 116029) ((-1081 . -644) 115954) ((-695 . -614) 115889) ((-779 . -644) 115814) ((-621 . -1052) 115801) ((-479 . -1209) T) ((-343 . -368) T) ((-141 . -489) 115783) ((-777 . -644) 115708) ((-1135 . -1209) T) ((-549 . -847) T) ((-461 . -644) 115679) ((-264 . -883) 115538) ((-247 . -883) NIL) ((-117 . -1052) 115483) ((-454 . -644) 115408) ((-660 . -1035) 115385) ((-621 . -111) 115370) ((-355 . -1035) 115354) ((-352 . -1035) 115338) ((-344 . -1035) 115322) ((-264 . -1035) 115166) ((-247 . 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. -243) T) ((-48 . -233) T) ((-650 . -286) 110051) ((-550 . -235) 110001) ((-139 . -611) 109968) ((-136 . -611) 109950) ((-114 . -611) 109932) ((-477 . -38) 109897) ((-1283 . -1280) 109876) ((-1274 . -131) T) ((-1282 . -1053) T) ((-1076 . -102) T) ((-88 . -1209) T) ((-500 . -309) NIL) ((-997 . -107) 109860) ((-886 . -1094) T) ((-882 . -1094) T) ((-1259 . -647) 109844) ((-1259 . -373) 109828) ((-327 . -1209) T) ((-592 . -847) T) ((-1136 . -1094) T) ((-1136 . -1049) 109768) ((-103 . -514) 109701) ((-924 . -611) 109683) ((-343 . -723) T) ((-30 . -611) 109665) ((-863 . -1094) T) ((-840 . -1053) 109644) ((-40 . -644) 109589) ((-225 . -1213) T) ((-407 . -1053) T) ((-1152 . -151) 109571) ((-996 . -290) 109522) ((-615 . -1094) T) ((-225 . -556) T) ((-319 . -1240) 109506) ((-319 . -1237) 109476) ((-1182 . -1185) 109455) ((-1069 . -611) 109437) ((-643 . -151) 109421) ((-630 . -151) 109367) ((-1182 . -107) 109317) ((-479 . -1185) 109296) ((-487 . -147) T) ((-487 . -145) NIL) ((-1114 . -612) 109211) ((-438 . -611) 109193) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 109175) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 109127) ((-479 . -107) 109077) ((-990 . -23) T) ((-1283 . -38) 109047) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1057 . -1213) T) ((-311 . -102) T) ((-851 . -1106) T) ((-949 . -1213) 109026) ((-481 . -1213) 109005) ((-728 . -847) 108984) ((-1057 . -556) T) ((-949 . -556) 108915) ((-1166 . -23) T) ((-1119 . -23) T) ((-851 . -23) T) ((-481 . -556) 108846) ((-1136 . -714) 108778) ((-1140 . -514) 108711) ((-1032 . -612) NIL) ((-1032 . -611) 108693) ((-96 . -1077) T) ((-863 . -714) 108663) ((-1203 . -47) 108632) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-1000 . -1094) T) ((-62 . -611) 108614) ((-1161 . -847) NIL) ((-1021 . -789) T) ((-1021 . -792) T) ((-1287 . -1052) 108601) ((-1287 . -111) 108586) ((-867 . -644) 108573) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) 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-883) NIL) ((-868 . -1106) T) ((-117 . -906) NIL) ((-1281 . -1280) 105427) ((-1279 . -1280) 105406) ((-779 . -883) NIL) ((-777 . -883) 105265) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105243) ((-1100 . -395) T) ((-621 . -644) 105230) ((-454 . -883) NIL) ((-671 . -102) 105208) ((-1081 . -1035) 105035) ((-868 . -23) T) ((-779 . -1035) 104894) ((-777 . -1035) 104751) ((-117 . -644) 104696) ((-454 . -1035) 104572) ((-316 . -614) 104136) ((-313 . -614) 104019) ((-645 . -1035) 104003) ((-625 . -102) T) ((-222 . -489) 103987) ((-1259 . -34) T) ((-136 . -614) 103971) ((-633 . -714) 103955) ((-605 . -714) 103939) ((-666 . -38) 103899) ((-319 . -102) T) ((-85 . -611) 103881) ((-50 . -1035) 103865) ((-1114 . -1052) 103852) ((-1081 . -377) 103836) ((-779 . -377) 103820) ((-695 . -723) T) ((-695 . -791) T) ((-695 . -788) T) ((-581 . -1035) 103807) ((-518 . -1035) 103784) ((-60 . -57) 103746) ((-324 . -131) T) ((-316 . -1046) 103636) ((-313 . -1046) T) ((-169 . -1106) T) ((-777 . -377) 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95219) ((-1243 . -556) 95170) ((-711 . -1106) T) ((-1222 . -556) 95121) ((-564 . -1035) 95103) ((-594 . -147) 95082) ((-594 . -145) 95061) ((-495 . -1035) 95004) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-869 . -363) T) ((-833 . -131) T) ((-824 . -131) T) ((-711 . -23) T) ((-506 . -611) 94970) ((-502 . -611) 94952) ((-1283 . -1053) T) ((-379 . -1055) T) ((-1023 . -1094) 94930) ((-55 . -1035) 94912) ((-898 . -34) T) ((-482 . -309) 94850) ((-591 . -102) T) ((-1150 . -612) 94811) ((-1150 . -611) 94743) ((-1166 . -847) 94722) ((-45 . -102) T) ((-1119 . -847) 94701) ((-814 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-852 . -25) T) ((-44 . -367) 94685) ((-852 . -21) T) ((-728 . -452) 94636) ((-1282 . -611) 94618) ((-1050 . -309) 94556) ((-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 . -883) 94538) ((-1259 . -1209) T) ((-227 . -309) 94476) ((-144 . -368) T) ((-1043 . -612) 94418) ((-1043 . -611) 94361) ((-313 . -906) NIL) ((-1217 . -841) T) ((-695 . -1035) 94306) ((-708 . -917) T) ((-474 . -1213) 94285) ((-1167 . -452) 94264) ((-1161 . -452) 94243) ((-330 . -102) T) ((-869 . -1106) T) ((-316 . -644) 94064) ((-313 . -644) 93993) ((-474 . -556) 93944) ((-339 . -514) 93910) ((-550 . -151) 93860) ((-40 . -307) T) ((-840 . -611) 93842) ((-697 . -290) T) ((-869 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93812) ((-512 . -102) T) ((-407 . -612) 93619) ((-407 . -611) 93601) ((-263 . -611) 93583) ((-116 . -290) T) ((-1245 . -723) T) ((-1243 . -363) 93562) ((-1222 . -363) 93541) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93523) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93507) ((-734 . -34) T) ((-482 . -38) 93477) ((-141 . -34) T) ((-117 . -881) 93454) ((-117 . -883) NIL) ((-621 . -1035) 93337) ((-641 . -847) 93316) ((-1271 . -102) T) ((-295 . -102) T) ((-709 . -368) 93295) 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91246) ((-863 . -111) 91211) ((-690 . -1035) 91156) ((-1001 . -452) T) ((-907 . -556) T) ((-533 . -611) 91138) ((-581 . -917) T) ((-474 . -1106) T) ((-518 . -917) T) ((-1150 . -288) 91115) ((-911 . -452) T) ((-65 . -611) 91097) ((-630 . -229) 91043) ((-474 . -23) T) ((-1114 . -791) T) ((-869 . -131) T) ((-1114 . -788) T) ((-1274 . -1276) 91022) ((-1114 . -723) T) ((-650 . -644) 90996) ((-294 . -611) 90737) ((-1136 . -614) 90655) ((-1032 . -34) T) ((-812 . -845) 90634) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -714) 90604) ((-690 . -377) 90586) ((-690 . -338) 90568) ((-477 . -172) T) ((-381 . -714) 90538) ((-863 . -614) 90473) ((-868 . -847) NIL) ((-564 . -1019) T) ((-495 . -1019) T) ((-1127 . -611) 90455) ((-1107 . -238) 90434) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90416) ((-1136 . -1046) T) ((-1172 . -38) 90313) ((-855 . -611) 90295) ((-564 . -545) T) ((-666 . -1053) T) ((-728 . -946) 90248) ((-1136 . -233) 90227) ((-1076 . -1094) T) ((-1031 . -25) T) ((-1031 . -21) T) ((-1000 . -1052) 90172) ((-902 . -102) T) ((-863 . -1046) T) ((-690 . -897) NIL) ((-355 . -329) 90156) ((-355 . -363) T) ((-352 . -329) 90140) ((-352 . -363) T) ((-344 . -329) 90124) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90094) ((-546 . -847) T) ((-523 . -683) 90044) ((-217 . -102) T) ((-1021 . -1035) 89924) ((-1000 . -111) 89853) ((-1168 . -970) 89822) ((-1167 . -970) 89784) ((-520 . -151) 89768) ((-1074 . -370) 89747) ((-351 . -611) 89729) ((-322 . -21) T) ((-354 . -1035) 89706) ((-322 . -25) T) ((-1161 . -970) 89675) ((-1120 . -970) 89642) ((-76 . -611) 89624) ((-695 . -307) T) ((-169 . -847) 89603) ((-129 . -841) T) ((-907 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-907 . -329) 89590) ((-86 . -611) 89572) ((-695 . -1019) T) ((-673 . -847) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-898 . -1007) 89556) ((-833 . -21) T) ((-48 . -1035) 89499) ((-833 . -25) T) ((-824 . -25) T) ((-824 . -21) T) ((-1281 . -1053) T) ((-549 . -102) T) ((-1279 . -1053) T) ((-650 . -723) T) ((-1098 . -616) 89402) ((-1000 . -614) 89332) ((-1282 . -1052) 89316) ((-1232 . -847) 89295) ((-812 . -411) 89264) ((-103 . -119) 89248) ((-129 . -1094) T) ((-52 . -1094) T) ((-923 . -611) 89230) ((-868 . -989) 89207) ((-820 . -102) T) ((-1282 . -111) 89186) ((-649 . -38) 89156) ((-571 . -847) T) ((-355 . -1106) T) ((-352 . -1106) T) ((-344 . -1106) T) ((-264 . -1106) T) ((-247 . -1106) T) ((-621 . -307) 89135) ((-1144 . -309) 88939) ((-524 . -1077) T) ((-311 . -1094) T) ((-660 . -23) T) ((-482 . -231) 88908) ((-152 . -1053) T) ((-355 . -23) T) ((-352 . -23) T) ((-344 . -23) T) ((-117 . -307) T) ((-264 . -23) T) ((-247 . -23) T) ((-1000 . -1046) T) ((-709 . -906) 88887) ((-1150 . -614) 88864) ((-1000 . -233) 88836) ((-1000 . -243) T) ((-117 . -1019) NIL) ((-907 . -1106) T) ((-1244 . -452) 88815) ((-1223 . -452) 88794) ((-523 . -611) 88726) ((-709 . -644) 88651) ((-407 . -1052) 88603) ((-504 . -611) 88585) ((-907 . -23) T) ((-487 . -309) NIL) ((-1282 . -614) 88541) 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-1219) 87595) ((-407 . -1046) T) ((-319 . -1053) T) ((-690 . -307) T) ((-108 . -845) T) ((-709 . -723) T) ((-407 . -243) T) ((-407 . -233) 87574) ((-487 . -38) 87524) ((-217 . -38) 87474) ((-474 . -493) 87440) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87422) ((-697 . -612) 87337) ((-711 . -21) T) ((-711 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87319) ((-116 . -611) 87301) ((-157 . -25) T) ((-1281 . -1094) T) ((-869 . -637) 87249) ((-1279 . -1094) T) ((-960 . -102) T) ((-732 . -102) T) ((-712 . -102) T) ((-453 . -102) T) ((-813 . -452) 87200) ((-44 . -1094) T) ((-1082 . -847) T) ((-660 . -131) T) ((-1058 . -309) 87051) ((-666 . -714) 87035) ((-289 . -1053) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86985) ((-955 . -847) 86964) ((-996 . -644) 86902) ((-240 . -1266) 86872) ((-1021 . -307) T) ((-294 . -1052) 86793) ((-907 . -131) T) ((-40 . -917) T) ((-487 . -400) 86775) ((-354 . -307) T) ((-217 . -400) 86757) ((-1074 . -411) 86741) ((-294 . -111) 86657) ((-1177 . -847) T) ((-1176 . -847) T) ((-869 . -25) T) ((-869 . -21) T) ((-339 . -611) 86639) ((-1245 . -47) 86583) ((-225 . -147) T) ((-174 . -611) 86565) ((-1107 . -845) 86544) ((-771 . -611) 86526) ((-128 . -847) T) ((-606 . -235) 86473) ((-475 . -235) 86423) ((-1281 . -714) 86393) ((-48 . -307) T) ((-1279 . -714) 86363) ((-65 . -614) 86292) ((-961 . -1094) T) ((-812 . -1094) 86082) ((-312 . -102) T) ((-898 . -1209) T) ((-48 . -1019) T) ((-1222 . -637) 85990) ((-685 . -102) 85968) ((-44 . -714) 85952) ((-550 . -102) T) ((-294 . -614) 85883) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -758) T) ((-1206 . -1094) 85861) ((-351 . -1052) 85806) ((-671 . -1094) 85784) ((-1057 . -147) T) ((-949 . -147) 85763) ((-949 . -145) 85742) ((-796 . -102) T) ((-152 . -714) 85726) ((-481 . -147) 85705) ((-481 . -145) 85684) ((-351 . -111) 85613) ((-1074 . -1053) T) ((-322 . -847) 85592) ((-1251 . -970) 85561) ((-625 . -1094) T) ((-1244 . -970) 85523) ((-511 . -131) T) ((-507 . -131) T) ((-295 . -229) 85473) ((-359 . -1053) T) ((-353 . -1053) T) ((-345 . -1053) T) ((-294 . -1046) 85415) ((-1223 . -970) 85384) ((-379 . -847) T) ((-108 . -1053) T) ((-996 . -723) T) ((-867 . -917) T) ((-840 . -792) 85363) ((-840 . -789) 85342) ((-418 . -309) 85281) ((-468 . -102) T) ((-594 . -970) 85250) ((-319 . -1094) T) ((-407 . -792) 85229) ((-407 . -789) 85208) ((-500 . -489) 85190) ((-1245 . -1035) 85156) ((-1243 . -21) T) ((-1243 . -25) T) ((-1222 . -21) T) ((-1222 . -25) T) ((-812 . -714) 85098) ((-351 . -614) 85028) ((-695 . -404) T) ((-1272 . -1209) T) ((-604 . -102) T) ((-1107 . -411) 84997) ((-1000 . -368) NIL) ((-667 . -102) T) ((-180 . -102) T) ((-161 . -102) T) ((-156 . -102) T) ((-154 . -102) T) ((-103 . -34) T) ((-734 . -1209) T) ((-44 . -758) T) ((-592 . -102) T) ((-77 . -396) T) ((-77 . -395) T) ((-649 . -652) 84981) ((-141 . -1209) T) ((-868 . -147) T) ((-868 . -145) NIL) ((-1208 . -93) T) ((-351 . -1046) T) ((-70 . -383) T) ((-70 . -395) T) ((-1159 . -102) T) ((-666 . -514) 84914) ((-685 . -309) 84852) ((-960 . -38) 84749) ((-732 . -38) 84719) ((-550 . -309) 84523) ((-316 . -1209) T) ((-351 . -233) T) ((-351 . -243) T) ((-313 . -1209) T) ((-289 . -1094) T) ((-1174 . -611) 84505) ((-708 . -1213) T) ((-1150 . -647) 84489) ((-1203 . -556) 84468) ((-708 . -556) T) ((-316 . -881) 84452) ((-316 . -883) 84377) ((-313 . -881) 84338) ((-313 . -883) NIL) ((-796 . -309) 84303) ((-319 . -714) 84144) ((-324 . -323) 84121) ((-485 . -102) T) ((-474 . -25) T) ((-474 . -21) T) ((-418 . -38) 84095) ((-316 . -1035) 83758) ((-225 . -1194) T) ((-225 . -1197) T) ((-3 . -611) 83740) ((-313 . -1035) 83670) ((-2 . -1094) T) ((-2 . |RecordCategory|) T) ((-830 . -611) 83652) ((-1107 . -1053) 83582) ((-580 . -917) T) ((-564 . -817) T) ((-564 . -917) T) ((-495 . -917) T) ((-136 . -1035) 83566) ((-225 . -95) T) ((-75 . -441) T) ((-75 . -395) T) ((0 . -611) 83548) ((-169 . -147) 83527) ((-169 . -145) 83478) ((-225 . -35) T) ((-49 . -611) 83460) ((-477 . -1053) T) ((-487 . -231) 83442) ((-484 . -965) 83426) ((-482 . -845) 83405) ((-217 . -231) 83387) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-812 . -172) 83366) ((-728 . -102) T) ((-1023 . -611) 83333) ((-500 . -286) 83308) ((-316 . -377) 83277) ((-313 . -377) 83238) ((-313 . -338) 83199) ((-1079 . -611) 83181) ((-813 . -946) 83128) ((-658 . -131) T) ((-1232 . -145) 83107) ((-1232 . -147) 83086) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -714) 83073) ((-1153 . -608) 83049) ((-592 . -309) NIL) ((-484 . -1094) 83027) ((-390 . -611) 83009) ((-510 . -847) T) ((-1144 . -229) 82959) ((-1251 . -1250) 82943) ((-1251 . -1237) 82920) ((-1244 . -1242) 82881) ((-1244 . -1237) 82851) ((-1244 . -1240) 82835) ((-1223 . -1221) 82796) ((-1223 . -1237) 82773) ((-619 . -611) 82755) ((-1223 . -1219) 82739) ((-695 . -917) T) ((-1168 . -284) 82705) ((-1167 . -284) 82671) ((-1161 . -284) 82637) ((-1074 . -1094) T) ((-1056 . -1094) T) ((-48 . -302) T) ((-316 . -897) 82603) ((-313 . -897) NIL) ((-1056 . -1063) 82582) ((-1114 . -883) 82564) ((-796 . -38) 82548) ((-264 . -637) 82496) ((-247 . -637) 82444) ((-697 . -1052) 82431) ((-594 . -1237) 82408) ((-1120 . -284) 82374) ((-319 . -172) 82305) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82287) ((-1114 . -1035) 82269) ((-1096 . -151) 82253) ((-108 . -1094) T) ((-116 . -1052) 82240) ((-708 . -363) T) ((-500 . -602) 82215) ((-697 . -111) 82200) ((-436 . -102) T) ((-45 . -1143) 82150) ((-116 . -111) 82135) ((-633 . -717) T) ((-605 . -717) T) ((-812 . -514) 82068) ((-1032 . -1209) T) ((-940 . -151) 82052) ((-1217 . -611) 82034) ((-1166 . -452) 81965) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81915) ((-1136 . -644) 81889) ((-1119 . -452) 81840) ((-1081 . -1213) 81819) ((-779 . -1213) 81798) ((-777 . -1213) 81777) ((-62 . -1209) T) ((-477 . -611) 81729) ((-477 . -612) 81651) ((-1081 . -556) 81582) ((-991 . -1094) T) ((-779 . -556) 81493) ((-777 . -556) 81424) ((-482 . -411) 81393) ((-621 . -917) 81372) ((-454 . -1213) 81351) ((-728 . -309) 81338) ((-697 . -614) 81310) ((-398 . -611) 81292) ((-671 . -514) 81225) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81156) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -917) T) ((-117 . -817) 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) 81138) ((-116 . -614) 81110) ((-1261 . -611) 81092) ((-1215 . -847) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80977) ((-1120 . -309) 80964) ((-1074 . -714) 80832) ((-863 . -644) 80792) ((-940 . -977) 80776) ((-907 . -21) T) ((-289 . -172) T) ((-907 . -25) T) ((-311 . -93) T) ((-869 . -847) 80727) ((-708 . -1106) T) ((-708 . -23) T) ((-697 . -1046) T) ((-643 . -1094) 80705) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80680) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -714) 80632) ((-339 . -1052) 80616) ((-353 . -714) 80568) ((-345 . -714) 80520) ((-174 . -1052) 80452) ((-174 . -111) 80363) ((-108 . -714) 80313) ((-339 . -111) 80292) ((-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) 80270) ((-169 . -1194) 80248) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1046) 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) 80038) ((-169 . -35) 80016) ((-169 . -95) 79994) ((-650 . -1035) 79890) ((-482 . -1053) 79820) ((-1107 . -1094) 79610) ((-1136 . -34) T) ((-666 . -489) 79594) ((-73 . -1209) T) ((-105 . -611) 79576) ((-1283 . -611) 79558) ((-381 . -611) 79540) ((-339 . -614) 79492) ((-174 . -614) 79409) ((-1208 . -490) 79390) ((-728 . -38) 79239) ((-571 . -1197) T) ((-571 . -1194) T) ((-531 . -611) 79221) ((-520 . -309) 79159) ((-500 . -611) 79141) ((-500 . -612) 79123) ((-1208 . -611) 79089) ((-1161 . -1145) NIL) ((-1024 . -1066) 79058) ((-1024 . -1094) T) ((-1001 . -102) T) ((-968 . -102) T) ((-911 . -102) T) ((-890 . -1035) 79035) ((-1136 . -723) T) ((-1000 . -644) 78980) ((-476 . -1094) T) ((-463 . -1094) T) ((-585 . -23) T) ((-571 . -35) T) ((-571 . -95) T) ((-427 . -102) T) ((-1058 . -229) 78926) ((-1168 . -38) 78823) ((-863 . -723) T) ((-690 . -917) T) ((-511 . -25) T) ((-507 . -21) T) ((-507 . -25) T) ((-1167 . -38) 78664) ((-339 . -1046) T) ((-1161 . -38) 78460) ((-1074 . -172) T) ((-174 . -1046) T) ((-1120 . -38) 78357) ((-709 . -47) 78334) ((-359 . -172) T) ((-353 . -172) T) ((-519 . -57) 78308) ((-497 . -57) 78258) ((-351 . -1278) 78235) 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. -611) 77339) ((-1076 . -612) 77320) ((-407 . -906) 77299) ((-50 . -1106) T) ((-1021 . -917) T) ((-1000 . -723) T) ((-709 . -883) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-840 . -644) 77272) ((-1203 . -131) T) ((-1161 . -400) 77224) ((-1001 . -309) NIL) ((-812 . -489) 77208) ((-354 . -917) T) ((-1150 . -34) T) ((-407 . -644) 77160) ((-50 . -23) T) ((-708 . -131) T) ((-709 . -1035) 77040) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 77011) ((-1134 . -1094) T) ((-1274 . -1273) 76995) ((-697 . -792) T) ((-697 . -789) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76977) ((-1222 . -989) 76947) ((-48 . -917) T) ((-671 . -489) 76931) ((-251 . -1266) 76901) ((-250 . -1266) 76871) ((-1170 . -847) T) ((-1107 . -172) 76850) ((-1114 . -1019) T) ((-1043 . -34) T) ((-833 . -147) 76829) ((-833 . -145) 76808) ((-734 . -107) 76792) ((-610 . -132) T) ((-482 . -1094) 76582) ((-1172 . -1053) T) ((-868 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76552) ((-141 . -107) 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. -102) T) ((-1119 . -102) T) ((-851 . -102) T) ((-227 . -489) 67106) ((-1281 . -111) 67085) ((-1279 . -111) 67064) ((-44 . -1052) 67048) ((-1232 . -1235) 67032) ((-852 . -849) 67016) ((-1281 . -614) 66962) ((-1172 . -290) 66941) ((-110 . -286) 66916) ((-1214 . -1094) T) ((-128 . -151) 66898) ((-1136 . -897) 66857) ((-44 . -111) 66836) ((-1175 . -1254) T) ((-1160 . -490) 66817) ((-1160 . -611) 66783) ((-1152 . -612) NIL) ((-666 . -1046) T) ((-1152 . -611) 66765) ((-1058 . -608) 66740) ((-1058 . -1094) T) ((-991 . -490) 66721) ((-991 . -611) 66687) ((-74 . -441) T) ((-74 . -395) T) ((-699 . -1094) T) ((-152 . -1052) 66671) ((-666 . -233) 66650) ((-571 . -554) 66634) ((-355 . -147) 66613) ((-355 . -145) 66564) ((-352 . -147) 66543) ((-352 . -145) 66494) ((-344 . -147) 66473) ((-344 . -145) 66424) ((-264 . -145) 66403) ((-264 . -147) 66382) ((-251 . -38) 66352) ((-247 . -147) 66331) ((-117 . -363) T) ((-247 . -145) 66310) ((-250 . -38) 66280) ((-152 . -111) 66259) ((-1000 . -1035) 66147) 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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 f15930f8..ecefc886 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3449460959) +(30 . 3449600528) (4414 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,662 +477,663 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |ground?| |maxdeg| |units| |readInt32!| |rational| - |hypergeometric0F1| |subHeight| |testDim| |fixedPoints| |s14abf| - |subTriSet?| |seriesToOutputForm| |ground| |s20adf| |cAcos| - |OMputEndBVar| |physicalLength!| |numFunEvals| |ramified?| - |normalForm| |leftRecip| |ScanRoman| |singRicDE| |f04atf| |asinIfCan| - 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|abelianGroup| |binaryTree| |reciprocalPolynomial| |clikeUniv| |reify| - |rightExtendedGcd| |rem| |match| |qsetelt!| |outputFloating| - |LazardQuotient2| |parse| |mainMonomial| |dot| |countable?| - |oblateSpheroidal| |operators| |sPol| |factorByRecursion| - |quotientByP| |substring?| |idealiserMatrix| |returnTypeOf| |atoms| - |lazyGintegrate| |rootSplit| |rootBound| |eof?| |s13acf| - |probablyZeroDim?| |stoseInvertibleSet| |denominators| |iicoth| - |conjug| |doubleFloatFormat| |closeComponent| |harmonic| - |pleskenSplit| |symmetricProduct| |realEigenvalues| |assign| - |curryLeft| |suffix?| |subtractIfCan| |imagK| - |selectNonFiniteRoutines| |aQuartic| |c06fuf| |merge| - |fortranLinkerArgs| |makeViewport2D| |leftDivide| |airyAi| |gbasis| - |vertConcat| |characteristicSerie| |inHallBasis?| |conjugates| - |setfirst!| |chvar| |showSummary| |createGenericMatrix| |iisin| - |elem?| |aspFilename| |prefix?| |gcdcofact| |squareFreeFactors| - |addPoint2| |colorDef| |e02akf| |acsch| |d02cjf| |birth| |freeOf?| - |nextNormalPoly| |indices| |getExplanations| |mainSquareFreePart| - |components| |multiple?| |extractPoint| |setPosition| |showAttributes| - |d02gaf| |purelyTranscendental?| |every?| |leftExactQuotient| - |deepCopy| |numberOfChildren| |sequences| |even?| - |removeSuperfluousQuasiComponents| |socf2socdf| |forLoop| - |leftCharacteristicPolynomial| |reset| |hexDigit| |coefChoose| - |unravel| |permanent| BY |intersect| |ode1| |palgint| |normalElement| - |regularRepresentation| |monomRDEsys| |uncouplingMatrices| |shiftLeft| - |edf2ef| |fi2df| |yellow| |makeTerm| |presub| |charpol| - |wronskianMatrix| |norm| |write| |f02bjf| |denomLODE| |connectTo| - |reduceByQuasiMonic| |OMencodingSGML| |viewWriteDefault| |setColumn!| - |wreath| |save| |standardBasisOfCyclicSubmodule| |cAcosh| |infix?| - |critB| |singularAtInfinity?| |ListOfTerms| |delay| |exponent| - |sample| |computeCycleLength| |dictionary| |mask| |zero| |f01bsf| - |removeCosSq| |bezoutResultant| |gcdprim| |e01bgf| |infRittWu?| - |initiallyReduce| |OMwrite| |leftTrace| |increasePrecision| |vector| - 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|getMeasure| |sum| |signAround| |cTanh| |interval| |OMgetSymbol| - |multinomial| |clearTheIFTable| |hspace| |OMgetEndApp| |mathieu24| - |setCondition!| |psolve| |stFuncN| |comparison| |userOrdered?| |cons| - |RemainderList| |palgextint0| |trunc| |negative?| |genericRightNorm| - |integerIfCan| |morphism| |bigEndian| |expPot| |createZechTable| - |e02dcf| |rur| |fill!| |horizConcat| |s17dlf| |expIfCan| |mr| - |qfactor| |primextendedint| |parts| |mainForm| |preprocess| |imagI| - |rischDEsys| |subset?| |permutationRepresentation| |lp| |remainder| - |makeSin| |numberOfFractionalTerms| |iiacsch| |lflimitedint| - |matrixDimensions| |stoseInvertibleSetsqfreg| |nextColeman| |more?| - |tRange| |upperCase| |thetaCoord| |cyclotomic| |integers| - |OMputObject| |printHeader| |firstSubsetGray| |point?| |systemCommand| - |readLine!| |sec2cos| |removeRedundantFactorsInContents| - |toseInvertible?| |totalDifferential| |tubeRadius| |stirling1| - |source| |lhs| |OMputAttr| |contractSolve| |makeUnit| |style| |recip| - |simplifyPower| |startStats!| |pack!| |rhs| |characteristic| - |parametersOf| |solveInField| |duplicates?| |mdeg| |iiacosh| |submod| - |palginfieldint| |withPredicates| |s17aff| |normal| |exponentialOrder| - |commutative?| |d02kef| |rationalPoints| |vark| |insert!| |push| - |stoseInternalLastSubResultant| |hitherPlane| |cSin| - |pointColorDefault| |setprevious!| |zeroSetSplitIntoTriangularSystems| - |stirling2| |complex?| |bitCoef| |drawToScale| |stop| |setButtonValue| - |iiatanh| |getMultiplicationTable| |e04gcf| |addMatchRestricted| - |target| |branchIfCan| |polygon| |f01maf| |powerSum| |addMatch| - |trace2PowMod| |symbolIfCan| |datalist| |basisOfCenter| - |absolutelyIrreducible?| |exactQuotient| |cycleLength| |compdegd| - |totalLex| |lifting| |isPlus| |getCode| |musserTrials| |vspace| - |OMParseError?| |zeroDim?| |BasicMethod| |generic?| |f02adf| |s18aff| - |removeRoughlyRedundantFactorsInPols| |tryFunctionalDecomposition?| - |e02def| |f02awf| |inverseIntegralMatrixAtInfinity| - |createPrimitivePoly| |scalarTypeOf| |component| |maxIndex| - 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|rename| |update| |errorInfo| |mapUnivariate| |wrregime| |lSpaceBasis| - |wordsForStrongGenerators| |inGroundField?| |vectorise| |graphCurves| - |oneDimensionalArray| |cartesian| |chineseRemainder| ** |zerosOf| - |torsion?| |zeroSquareMatrix| |hasSolution?| |youngGroup| |init| - |OMopenString| |presuper| |reduced?| |duplicates| UTS2UP |setClosed| - |UP2ifCan| |frst| |kroneckerDelta| |e04fdf| |changeMeasure| - |complexEigenvalues| |mainContent| |hasTopPredicate?| |outputAsTex| EQ - |coordinates| |kmax| |tube| |hexDigit?| |ksec| |leastMonomial| - |ScanArabic| |position| |viewport2D| |equality| |sylvesterMatrix| - |just| |rationalApproximation| |ScanFloatIgnoreSpacesIfCan| - |OMputError| |critMTonD1| |viewpoint| |stoseInvertibleSetreg| - |rightMinimalPolynomial| |formula| |infieldint| |mapUnivariateIfCan| - |generalTwoFactor| |nonSingularModel| |eigenvalues| |edf2efi| - |nilFactor| |c06fpf| |countRealRootsMultiple| |symbolTable| |nextItem| - |char| |sizeLess?| |kovacic| |doubleDisc| |outputAsScript| - |buildSyntax| |leftTraceMatrix| |sinIfCan| |entry?| |checkPrecision| - |identitySquareMatrix| |evenInfiniteProduct| |discriminantEuclidean| - |specialTrigs| |sumSquares| |index| |rightQuotient| |low| - |subResultantsChain| |rightFactorIfCan| |integrate| |setFormula!| - |baseRDE| |nonQsign| |basisOfLeftNucloid| |elementary| |interpret| - |nrows| |normalized?| |hMonic| |minPoly| |whatInfinity| |relerror| - |ncols| |plot| |argscript| |rk4| |makingStats?| |setref| |changeName| - |minus!| |pair| |curve| |tab1| |numberOfComputedEntries| - |irreducibleFactor| |conditionP| |matrixConcat3D| |critMonD1| - |approxNthRoot| |lo| |factorFraction| |graphs| |separateDegrees| - |triangulate| |associatorDependence| |value| |mulmod| |makeCrit| |row| - |incr| |kind| |argumentList!| |fillPascalTriangle| |groebnerFactorize| - |empty?| |rst| |messagePrint| |nthExpon| |digamma| |point| - |lyndonIfCan| |indiceSubResultant| |op| |sts2stst| |nlde| |Beta| - |lowerCase!| |orOperands| |transcendent?| |OMclose| |janko2| - |direction| |imagj| |deepExpand| |genericLeftTraceForm| |bits| - |gcdcofactprim| |pdct| |derivative| |iiexp| |top!| |iterationVar| - |OMunhandledSymbol| |remove!| |prem| |series| |lazyEvaluate| |varList| - |lazyIrreducibleFactors| |atanhIfCan| |fibonacci| |divide| - |sortConstraints| |c06ekf| - |rewriteSetByReducingWithParticularGenerators| |shuffle| F - |startTable!| |abs| |coord| |symmetricDifference| - |stoseLastSubResultant| |newTypeLists| |comment| |generalPosition| - |groebner| |zeroDimensional?| |prod| |coerceP| |logGamma| |operation| - |unmakeSUP| |quadratic?| |setPrologue!| |matrix| |explicitlyFinite?| - |limitPlus| |mainCharacterization| |clearTheSymbolTable| |bitTruth| - |cCosh| |triangular?| |union| |OMgetInteger| |monicDecomposeIfCan| - |basisOfLeftNucleus| |inverseIntegralMatrix| |hostByteOrder| - |printInfo!| |exponential1| |min| |node?| |completeEval| - |leftDiscriminant| |genericLeftNorm| |monicRightFactorIfCan| - |alternative?| |isAbsolutelyIrreducible?| |localReal?| - |setProperties!| |s17def| |returnType!| |curry| |subscript| |biRank| - |d01asf| |close| |iiGamma| |complexEigenvectors| |scripted?| |largest| - |patternVariable| |squareFreePart| |antiCommutative?| |logpart| - |df2st| |tablePow| |primaryDecomp| |recur| |lambert| |maxrank| |hi| - |modularGcd| |permutations| |charClass| |innerSolve1| |imagk| |sqfree| - |display| |f01rdf| |subresultantSequence| |invertIfCan| |enterInCache| - |setScreenResolution3D| |nor| |genericPosition| |cyclicEntries| - |functionIsFracPolynomial?| |shellSort| |s17agf| |generalLambert| - |basisOfNucleus| |integer?| |numberOfDivisors| |droot| |linearPart| - |id| |column| |iicsc| |showTheSymbolTable| |f02akf| |endOfFile?| - |indiceSubResultantEuclidean| |bat| |cycles| |e02bbf| |extractTop!| - |lowerCase| |digits| |decomposeFunc| |unitCanonical| |deleteRoutine!| - |nullary?| |rightPower| |squareFreePolynomial| |weight| |e02ahf| - |palgRDE0| |table| |quotient| |reduction| |d01amf| |quoByVar| - |genericLeftTrace| |areEquivalent?| |recolor| |new| |sincos| - 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|polygon?| |sinh2csch| |nullary| |normal01| |package| |f02axf| - |expandPower| |shanksDiscLogAlgorithm| |factorList| |rspace| - |certainlySubVariety?| |ocf2ocdf| |fixPredicate| |swap!| |over| - |mathieu11| |radix| |palgRDE| |denomRicDE| |cyclicGroup| |outputForm| - |multMonom| |crushedSet| |removeSquaresIfCan| - |linearlyDependentOverZ?| |genericRightDiscriminant| |mapmult| - |d02bhf| |rootDirectory| |ffactor| |mergeDifference| |height| |regime| - |float?| |Ci| |minPol| |cAtanh| |d01apf| |midpoint| |laurentRep| - |cos2sec| |laguerre| |setchildren!| |extractIndex| |getZechTable| - |removeSuperfluousCases| |Nul| ~= |nthRootIfCan| |eq?| |dark| - |noKaratsuba| |degreeSubResultantEuclidean| |separant| |weierstrass| - |setErrorBound| |internal?| |depth| |roughEqualIdeals?| - |viewDeltaYDefault| |coerce| |mainCoefficients| |getPickedPoints| - |pointData| |conical| |isobaric?| |getConstant| |adaptive?| - |semicolonSeparate| |tanNa| |escape| |rewriteIdealWithHeadRemainder| - |construct| |square?| |makeYoungTableau| |complexForm| |setProperty!| - 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|physicalLength| |infinite?| |numericalOptimization| |radicalSolve| - |exprToUPS| |unknown| |leftExtendedGcd| |dflist| |OMsupportsCD?| - |basisOfRightNucleus| |makeFR| |singularitiesOf| |multiset| |true| - |stFunc1| |euler| |merge!| |plotPolar| |possiblyInfinite?| - |curveColorPalette| |showTheFTable| |bytes| |pole?| - |combineFeatureCompatibility| |intermediateResultsIF| |pow| - |interReduce| |headReduced?| |variable| |f07fdf| |monic?| |rk4a| - |legendre| |cylindrical| |branchPointAtInfinity?| |s18aef| |simpsono| - |rightOne| |diagonals| |iterators| |outputList| |f02wef| |s21bbf| - |bandedJacobian| |SturmHabichtCoefficients| |inverse| |cot2trig| - |binaryFunction| |normalise| |branchPoint?| |explogs2trigs| |hash| - |integralCoordinates| |pToDmp| |algebraicCoefficients?| |decompose| - |predicate| |OMputBVar| |setLegalFortranSourceExtensions| - |genericRightTrace| |OMputString| |innerSolve| |internalAugment| - |constantOperator| |count| |collect| |setelt| |eigenvector| |cycle| - |collectUnder| |nextNormalPrimitivePoly| |normalizedDivide| - |usingTable?| |addmod| |csch2sinh| |exprToGenUPS| |HermiteIntegrate| - |halfExtendedResultant1| |li| |makeResult| |lazyVariations| |middle| - |fTable| |reverse!| |red| |LowTriBddDenomInv| |imaginary| - |constantRight| |copy| |companionBlocks| |SturmHabichtMultiple| - |univariatePolynomial| |headRemainder| |nextsousResultant2| - |supRittWu?| |d03edf| |localIntegralBasis| |integral?| |qqq| |equiv| - |fortran| |crest| |quickSort| |next| |e04mbf| |getGoodPrime| - |removeRedundantFactorsInPols| |d01alf| |string?| |sizePascalTriangle| - |create| |lowerPolynomial| |typeList| |latex| - |cyclotomicFactorization| |coleman| |invmod| |semiResultantEuclidean1| - |root?| |autoCoerce| |mpsode| |integralRepresents| |factorSFBRlcUnit| - |sorted?| |nodes| |OMUnknownSymbol?| |tan2trig| |f02agf| |sinhIfCan| - |options| |ParCondList| |unvectorise| |rightFactorCandidate| |shade| - |internalZeroSetSplit| |countRealRoots| |insertMatch| - |removeIrreducibleRedundantFactors| |squareFreeLexTriangular| - |setlast!| |fortranCompilerName| |selectPolynomials| |rightNorm| - |module| |parameters| FG2F |complexIntegrate| |FormatRoman| - |resultantnaif| |leftPower| |supDimElseRittWu?| |bipolar| |setEmpty!| - |blue| |e04ucf| |OMencodingUnknown| |besselK| |partialQuotients| - |e02bef| |string| |increase| |algDsolve| |getDatabase| - |cyclicSubmodule| |createNormalElement| |outputSpacing| |eigenvectors| - |scale| |df2ef| |leadingExponent| |deref| |stFunc2| - |complementaryBasis| |setEpilogue!| |selectsecond| |updatF| - |bezoutDiscriminant| |resultantEuclideannaif| |pushdterm| |c06gcf| - |d03eef| |getCurve| |points| |cExp| |f02aaf| |showFortranOutputStack| - |fracPart| |euclideanGroebner| |coshIfCan| |rationalPoint?| - |antiAssociative?| |createRandomElement| |close!| |rCoord| - |primlimitedint| |tower| |e02bdf| |subResultantGcdEuclidean| - |oddintegers| NOT |s15adf| |currentSubProgram| |makeSketch| - |goodPoint| |bezoutMatrix| |subMatrix| |tableForDiscreteLogarithm| - |setStatus| |OMputApp| |binaryTournament| |positiveSolve| OR - |cyclotomicDecomposition| |moreAlgebraic?| |singleFactorBound| |floor| - 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|incrementBy| |cAsec| |approximants| |hdmpToDmp| |generalizedInverse| - |univariate| |primitivePart| |fmecg| |primitivePart!| |fortranTypeOf| - |generators| |atom?| |expand| |f01qef| |rewriteIdealWithRemainder| - |createLowComplexityTable| |poisson| |pToHdmp| |setrest!| |isOp| - |gderiv| |groebnerIdeal| |tensorProduct| |filterWhile| |elseBranch| - |systemSizeIF| |factors| |schema| |algebraicVariables| |exp| - |predicates| |whitePoint| |isOpen?| |symbol?| |primes| |filterUntil| - |numberOfPrimitivePoly| |pushucoef| |dmp2rfi| - |rewriteIdealWithQuasiMonicGenerators| |factor| * |partition| - |computeInt| |taylorQuoByVar| |rootKerSimp| |s18adf| |henselFact| - |select| |intPatternMatch| |laplacian| |sqrt| |pointSizeDefault| - |stiffnessAndStabilityOfODEIF| |indicialEquations| |unitNormalize| - |pseudoQuotient| |atrapezoidal| |completeEchelonBasis| - |realElementary| |leftRegularRepresentation| |diag| |belong?| |real| - |associates?| |relativeApprox| |inverseLaplace| |f02bbf| - |simpleBounds?| |sub| |legendreP| |explicitlyEmpty?| |ratDsolve| - |infiniteProduct| |imag| |isExpt| |ref| |OMconnOutDevice| - |numberOfCycles| |iisqrt2| |transcendenceDegree| |normInvertible?| - |associatedSystem| |anticoord| |rotatex| |directProduct| |unary?| - |OMputAtp| |clip| |adjoint| |inspect| |checkForZero| |associator| - |basisOfLeftAnnihilator| |solveLinearPolynomialEquationByFractions| - |leftScalarTimes!| |isConnected?| |evenlambert| |identity| |prinb| - |mainValue| |selectPDERoutines| |OMserve| |arrayStack| - |decreasePrecision| |prime| |brace| |bubbleSort!| |empty| - |getSyntaxFormsFromFile| |resetNew| Y |ptFunc| |maxRowIndex| |gethi| - |makeRecord| |leadingIndex| |lift| |basis| |stosePrepareSubResAlgo| - |compile| |destruct| |prepareDecompose| |squareFree| |doubleRank| - |setnext!| |tab| |quasiRegular| |meshFun2Var| |reduce| |minIndex| - |rightMult| |twist| SEGMENT |f04asf| |nthr| |getButtonValue| |iprint| - |numeric| |d02raf| |outputBinaryFile| |bfKeys| |key?| |c05adf| - |cycleSplit!| |hex| |prevPrime| |radical| |identification| |leftLcm| - |rubiksGroup| |linearPolynomials| |modularGcdPrimitive| |null| - |maxPoints| |maxint| |wholePart| |conditionsForIdempotents| - |primextintfrac| |lyndon| |sechIfCan| |logical?| |sech2cosh| - |hermiteH| |not| |getProperties| |processTemplate| - |indicialEquationAtInfinity| |monomial| |f2st| |acoshIfCan| |ord| - |quadraticForm| |generic| |composite| |leadingCoefficientRicDE| |and| - |s18dcf| |pushup| |shufflein| |multivariate| |e02dff| |writeInt8!| - |hessian| |rk4f| |finiteBound| |ricDsolve| |split!| |or| - |knownInfBasis| |OMputInteger| |exptMod| |variables| - |rightExactQuotient| |tableau| |iiacos| |evaluateInverse| |cSinh| - |sup| |mapdiv| |xor| |internalDecompose| |e01bef| |mix| |sdf2lst| - |ScanFloatIgnoreSpaces| |localAbs| |complement| |printTypes| |pop!| - |signature| |fortranDouble| |case| |getBadValues| |tracePowMod| - |s17aef| |retractable?| |UpTriBddDenomInv| |listConjugateBases| - |entries| |iExquo| |writeBytes!| |index?| |Zero| |log2| |var2Steps| - |rightCharacteristicPolynomial| |polyRicDE| |stopTableInvSet!| - |lifting1| |complexRoots| |smith| |leftAlternative?| |OMgetBind| - |e02daf| |One| |critM| |scaleRoots| |linGenPos| |f01brf| |monicDivide| - |reopen!| |iiabs| |modifyPoint| |lazyIntegrate| RF2UTS |epilogue| - |possiblyNewVariety?| |zoom| |irreducibleFactors| |taylor| |rightUnit| - |subResultantGcd| |setsubMatrix!| |subCase?| |byteBuffer| - |linearDependenceOverZ| |removeConstantTerm| |byte| |whileLoop| - |acschIfCan| |bsolve| |name| |laurent| - |generalizedContinuumHypothesisAssumed| |high| |monomials| |aCubic| - |headAst| |algebraicSort| |initial| |lprop| |property| |dmpToHdmp| - |body| |realSolve| |interpretString| |puiseux| |infix| - |sylvesterSequence| |light| |axesColorDefault| |upperCase?| |makeprod| - |edf2df| |mindegTerm| |iiatan| |e01baf| |rootsOf| - |lastSubResultantEuclidean| |antiCommutator| |sinhcosh| - |continuedFraction| |stoseInvertible?sqfreg| |mapDown!| |int| |elt| - |inv| |halfExtendedSubResultantGcd2| |setMaxPoints| - |degreeSubResultant| |romberg| |wordInGenerators| |iidprod| |evaluate| - |OMconnInDevice| |fractionPart| |nthCoef| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |sech2cosh| |squareFreeFactors| |xn| |isPlus| + |finiteBasis| |rightFactorCandidate| |uniform01| |hermiteH| + |addPoint2| |getCode| |child| |alternatingGroup| |shade| |update| + |tryFunctionalDecomposition| |d01asf| |s17ajf| |getProperties| + |colorDef| |noLinearFactor?| |musserTrials| |algebraicDecompose| + |internalZeroSetSplit| |Lazard| |iiGamma| |simplifyLog| + |processTemplate| |e02akf| |vspace| |bivariate?| |reducedForm| + |countRealRoots| |character?| |complexEigenvectors| |fixedPointExquo| + |entry| |indicialEquationAtInfinity| |zeroMatrix| |d02cjf| + |OMParseError?| |port| |outputList| |sum| |setTopPredicate| + |integralLastSubResultant| |scripted?| |f2st| |makeFR| |birth| + |zeroDim?| |setMinPoints| |exquo| |opeval| |flexibleArray| + |mainMonomials| |largest| |singularitiesOf| |acoshIfCan| |freeOf?| + |BasicMethod| |gcdPrimitive| |t| |div| |B1solve| |position| + |UnVectorise| |dihedral| |patternVariable| |ord| |range| + |nextNormalPoly| |generic?| |rowEchelon| |multiset| |quo| |rischDE| + |squareFreePart| |extensionDegree| |leader| |indices| |paraboloidal| + |f02adf| |pointPlot| |stFunc1| |call| |byte| |roughBase?| + |antiCommutative?| |s19aaf| |partition| |lp| |safetyMargin| + |getExplanations| |s18aff| |OMReadError?| |rem| |euler| + |startTableInvSet!| |logpart| |extractClosed| |computeInt| + |mainSquareFreePart| |imagE| |removeRoughlyRedundantFactorsInPols| + |readInt8!| |merge!| |zero| |hasHi| |clipWithRanges| |df2st| + |taylorQuoByVar| |index| |components| |tryFunctionalDecomposition?| + |unrankImproperPartitions1| |rk4qc| |plotPolar| |selectAndPolynomials| + |int| |tablePow| |lfintegrate| |rootKerSimp| |e02def| |multiple?| + |firstDenom| |top| |possiblyInfinite?| |viewPosDefault| |And| + |primintegrate| |iiasin| |primaryDecomp| |s18adf| |extractPoint| + |f02awf| |multisect| |curveColorPalette| |term?| |Or| + |expenseOfEvaluationIF| |recur| |s21bcf| |pair| |henselFact| + |setPosition| |clipParametric| |inverseIntegralMatrixAtInfinity| + |showTheFTable| |cAsech| |Not| |tValues| F2FG |lambert| + |intPatternMatch| |d02gaf| |mat| |createPrimitivePoly| |bytes| + |setValue!| |value| |startPolynomial| |numerators| |maxrank| + |laplacian| |purelyTranscendental?| |scalarTypeOf| |virtualDegree| + |pole?| |quasiAlgebraicSet| |ramified?| |pureLex| BY |modularGcd| + |pquo| |pointSizeDefault| |every?| |component| |screenResolution| + |setRow!| |combineFeatureCompatibility| |normalForm| |rangeIsFinite| + |permutations| |besselJ| |stiffnessAndStabilityOfODEIF| + |leftExactQuotient| |cAcot| |maxIndex| |intermediateResultsIF| + |idealiser| |critBonD| |charClass| |factorset| |indicialEquations| + |interpret| |deepCopy| |constantCoefficientRicDE| |lastSubResultant| + |pow| |supersub| |checkPrecision| |complexExpand| |iipow| + |innerSolve1| |unitNormalize| |numberOfChildren| |internalIntegrate| + |nsqfree| |interReduce| |radicalSimplify| |generator| |cTan| + |discreteLog| |imagk| |pseudoQuotient| |numer| |sequences| + |antisymmetric?| |mightHaveRoots| |c05nbf| |headReduced?| + |symmetricSquare| |se2rfi| |sqfree| |atrapezoidal| |denom| |even?| + |lo| |e02aef| |factorSquareFreeByRecursion| |minGbasis| |f07fdf| + |e01sff| |f01rdf| |weighted| |completeEchelonBasis| |outputFloating| + |incr| |removeSuperfluousQuasiComponents| |coercePreimagesImages| + |extractSplittingLeaf| |getMatch| |monic?| |printingInfo?| |subSet| + |subresultantSequence| |realElementary| |pi| |socf2socdf| |d01gaf| + |subspace| |rk4a| |extendedSubResultantGcd| |invertIfCan| |f04qaf| + |max| LODO2FUN |leftRegularRepresentation| |forLoop| |infinity| + |d01fcf| |plusInfinity| |f02ajf| |quoted?| |legendre| + |LazardQuotient2| |OMputEndAtp| |enterInCache| |Frobenius| |diag| + |showTypeInOutput| |leftCharacteristicPolynomial| |minusInfinity| + |cylindrical| |firstUncouplingMatrix| |mainMonomial| + |setVariableOrder| ~ |meatAxe| |iisqrt3| |setScreenResolution3D| + |belong?| |hexDigit| |cosh2sech| |monicCompleteDecompose| + |branchPointAtInfinity?| |fullPartialFraction| |notelem| |nor| + |taylorRep| |associates?| |kernel| |coefChoose| |mkcomm| + |radicalEigenvalues| |s18aef| |chiSquare1| |open| |mapSolve| + |genericPosition| |leftMult| |relativeApprox| |draw| |unravel| + |s17adf| |coHeight| |simpsono| |autoReduced?| |id| |c06gsf| + |symmetricPower| |cyclicEntries| |inverseLaplace| |matrix| |permanent| + |useEisensteinCriterion| |OMputEndError| |rightOne| |goto| |init| + |argumentListOf| |factorial| |functionIsFracPolynomial?| |f02bbf| + |type| |intersect| |df2fi| |algint| |subNode?| |diagonals| |table| + |enqueue!| |shellSort| |expandLog| |simpleBounds?| |ode1| + |strongGenerators| |odd?| |f02wef| |setStatus!| |operations| |new| + |viewWriteAvailable| |getStream| |s17agf| |sub| |makeObject| + |reciprocalPolynomial| |palgint| |primPartElseUnitCanonical| + |shallowCopy| |e02adf| |s21bbf| |search| |pushNewContour| |arbitrary| + |generalLambert| |legendreP| |normalElement| |bandedJacobian| |hi| + |f01qcf| |split| |leftRemainder| |clikeUniv| |measure| + |basisOfNucleus| |readUInt8!| |explicitlyEmpty?| |symbolTable| |coef| + |regularRepresentation| |elliptic| |lfextlimint| |reorder| + |SturmHabichtCoefficients| |untab| |acosIfCan| |integer?| |ratDsolve| + |monomRDEsys| |setleaves!| |rectangularMatrix| |inverse| |ode| + |flagFactor| |rightRank| |numberOfDivisors| |infiniteProduct| + |clearCache| |uncouplingMatrices| |skewSFunction| |checkRur| + |outlineRender| = |cot2trig| |chainSubResultants| |droot| |f04axf| + |isExpt| |shiftLeft| |linkToFortran| |omError| |packageCall| + |binaryFunction| |graeffe| |linearPart| |compound?| |ref| + |polynomialZeros| |edf2ef| |powerAssociative?| |linearDependence| < + |normalise| |variable?| |setImagSteps| |column| |OMconnOutDevice| + |fi2df| |branchPoint?| |monomialIntPoly| |numFunEvals3D| > + |signatureAst| |setProperty| |iicsc| |box| |oddlambert| |vector| + |numberOfCycles| |yellow| |rischNormalize| + |rightRegularRepresentation| |OMgetObject| |explogs2trigs| <= + |sin2csc| |reseed| |showTheSymbolTable| |iisqrt2| |reify| + |integralCoordinates| |makeTerm| |hconcat| |viewZoomDefault| >= + |removeRoughlyRedundantFactorsInPol| |child?| |e04jaf| |f02akf| + |transcendenceDegree| |getIdentifier| |presub| |s18def| + |trivialIdeal?| |rightExtendedGcd| |pToDmp| |quotedOperators| + |positive?| |endOfFile?| |normInvertible?| ~= |charpol| + |jacobiIdentity?| |coefficient| |e04naf| |algebraicCoefficients?| + |isQuotient| |factorPolynomial| |commutator| + |indiceSubResultantEuclidean| |associatedSystem| |coerce| + |trailingCoefficient| |wronskianMatrix| |normalizedAssociate| + |generalInfiniteProduct| |decompose| + |superscript| |chebyshevT| + |bat| |anticoord| |construct| |sPol| |elRow2!| |norm| + |maximumExponent| |OMgetAtp| |OMputBVar| - |unexpand| |cycles| + |minRowIndex| |rotatex| |factorByRecursion| + |setLegalFortranSourceExtensions| |numericIfCan| |integralBasis| + |unaryFunction| / |writeUInt8!| |e02bbf| |univariateSolve| |unary?| + |quotientByP| |leastAffineMultiple| |semiSubResultantGcdEuclidean1| + |genericRightTrace| |GospersMethod| |listBranches| |extractTop!| + |df2mf| |comment| |OMputAtp| |idealiserMatrix| |copies| |zCoord| + |OMputString| |create3Space| |height| |roughBasicSet| |movedPoints| + |lowerCase| |clip| |extendedint| |monicRightDivide| |innerSolve| + |head| |lists| |newLine| |digits| |adjoint| |operator| |nextPartition| + |hermite| |internalAugment| |stoseInvertible?reg| |decomposeFunc| + |complexElementary| |inspect| |genus| |Is| |constantOperator| + |nextsubResultant2| |setProperties| |stop| |unitCanonical| + |lexGroebner| |checkForZero| |balancedBinaryTree| |viewDeltaXDefault| + |collect| |llprop| |sizeMultiplication| |myDegree| |deleteRoutine!| + |associator| |eigenvector| |var2StepsDefault| |mainVariable?| + |nullary?| |stopTableGcd!| |basisOfLeftAnnihilator| |bright| + |showIntensityFunctions| |toseInvertible?| |HenselLift| |cycle| + |ParCond| |weakBiRank| |rightPower| + |solveLinearPolynomialEquationByFractions| |totalDifferential| + |cyclic?| |solveLinearPolynomialEquationByRecursion| |collectUnder| + |rightDiscriminant| |squareFreePolynomial| |move| |leftScalarTimes!| + |output| |tubeRadius| |sn| |nextNormalPrimitivePoly| |randnum| + |drawCurves| |isConnected?| |setelt| |tail| |stirling1| |sayLength| + |interactiveEnv| |normalizedDivide| |setright!| |iterationVar| + |perfectSquare?| |evenlambert| |s17dhf| |OMputAttr| |minordet| + |usingTable?| |OMmakeConn| |OMunhandledSymbol| |optpair| |identity| + |copy| |c06gqf| |contractSolve| |nand| |addmod| |currentEnv| + |infieldIntegrate| |OMUnknownCD?| |remove!| |prinb| |makeUnit| + |showClipRegion| |tanintegrate| |prem| |diophantineSystem| |mainValue| + |style| |definingPolynomial| |OMgetString| |seed| |error| |OMreceive| + |numberOfFactors| |lazyEvaluate| |selectPDERoutines| |autoCoerce| + |rightScalarTimes!| |recip| |exists?| |stoseIntegralLastSubResultant| + |infinityNorm| |super| |lazyIrreducibleFactors| |inverseColeman| + |options| |assert| |nthRoot| |OMserve| |simplifyPower| |discriminant| + |binomial| |stronglyReduced?| |credPol| |atanhIfCan| + |viewThetaDefault| |overbar| |froot| |startStats!| |initTable!| + |setOrder| |elRow1!| |unit| |fibonacci| |drawComplex| |multiEuclidean| + |li| |pack!| |semiDiscriminantEuclidean| |numerator| |besselY| + |divide| |rename!| |string| |ran| |iiperm| |isTimes| |characteristic| + |failed| |getOperator| |cCot| |sortConstraints| |partitions| + |completeSmith| |parametersOf| |medialSet| |normalDenom| |f04arf| + |resultantEuclidean| |c06ekf| |rationalIfCan| |compose| + |parabolicCylindrical| |solveInField| |parabolic| |prefixRagits| + |evaluate| |radPoly| |decrease| + |rewriteSetByReducingWithParticularGenerators| |updateStatus!| + |duplicates?| |primitiveElement| |useNagFunctions| |matrixGcd| + |OMconnInDevice| |term| |jordanAlgebra?| |shuffle| |lexTriangular| + |clipPointsDefault| |mdeg| |useEisensteinCriterion?| + |expressIdealMember| |fractionPart| |difference| |FormatArabic| + |startTable!| |numberOfVariables| |iiacosh| |delete| |OMgetEndAttr| + |universe| |readInt16!| |nthCoef| |retractIfCan| |calcRanges| + |doubleComplex?| |abs| |getVariableOrder| |submod| |repeating?| + |zeroVector| |readByte!| |mainVariable| |coord| |sh| + |integralAtInfinity?| |palginfieldint| |c05pbf| |OMcloseConn| + |commaSeparate| |integralDerivationMatrix| |iiasinh| + |symmetricDifference| |integralBasisAtInfinity| |digit?| |elliptic?| + |withPredicates| |leftOne| |moduleSum| |drawStyle| |swap| + |stoseLastSubResultant| |factorsOfCyclicGroupSize| |LyndonWordsList1| + |s17aff| |qPot| |quasiRegular?| |totalfract| |newTypeLists| UP2UTS + |equivOperands| |outputMeasure| |exponentialOrder| + |noncommutativeJordanAlgebra?| |inputBinaryFile| |generalPosition| + |quartic| |depth| |quasiComponent| |rightZero| |commutative?| + |exprToXXP| |numberOfIrreduciblePoly| |quasiMonicPolynomials| + |retract| |prindINFO| |dAndcExp| |groebner| |unparse| + |inputOutputBinaryFile| |d02kef| |factorials| |c06ebf| + |changeThreshhold| |palgintegrate| |zeroDimensional?| |eq| + |symbolTableOf| |rationalPoints| |symmetricGroup| |expintegrate| + |part?| |map| |cRationalPower| |fortranLiteral| |prod| |iter| + |resultantReduit| |leastPower| |vark| |constantIfCan| |d01aqf| + |condition| |mapGen| |coerceP| |lfunc| |graphImage| + |purelyAlgebraicLeadingMonomial?| |insert!| |listOfMonoms| + |endSubProgram| |setOfMinN| |logGamma| |numberOfComponents| + |maxColIndex| |push| |e02agf| |generate| |rootPower| |deriv| + |coerceImages| |solveLinearPolynomialEquation| |unmakeSUP| + |createMultiplicationMatrix| |isList| |stoseInternalLastSubResultant| + |f04mcf| |selectIntegrationRoutines| |minPoints3D| |quadratic?| + |leftFactor| |contract| |incrementBy| |reducedDiscriminant| + |hitherPlane| |complexZeros| |lineColorDefault| |convert| + |getMultiplicationMatrix| |mappingAst| |setPrologue!| |meshPar2Var| + |mapCoef| |cSin| |expand| |sparsityIF| |lexico| |mantissa| + |fortranDoubleComplex| |float| |intChoose| |explicitlyFinite?| + |geometric| |secIfCan| |filterWhile| |pointColorDefault| |jacobian| + |cycleRagits| |palgint0| |option?| |limitPlus| |cAsec| |exp| + |setprevious!| |outputArgs| |filterUntil| |iidsum| |iiasech| + |qualifier| |leadingIdeal| |mainCharacterization| |approximants| + |OMgetAttr| |zeroSetSplitIntoTriangularSystems| |select| |cardinality| + |const| SEGMENT |setFieldInfo| |subHeight| |bernoulliB| + |clearTheSymbolTable| |hdmpToDmp| |stirling2| |d03faf| |linearMatrix| + |modifyPointData| |testDim| |divideIfCan| |bitTruth| |twoFactor| + |generalizedInverse| |SFunction| |complex?| |primeFrobenius| + |commutativeEquality| |log| |jordanAdmissible?| |cCosh| |arity| + |primitivePart| |bitCoef| |addPoint| |transform| |coerceL| + |OMgetEndBVar| |bothWays| |triangular?| |fmecg| |drawToScale| |leaf?| + |functionIsContinuousAtEndPoints| |s15aef| |refine| + |fortranCarriageReturn| |OMgetInteger| |primitivePart!| + |setButtonValue| |pushuconst| |lookup| |redmat| |ipow| GE |power| + |monicDecomposeIfCan| |fortranTypeOf| |iiatanh| |makeRecord| |exprex| + |pointColor| |extendedIntegrate| |datalist| |compile| |dequeue!| GT + |basisOfLeftNucleus| |selectfirst| |generators| + |getMultiplicationTable| |prologue| |btwFact| |f01qdf| |outputFixed| + LE |inverseIntegralMatrix| |hostPlatform| |atom?| |any?| |e04gcf| + |pmintegrate| |lazyPseudoDivide| |compBound| LT |hostByteOrder| + |tanh2trigh| |f01qef| |addMatchRestricted| |monomRDE| |readBytes!| + |viewPhiDefault| |showScalarValues| |factor1| |printInfo!| |times| + |rewriteIdealWithRemainder| |branchIfCan| |createThreeSpace| + |applyRules| |central?| |revert| |exponential1| |order| + |createLowComplexityTable| |directory| |pointColorPalette| |polygon| + |balancedFactorisation| |createLowComplexityNormalBasis| |nil| + |precision| |bivariatePolynomials| |setPredicates| |node?| |poisson| + |cLog| |rowEchelonLocal| |f01maf| |property| |permutationGroup| |comp| + |OMgetBVar| |drawComplexVectorField| |completeEval| |pToHdmp| |rotate| + |powerSum| |copyInto!| |setelt!| |consnewpol| |colorFunction| + |littleEndian| |leftDiscriminant| |monom| |setrest!| |cycleTail| + |nary?| |addMatch| |clipBoolean| |invertibleSet| |approximate| + |multiplyExponents| |reducedContinuedFraction| |genericLeftNorm| + |LazardQuotient| |isOp| |complex| |trace2PowMod| |nextIrreduciblePoly| + |s14baf| |f01rcf| |units| |inc| |resetBadValues| + |currentCategoryFrame| |permutation| |monicRightFactorIfCan| |gderiv| + |symbolIfCan| |collectUpper| |expenseOfEvaluation| + |halfExtendedSubResultantGcd1| |times!| |toScale| |alternative?| + |common| |groebnerIdeal| |basisOfCenter| |reflect| |copy!| |addiag| + |totalGroebner| |zag| |isAbsolutelyIrreducible?| |tensorProduct| + |absolutelyIrreducible?| |toseSquareFreePart| |att2Result| + |OMputEndBind| |digit| |localReal?| |elseBranch| |c02agf| + |exactQuotient| |find| |separateFactors| |initial| |listYoungTableaus| + |loadNativeModule| |exprHasWeightCosWXorSinWX| |setProperties!| + |systemSizeIF| |key| |reindex| |code| |mr| |cycleLength| + |physicalLength| |d01bbf| |setLabelValue| |remove| |pdf2ef| |s17def| + |factors| |compdegd| |definingEquations| |infinite?| |rightRemainder| + |tree| |cAcsc| |OMreadFile| |returnType!| |filename| |schema| + |numericalOptimization| |prepareSubResAlgo| |isMult| |last| |argument| + |curry| |not?| |algebraicVariables| |complexSolve| |OMgetSymbol| + |nonLinearPart| |radicalSolve| |assoc| |antisymmetricTensors| + |function| |iiasec| |subscript| |predicates| |parse| |multinomial| + |genericLeftDiscriminant| |exprToUPS| |bombieriNorm| + |representationType| |any| |biRank| |mapBivariate| |whitePoint| + |clearTheIFTable| |Hausdorff| |npcoef| |optimize| |leftExtendedGcd| + |backOldPos| |eval| |isOpen?| |ratPoly| |hspace| |dflist| |mesh| + |characteristicSet| |gradient| |normalized?| |symbol?| |OMgetEndApp| + |makeSUP| |one?| |OMsupportsCD?| |expint| |hMonic| |divergence| + |primes| |unknownEndian| |mathieu24| |basisOfRightNucleus| |iicsch| + |showSummary| |createMultiplicationTable| |minPoly| |purelyAlgebraic?| + |numberOfPrimitivePoly| |toseInvertibleSet| |setCondition!| |separate| + |nextPrimitivePoly| |whatInfinity| |pushucoef| |totolex| |psolve| + |quatern| |float?| |showAttributes| |deleteProperty!| |relerror| + |f04jgf| |dmp2rfi| |boundOfCauchy| |stFuncN| |Ci| |closedCurve| + |perfectSqrt| |setAttributeButtonStep| |plot| + |rewriteIdealWithQuasiMonicGenerators| |basisOfCommutingElements| + |comparison| |minPol| |scalarMatrix| |c06frf| |setRealSteps| + |argscript| |exprHasAlgebraicWeight| |userOrdered?| |cAtanh| + |splitNodeOf!| |f04maf| |s19adf| |rk4| |substring?| |primlimitedint| + |radicalRoots| |linSolve| |RemainderList| |polarCoordinates| |d01apf| + |concat!| |cscIfCan| |makingStats?| |getlo| |e02bdf| + |leadingBasisTerm| |palgextint0| |in?| |midpoint| |zeroOf| |lcm| + |cyclicCopy| |suffix?| |setref| |subResultantGcdEuclidean| + |nextLatticePermutation| |sort| |OMputEndAttr| |trunc| |f02xef| + |laurentRep| |iiacoth| |changeName| |generalizedEigenvectors| + |conjugate| |oddintegers| |printCode| |scaleRoots| |negative?| + |writeByte!| |cos2sec| |nothing| |result| |operation| |trueEqual| + |minimalPolynomial| |append| |minus!| |prefix?| |s15adf| + |OMgetEndError| |beauzamyBound| |genericRightNorm| |rotatey| + |laguerre| |linGenPos| |e01sbf| |reset| |bumprow| |gcd| |curve| + |KrullNumber| |currentSubProgram| |prinshINFO| |integerIfCan| + |imports| |setchildren!| |f01brf| |leadingTerm| |graphState| |false| + |tab1| |makeSketch| |constDsolve| |random| |morphism| |plenaryPower| + |createIrreduciblePoly| |extractIndex| |monicDivide| |write| + |patternMatch| |factorAndSplit| |numberOfComputedEntries| |goodPoint| + |raisePolynomial| |rightLcm| |bigEndian| |completeHermite| + |getZechTable| |lquo| |reopen!| |save| |irreducibleFactor| + |stopTable!| |cosSinInfo| |length| |bezoutMatrix| |randomLC| |trim| + |expPot| |stripCommentsAndBlanks| |removeSuperfluousCases| + |defineProperty| |iiabs| |cAsin| |conditionP| |symmetricTensors| + |scripts| |subMatrix| |internalInfRittWu?| |width| |createZechTable| + |expintfldpoly| |Nul| |sequence| |modifyPoint| |normalizeAtInfinity| + |matrixConcat3D| |setMaxPoints3D| |infix?| |#| + |tableForDiscreteLogarithm| |simplifyExp| |dim| |numberOfNormalPoly| + |e02dcf| |clearTheFTable| |nthRootIfCan| |lazyIntegrate| |alphabetic| + |critMonD1| |mask| |curryRight| |setStatus| |subQuasiComponent?| + |phiCoord| |rur| |eq?| |replaceKthElement| RF2UTS |fortranComplex| + |approxNthRoot| |s13aaf| |OMputApp| |uniform| |fill!| |power!| |dark| + |firstNumer| |epilogue| |cPower| |reducedSystem| |factorFraction| + |binaryTournament| |dfRange| |horizConcat| |cubic| |acotIfCan| + |noKaratsuba| |possiblyNewVariety?| |insertBottom!| |showTheIFTable| + |graphs| |extendedResultant| |positiveSolve| |build| |s17dlf| |OMsend| + |degreeSubResultantEuclidean| |zoom| |cyclotomicDecomposition| + |squareMatrix| |separateDegrees| |besselI| |polyred| |subTriSet?| + |OMlistCDs| |expIfCan| |separant| |airyBi| |irreducibleFactors| + |basisOfMiddleNucleus| |d01anf| |bag| |triangulate| + |seriesToOutputForm| |moreAlgebraic?| |optional| |qfactor| + |palglimint| |lyndon?| |weierstrass| |rightUnit| |subst| + |associatorDependence| |lazyPseudoQuotient| |singleFactorBound| + |genericLeftMinimalPolynomial| |updatD| |flatten| |primextendedint| + |fractRadix| |setErrorBound| |determinant| |subResultantGcd| + |perfectNthRoot| |alternating| |mulmod| |floor| |extend| |figureUnits| + |mainForm| |curve?| |internal?| |setsubMatrix!| |mathieu12| + |rightTraceMatrix| |makeCrit| |inrootof| |distdfact| |delta| + |printInfo| |semiResultantReduitEuclidean| |preprocess| |returns| + |roughEqualIdeals?| |subCase?| |paren| |solveid| |row| |block| + |pascalTriangle| |imagI| |loopPoints| |weights| |viewDeltaYDefault| + |byteBuffer| |lazyPrem| |argumentList!| |factorSquareFree| |rational?| + |generalSqFr| |second| |content| |rischDEsys| |mainCoefficients| + |unitsColorDefault| |linearDependenceOverZ| |OMbindTCP| + |fillPascalTriangle| |halfExtendedResultant2| |anfactor| |listLoops| + |third| |subset?| |karatsubaDivide| |lfinfieldint| |getPickedPoints| + |removeConstantTerm| |exteriorDifferential| |heapSort| + |numberOfOperations| |groebnerFactorize| |linears| |objects| + |curveColor| |permutationRepresentation| |pointData| |laurentIfCan| + |whileLoop| |cCoth| |tanIfCan| |symmetric?| |empty?| |base| |nodeOf?| + |ratpart| |remainder| |conical| |expt| |acschIfCan| |summation| + |dualSignature| |rst| |makeVariable| |rationalFunction| |makeSin| + |OMputEndObject| |isobaric?| |removeZero| |categories| |bsolve| + |iicot| |palglimint0| |messagePrint| |yCoordinates| |resize| |lambda| + |innerEigenvectors| |numberOfFractionalTerms| |getConstant| + |external?| |generalizedContinuumHypothesisAssumed| + |transcendentalDecompose| |critT| |nthExpon| |bit?| |mirror| |iiacsch| + |monicModulo| |thenBranch| |adaptive?| |high| |vconcat| |shrinkable| + |digamma| |iisech| |e02ajf| |lflimitedint| |solveLinearlyOverQ| + |OMputEndApp| |semicolonSeparate| |monomials| |bounds| |lyndonIfCan| + |ridHack1| |constantKernel| |region| |matrixDimensions| |rotate!| + |octon| |tanNa| |aCubic| |OMsupportsSymbol?| |splitSquarefree| + |indiceSubResultant| |normal?| |root| |laplace| + |stoseInvertibleSetsqfreg| |escape| |minColIndex| |headAst| |vedf2vef| + |constant?| |quasiMonic?| |sts2stst| |goodnessOfFit| |concat| + |bandedHessian| |nextColeman| |fortranInteger| + |rewriteIdealWithHeadRemainder| |algebraicSort| |stack| |lieAlgebra?| + |toroidal| |nlde| |changeBase| |symFunc| |f04faf| |more?| + |totalDegree| |square?| |lprop| |parents| |eulerE| + |derivationCoordinates| |Beta| |wholeRagits| |rquo| |s19acf| |tRange| + |readUInt32!| |makeYoungTableau| |dmpToHdmp| |acscIfCan| |sncndn| + |lowerCase!| |pointLists| |e01sef| |cotIfCan| |upperCase| + |LyndonCoordinates| |complexForm| |realSolve| |previous| |replace| + |qroot| |orOperands| |dihedralGroup| |tan2cot| + |exprHasLogarithmicWeights| |thetaCoord| |setProperty!| |charthRoot| + |interpretString| |leftQuotient| |minimize| |transcendent?| |setPoly| + |elements| |cyclotomic| |mindeg| |bumptab| |removeCoshSq| |infix| + |inR?| |pomopo!| |OMclose| |alphanumeric| |univariate?| + |semiResultantEuclideannaif| |integers| |leftMinimalPolynomial| + |perspective| |operators| |sylvesterSequence| |extendedEuclidean| + |janko2| |coth2tanh| |cSech| |hasoln| |obj| |alphanumeric?| + |OMputObject| |mkIntegral| |hdmpToP| |light| |distribute| |singular?| + |direction| |nthExponent| |nthFactor| |insertRoot!| |cache| + |printHeader| |closedCurve?| |removeSinhSq| |axesColorDefault| + |integralMatrixAtInfinity| |represents| |bringDown| |imagj| + |abelianGroup| |logIfCan| |firstSubsetGray| |linear?| + |screenResolution3D| |setTex!| |upperCase?| |radicalOfLeftTraceForm| + |binaryTree| |deepExpand| |queue| |heap| |mkPrim| |makeCos| |point?| + |iilog| |interpolate| |makeprod| |genericLeftTraceForm| |OMgetEndBind| + |s19abf| |andOperands| |triangularSystems| |readLine!| + |measure2Result| |coerceS| |edf2df| |f02fjf| |bits| |moduloP| |ideal| + |semiIndiceSubResultantEuclidean| |brillhartTrials| |modularFactor| + |sec2cos| |Vectorise| |OMgetVariable| |mindegTerm| |approxSqrt| + |gcdcofactprim| |list| |padecf| |jacobi| |quote| |convergents| + |binomThmExpt| |removeRedundantFactorsInContents| |iitan| + |taylorIfCan| |iiatan| |squareTop| |mapExponents| |car| |pdct| + |cothIfCan| |SturmHabichtSequence| |fortranReal| |OMencodingBinary| + |e01baf| |less?| |derivative| |palgLODE0| |cdr| |iifact| |OMread| + |c06eaf| |rule| |shift| |deepestTail| |constantLeft| + |componentUpperBound| |rootsOf| |cond| |iicosh| |iiexp| |declare| + |setDifference| |clearTable!| |ceiling| |resetVariableOrder| |cCos| + |viewDefaults| |callForm?| |currentScope| |lastSubResultantEuclidean| + |push!| |top!| |setIntersection| |internalSubPolSet?| |domainOf| + |s17dcf| |resetAttributeButtons| |bipolarCylindrical| + |mainPrimitivePart| |polygamma| |antiCommutator| |dimensionsOf| + |setUnion| |scopes| |quadratic| |differentialVariables| |subNodeOf?| + |flexible?| |setMinPoints3D| |sinhcosh| |validExponential| + |changeMeasure| |pseudoRemainder| |apply| |algSplitSimple| |rdregime| + |capacity| |splitLinear| |localUnquote| |repSq| |continuedFraction| + |OMputFloat| |complexEigenvalues| |subPolSet?| |LiePoly| + |wordInStrongGenerators| |Aleph| |bivariateSLPEBR| |compiledFunction| + |closed?| |stoseInvertible?sqfreg| |round| |generalizedEigenvector| + |mainContent| |size| |LagrangeInterpolation| |diagonalProduct| + |sumOfSquares| |outputGeneral| |mapDown!| |void| |externalList| + |createPrimitiveNormalPoly| |hasTopPredicate?| |addPointLast| + |lighting| |generalizedContinuumHypothesisAssumed?| |getRef| + |setLength!| |s17dgf| |halfExtendedSubResultantGcd2| |mapMatrixIfCan| + |groebner?| |outputAsTex| |cyclic| |basicSet| |redPo| |surface| + |schwerpunkt| |position!| |properties| |setMaxPoints| |solveLinear| + |sumOfDivisors| |coordinates| |first| |explicitEntries?| |rightGcd| + |readUInt16!| |mathieu23| |tanSum| |rationalPower| |parts| + |degreeSubResultant| |translate| |removeDuplicates!| |kmax| + |internalSubQuasiComponent?| |rest| |f2df| + |genericRightMinimalPolynomial| |compactFraction| |implies?| |romberg| + |fullDisplay| |s17ahf| |substitute| |tube| |OMconnectTCP| + |insertMatch| |stopMusserTrials| |karatsuba| |linearlyDependent?| + |monomial?| |hexDigit?| |wordInGenerators| |removeDuplicates| + |palgextint| |say| |numberOfMonomials| |spherical| + |removeIrreducibleRedundantFactors| |makeSeries| |normFactors| + |realEigenvectors| |factorSquareFreePolynomial| |iidprod| |s20acf| + |mergeFactors| |ksec| |ignore?| |squareFreeLexTriangular| |lintgcd| + |parseString| |lex| |product| |traceMatrix| |hcrf| |satisfy?| + |leastMonomial| |match?| |setlast!| |leftGcd| + |internalLastSubResultant| |zeroDimPrime?| |simplify| |quadraticForm| + |linearAssociatedLog| |LyndonBasis| |ScanArabic| |double?| + |fortranCompilerName| |computeCycleEntry| |divisors| |list?| + |lagrange| |generic| |mainExpression| |findBinding| |viewport2D| + |useSingleFactorBound| |selectPolynomials| |monomialIntegrate| + |selectFiniteRoutines| |associatedEquations| |fractRagits| |composite| + |fprindINFO| |equality| |nthFractionalTerm| |rightNorm| |extendIfCan| + |categoryFrame| |bitLength| |mvar| |dimensions| + |leadingCoefficientRicDE| |structuralConstants| |script| |errorKind| + |sylvesterMatrix| |getGraph| |module| GF2FG |tubePoints| |ldf2vmf| + |exQuo| ** |s18dcf| |minPoints| |complexNumericIfCan| |debug| + |overlabel| |just| |putGraph| |subscriptedVariables| FG2F + |getProperty| |coerceListOfPairs| |SturmHabicht| |nil?| |pushup| D + |invmultisect| |rationalApproximation| |OMopenFile| |complexIntegrate| + |slash| |limitedIntegrate| |semiDegreeSubResultantEuclidean| + |dioSolve| |setScreenResolution| |shufflein| |tex| |rightAlternative?| + |ScanFloatIgnoreSpacesIfCan| |complete| EQ |FormatRoman| + |rewriteSetWithReduction| |dn| |cAcsch| |d02ejf| |keys| |repeating| + |e02dff| |double| |hclf| |characteristicPolynomial| |OMputError| + |resultantnaif| |terms| |d01gbf| |isPower| |lieAdmissible?| + |cyclicEqual?| |writeInt8!| |selectOrPolynomials| |differentiate| + |critMTonD1| |subResultantChain| |leftPower| |leftFactorIfCan| + |aromberg| |selectSumOfSquaresRoutines| |someBasis| |pr2dmp| + |fortranLiteralLine| |hessian| |rootPoly| |asinhIfCan| |viewpoint| + |supDimElseRittWu?| |prime?| |primitive?| |bernoulli| |padicFraction| + |definingInequation| |constant| |rk4f| |primPartElseUnitCanonical!| + |iteratedInitials| |baseRDEsys| |stoseInvertibleSetreg| |bipolar| + |leadingSupport| |constantToUnaryFunction| |e01bhf| + |incrementKthElement| |LiePolyIfCan| |finiteBound| |char| + |fixedDivisor| |rightMinimalPolynomial| |removeRedundantFactors| + |size?| |setEmpty!| |varList| |iibinom| |composites| |solid?| + |stiffnessAndStabilityFactor| |ricDsolve| |unrankImproperPartitions0| + |infieldint| |iCompose| |dequeue| |blue| |topFortranOutputStack| + |initials| |hasPredicate?| |eigenMatrix| |split!| |gcdPolynomial| + |mapUnivariateIfCan| |var1StepsDefault| |e04ucf| |randomR| + |knownInfBasis| |fixedPoint| |deepestInitial| |lazyPquo| |allRootsOf| + |print| |declare!| |divisor| |hyperelliptic| |/\\| |OMgetError| + |generalTwoFactor| |OMencodingUnknown| |level| |sin?| |makeViewport3D| + |f02aff| |univariatePolynomials| |resolve| |OMputInteger| |\\/| + |e01saf| |nonSingularModel| |color| |useSingleFactorBound?| |besselK| + |dec| |factorsOfDegree| |d02bbf| |groebgen| |bracket| |exptMod| + |upperCase!| |eigenvalues| |leftZero| |partialQuotients| |addBadValue| + |adaptive| |computeBasis| |linearAssociatedExp| |writeLine!| + |rightExactQuotient| |squareFreePrim| |edf2efi| |rootOf| |e02bef| + |aQuadratic| |wholeRadix| |showTheRoutinesTable| |stoseSquareFreePart| + |polygon?| |formula| |tableau| |kind| |maxrow| |nilFactor| + |zeroDimPrimary?| |increase| |degree| |setleft!| |readable?| + |insertTop!| |sinh2csch| |iiacos| |normDeriv2| |op| |c06fpf| |back| + |algDsolve| |mathieu22| |choosemon| |d01akf| |tanQ| |nullary| + |evaluateInverse| |diagonal| |countRealRootsMultiple| |pseudoDivide| + |accuracyIF| |getDatabase| |OMgetEndObject| |topPredicate| |cycleElt| + |normal01| |cSinh| |segment| |removeSinSq| |var1Steps| |nextItem| + |cyclicSubmodule| |Gamma| |Si| F |graphStates| |primintfldpoly| + |f02axf| |sup| |nrows| |leftRank| |sizeLess?| |finite?| + |createNormalElement| |printStatement| |extract!| |principal?| + |setAdaptive3D| |expandPower| |ncols| |mapdiv| |node| |iflist2Result| + |yCoord| |kovacic| |maxdeg| |outputSpacing| |element?| |quadraticNorm| + |e02bcf| |shanksDiscLogAlgorithm| |notOperand| |internalDecompose| + |binarySearchTree| |eigenvectors| |edf2fi| |readInt32!| |doubleDisc| + |insert| |htrigs| |plus| |center| |LyndonWordsList| |adaptive3D?| + |factorList| |palgLODE| |e01bef| |bindings| |factorGroebnerBasis| + |union| |rational| |outputAsScript| |tanh2coth| |scale| + |pushFortranOutputStack| |scanOneDimSubspaces| |collectQuasiMonic| + |redPol| |rspace| |mix| |hypergeometric0F1| |df2ef| |saturate| + |buildSyntax| |sign| |close| |eyeDistance| |popFortranOutputStack| + |makeFloatFunction| |numericalIntegration| |PollardSmallFactor| + |certainlySubVariety?| |sdf2lst| |oddInfiniteProduct| |rootNormalize| + |leftTraceMatrix| |leadingExponent| |changeWeightLevel| |ocf2ocdf| + |d02gbf| |orthonormalBasis| |qelt| |parametric?| + |ScanFloatIgnoreSpaces| |findConstructor| |complexNormalize| + |createNormalPoly| |sinIfCan| |deref| |display| |qsetelt| + |blankSeparate| |front| |fractionFreeGauss!| |fixPredicate| |localAbs| + |splitDenominator| |entry?| |radicalEigenvector| |unitVector| + |stFunc2| |doublyTransitive?| |swap!| |ptree| |OMencodingXML| |xRange| + |readLineIfCan!| |complement| |getOperands| |intensity| + |identitySquareMatrix| |lfextendedint| |prolateSpheroidal| + |complementaryBasis| |integerBound| |point| |rarrow| |headReduce| + |yRange| |over| |printTypes| |slex| |iicos| |varselect| |setEpilogue!| + |evenInfiniteProduct| |magnitude| |outputAsFortran| |lazy?| |e01bff| + |integral| |zRange| |mathieu11| |pop!| |principalIdeal| + |OMlistSymbols| |discriminantEuclidean| |sqfrFactor| |selectsecond| + |map!| |maxPoints3D| |printStats!| |radix| |recoverAfterFail| + |fortranDouble| |specialTrigs| |idealSimplify| |updatF| |critpOrder| + |input| |chiSquare| |ratDenom| |series| |principalAncestors| + |qsetelt!| |palgRDE| |diagonalMatrix| |getBadValues| + |bezoutDiscriminant| |iomode| |showAllElements| |sumSquares| |lepol| + |library| |left| |lowerCase?| |torsionIfCan| |denomRicDE| |tanhIfCan| + |tracePowMod| |s14aaf| |pastel| |rightQuotient| |algebraicOf| + |resultantEuclideannaif| |right| |rightUnits| |roman| |listexp| + |cyclicGroup| |s17aef| |f01mcf| |clearFortranOutputStack| |low| + |pushdterm| |is?| |sturmVariationsOf| |initiallyReduced?| |e01daf| + |outputForm| |retractable?| |partialNumerators| |equation| + |subResultantsChain| |solveRetract| |prinpolINFO| |c06gcf| |min| + |getMeasure| |aLinear| |multMonom| |viewSizeDefault| + |UpTriBddDenomInv| |genericRightTraceForm| |swapRows!| + |rightFactorIfCan| |d03eef| |set| |category| |signAround| |unitNormal| + |extractProperty| |acsch| |crushedSet| |listConjugateBases| |f02bjf| + |pmComplexintegrate| |integrate| |reduceBasisAtInfinity| |getCurve| + |alphabetic?| |domain| |cTanh| |makeMulti| |removeSquaresIfCan| + |entries| |denomLODE| |setFormula!| |augment| |cCsc| |points| + |package| |sort!| |interval| |padicallyExpand| + |linearlyDependentOverZ?| |iExquo| |connectTo| |rowEchLocal| |baseRDE| + |cExp| |overlap| |cn| |expr| |genericRightDiscriminant| + |OMsetEncoding| |writeBytes!| |reduceByQuasiMonic| |nonQsign| + |algebraic?| |primlimintfrac| |f02aaf| |open?| |selectODEIVPRoutines| + |mapmult| |index?| |OMencodingSGML| |basisOfLeftNucloid| + |homogeneous?| |showFortranOutputStack| |e04dgf| |fortran| + |optAttributes| |d02bhf| |f07fef| |log2| |viewWriteDefault| + |elementary| |f02aef| |fracPart| |BumInSepFFE| |linearAssociatedOrder| + |dom| |leftRecip| |null?| |rootDirectory| |var2Steps| |status| + |setColumn!| |internalIntegrate0| |euclideanGroebner| |expextendedint| + |ffactor| |variable| |ScanRoman| |transpose| + |rightCharacteristicPolynomial| |wreath| |reverseLex| |cross| |symbol| + |coshIfCan| |enumerate| |upDateBranches| |mergeDifference| |iterators| + |singRicDE| |listOfLists| |polyRicDE| |standardBasisOfCyclicSubmodule| + |e02baf| |member?| |rationalPoint?| |erf| |expression| + |semiSubResultantGcdEuclidean2| |fortranCharacter| |e02gaf| |f04atf| + |returnTypeOf| |regime| |stopTableInvSet!| |cAcosh| |bfEntry| + |repeatUntilLoop| |antiAssociative?| |integer| |diff| |show| + |putColorInfo| |atoms| |asinIfCan| |lifting1| |critB| + |resultantReduitEuclidean| |parent| |rightDivide| + |createRandomElement| |decimal| |weight| |moebiusMu| |lazyGintegrate| + |children| |complexRoots| |title| |singularAtInfinity?| |numberOfHues| + |ddFact| |euclideanSize| |close!| |dilog| |trace| |reverse| |plus!| + |e02ahf| |triangSolve| |rootSplit| |e02ddf| |smith| |ListOfTerms| + |cAcoth| |indicialEquation| |createPrimitiveElement| |sin| |rCoord| + |patternMatchTimes| |associative?| |palgRDE0| |rootBound| |OMputBind| + |leftAlternative?| |delay| |solid| |c06gbf| |next| |cos| |ef2edf| + |quotient| |truncate| |leftRankPolynomial| |eof?| |e| |OMgetBind| + |exponent| |cSec| |fglmIfCan| |host| |csch2sinh| |tan| |reduction| + |csubst| |label| |minrank| |s13acf| |asimpson| |e02daf| |sample| + |failed?| |denominator| |exprToGenUPS| |subresultantVector| |cot| + |basisOfRightNucloid| |d01amf| |setvalue!| |probablyZeroDim?| + |getOrder| |critM| |computeCycleLength| |true| |s01eaf| |po| + |HermiteIntegrate| |radicalEigenvectors| |sec| |debug3D| |lllp| + |quoByVar| |pile| |stoseInvertibleSet| |dictionary| |problemPoints| + |ip4Address| |iiacot| |halfExtendedResultant1| |csc| |arrayStack| + |ranges| |genericLeftTrace| |c02aff| |denominators| |Lazard2| |f01bsf| + |limit| |nullSpace| |distFact| |makeResult| |asin| |hash| |iicoth| + |makeop| |asecIfCan| |areEquivalent?| |decreasePrecision| |pol| + |removeCosSq| |innerint| |trigs| |changeNameToObjf| |lazyVariations| + |acos| |count| |recolor| |members| |perfectNthPower?| |prime| |conjug| + |viewport3D| |bezoutResultant| |symmetricRemainder| |imagJ| |exp1| + |middle| |atan| |rightRecip| |minimumDegree| |bubbleSort!| |sincos| + |doubleFloatFormat| |stoseInvertible?| |basisOfRightAnnihilator| + |gcdprim| |constructor| |distance| |relationsIdeal| |fTable| |acot| + |divisorCascade| |cyclePartition| |f04mbf| |asechIfCan| |empty| + |closeComponent| |e01bgf| |leaves| |multiplyCoefficients| |dimension| + |inf| |reverse!| |tower| |asec| |option| |harmonic| |fintegrate| + |changeVar| |pair?| |getSyntaxFormsFromFile| |findCycle| |infRittWu?| + |degreePartition| |showArrayValues| |red| |invertibleElseSplit?| + |acsc| |modTree| |powern| |directSum| |swapColumns!| |pleskenSplit| + |resetNew| |initiallyReduce| |optional?| |sturmSequence| + |explimitedint| |LowTriBddDenomInv| |sinh| |symmetricProduct| + |removeZeroes| |s17akf| |diagonal?| |ptFunc| |implies| |OMwrite| + |setClipValue| |mesh?| |imaginary| |nthFlag| |cosh| |cup| |read!| + |f07adf| |realEigenvalues| |maxRowIndex| |insertionSort!| + |oblateSpheroidal| |leftTrace| |cAsinh| |lazyPseudoRemainder| + |constantRight| |postfix| |tanh| |doubleResultant| |irreducible?| + |midpoints| |gethi| |numberOfImproperPartitions| |assign| + |roughSubIdeal?| |iisec| |increasePrecision| |polyRDE| |ReduceOrder| + |complexNumeric| |companionBlocks| |coth| |rightTrim| |binding| + |bottom!| |brillhartIrreducible?| |fortranLogical| + |sumOfKthPowerDivisors| |tubePointsDefault| |leadingIndex| |curryLeft| + |OMputSymbol| |or?| |readIfCan!| |s13adf| |SturmHabichtMultiple| + |sech| |leftTrim| |exponential| |subtractIfCan| |exportedOperators| + |orbit| |rroot| |realRoots| |basis| |mapUp!| |kernels| |continue| + |routines| |commonDenominator| |minset| |univariatePolynomial| |csch| + |rules| |unknown| |polCase| |selectMultiDimensionalRoutines| + |unprotectedRemoveRedundantFactors| |hue| |stosePrepareSubResAlgo| + |imagK| |identityMatrix| |rootProduct| |intcompBasis| |PDESolve| + |headRemainder| |asinh| |univariate| |test| |iiacsc| |trapezoidal| + |prepareDecompose| |realZeros| |dmpToP| |selectNonFiniteRoutines| + |has?| |binary| |orbits| |nextsousResultant2| |zero?| |acosh| + |predicate| |leftUnit| |atanIfCan| |squareFree| |partialFraction| + |exactQuotient!| |aQuartic| |basisOfCentroid| |multiEuclideanTree| + |partialDenominators| NOT |supRittWu?| |tubeRadiusDefault| |atanh| + |doubleRank| |stronglyReduce| |enterPointData| |shiftRight| |c06fuf| + |traverse| |rootRadius| |univcase| |prefix| |inconsistent?| OR + |computePowers| |d03edf| |acoth| |factor| |leviCivitaSymbol| + |frobenius| |leftNorm| |cAtan| |setnext!| |merge| |appendPoint| + |OMputVariable| AND |showRegion| |OMgetType| |localIntegralBasis| + |sqrt| |asech| |irreducibleRepresentation| |modulus| |normalizeIfCan| + |Ei| |fortranLinkerArgs| |tab| |dominantTerm| |safeFloor| |chebyshevU| + |integral?| |rangePascalTriangle| |real| |rotatez| |inRadical?| + |unit?| |quasiRegular| |pattern| |showAll?| |makeViewport2D| + |cschIfCan| |s18acf| |rename| |powmod| |qqq| |imag| |multiple| + |fixedPoints| |tubePlot| |minimumExponent| |meshFun2Var| + |karatsubaOnce| |leftDivide| |newSubProgram| |badValues| + |highCommonTerms| |errorInfo| |pade| |equiv| |directProduct| + |applyQuote| |s14abf| |nextPrimitiveNormalPoly| |f02abf| |increment| + |minIndex| |airyAi| |cot2tan| |createNormalPrimitivePoly| |log10| + |mapUnivariate| |positiveRemainder| |An| |crest| |gbasis| + |expandTrigProducts| |nextPrime| |scan| |testModulus| |rightMult| + |bitand| |mainDefiningPolynomial| |e04ycf| |wrregime| |ldf2lst| + |quickSort| |brace| |iisinh| |parameters| |rightRankPolynomial| + |twist| |message| |lazyResidueClass| |vertConcat| |rowEch| |s21baf| + |bitior| |lSpaceBasis| |OMgetEndAtp| |integralMatrix| |e04mbf| + |destruct| |ruleset| |contains?| |corrPoly| |coordinate| |powers| + |f04asf| |characteristicSerie| |extractBottom!| + |wordsForStrongGenerators| |univariatePolynomialsGcds| |writable?| + |getGoodPrime| |f07aef| |number?| |OMreadStr| |nthr| + |particularSolution| |cycleEntry| |inGroundField?| + |removeRedundantFactorsInPols| |real?| |restorePrecision| |f04adf| + |monicLeftDivide| |getButtonValue| |newReduc| |vectorise| |ODESolve| * + |listRepresentation| |algintegrate| |d01alf| |suchThat| + |divideExponents| |iitanh| |reduceLODE| |iprint| |shallowExpand| + |green| |meshPar1Var| |graphCurves| |mapExpon| |string?| |monomial| + |rdHack1| |outerProduct| |overset?| |clearDenominator| |d02raf| + |oneDimensionalArray| |moebius| |sizePascalTriangle| |setAdaptive| + |cosIfCan| |cons| |multivariate| |dot| |variationOfParameters| + |functionIsOscillatory| |rombergo| |outputBinaryFile| |cartesian| + |divideIfCan!| |s20adf| |extractIfCan| |linear| |normalize| |create| + |variables| |countable?| |tanAn| |elColumn2!| |cyclicParents| |bfKeys| + |lowerPolynomial| |roughUnitIdeal?| |chineseRemainder| + |dimensionOfIrreducibleRepresentation| |cAcos| + |lastSubResultantElseSplit| |polar| |delete!| |axes| |key?| |zerosOf| + |signature| |complexLimit| |acothIfCan| |OMputEndBVar| |polynomial| + |numberOfComposites| |typeList| |select!| |seriesSolve| |groebSolve| + |c05adf| |iroot| |rootSimp| |torsion?| |extension| |latex| Y + |splitConstant| |superHeight| |xCoord| |cycleSplit!| + |toseLastSubResultant| |zeroSquareMatrix| |c06fqf| + |cyclotomicFactorization| |makeEq| |ode2| |invertible?| |lllip| |hex| + |polyPart| |cfirst| |hasSolution?| |semiLastSubResultantEuclidean| + |coleman| |source| |taylor| |rank| |objectOf| |ramifiedAtInfinity?| + |nullity| |prevPrime| |arguments| |space| |neglist| |youngGroup| + |invmod| |nativeModuleExtension| |laurent| |makeGraphImage| + |trigs2explogs| |trapezoidalo| |lazyPremWithDefault| |identification| + |null| |shiftRoots| |OMopenString| |OMgetApp| |e02zaf| + |semiResultantEuclidean1| |arg1| |puiseux| |normalDeriv| + |selectOptimizationRoutines| |laguerreL| |and?| |leftLcm| |not| + |s17acf| |exponents| |presuper| |s21bdf| |root?| |arg2| + |constantOpIfCan| |startTableGcd!| |bumptab1| |coefficients| + |rubiksGroup| |and| |resultant| |eulerPhi| |reduced?| + |generateIrredPoly| |mpsode| |inv| |nextSubsetGray| |completeHensel| + |cap| |imagi| |or| |linearPolynomials| |integralRepresents| + |leftUnits| |physicalLength!| |duplicates| |redpps| |target| |ground?| + |conditions| |check| |eisensteinIrreducible?| |nextSublist| + |modularGcdPrimitive| |xor| |inHallBasis?| |mainKernel| |OMgetFloat| + UTS2UP |numFunEvals| |factorSFBRlcUnit| |ground| |match| + |systemCommand| |qinterval| |ellipticCylindrical| |primeFactor| + |maxPoints| |case| |conjugates| |safeCeiling| |setClosed| |write!| + |sorted?| |leadingMonomial| |lhs| |csc2sin| |semiResultantEuclidean2| + |RittWuCompare| |maxint| |Zero| |setfirst!| |UP2ifCan| |equiv?| + |nodes| |clipSurface| |leadingCoefficient| |rhs| |solve| |coth2trigh| + |One| |wholePart| |chvar| |frst| |infLex?| |simpson| + |OMUnknownSymbol?| |primitiveMonomials| |pdf2df| |normal| + |factorOfDegree| |connect| |conditionsForIdempotents| + |createGenericMatrix| |kroneckerDelta| |c06ecf| |mainVariables| + |tan2trig| |ravel| |reductum| |cCsch| |reducedQPowers| |rightTrace| + |primextintfrac| |iisin| |e04fdf| |bat1| |f02agf| |controlPanel| + |reshape| |rootOfIrreduciblePoly| |lift| |euclideanNormalForm| + |iFTable| |lyndon| |elem?| |name| |initializeGroupForWordProblem| + |sinhIfCan| |pushdown| |reduce| |solve1| |impliesOperands| |sechIfCan| + |mkAnswer| |aspFilename| |totalLex| |body| |numeric| |ParCondList| + |typeLists| |limitedint| |f01ref| |gramschmidt| |logical?| |elt| + |gcdcofact| |lifting| |removeRoughlyRedundantFactorsInContents| + |radical| |contours| |unvectorise| |zeroSetSplit| |d01ajf| |badNum| + |nil| |infinite| |arbitraryExponent| |approximate| |complex| + |shallowMutable| |canonical| |noetherian| |central| + |partiallyOrderedSet| |arbitraryPrecision| |canonicalsClosed| + |noZeroDivisors| |rightUnitary| |leftUnitary| |additiveValuation| + |unitsKnown| |canonicalUnitNormal| |multiplicativeValuation| + |finiteAggregate| |shallowlyMutable| |commutative|)
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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -4002 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -4002 (|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#) -4002 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -4002 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -4002 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -4002 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-859)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1019)) ((-612 (-169 (-379))) |has| |#1| (-1019)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-889 (-379))) |has| |#1| (-612 (-889 (-379)))) ((-612 (-889 (-564))) |has| |#1| (-612 (-889 (-564)))) ((-612 #1=(-1166 |#1|)) . 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T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4005 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4005 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4005 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4005 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4005 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-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| (-1046)) ((-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|) -4005 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4005 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4005 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4005 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4005 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4005 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4005 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4005 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4005 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) -((-2491 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-4213 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-2319 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2491 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4213 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2319 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-768) (-1209) (-1209)) (T -239)) -((-2319 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-4213 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-768)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-2491 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-768)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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(IF (|has| |t#2| (-723)) (PROGN (-6 (-723)) (-15 * ($ |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 -4408)) (-6 -4408) |%noBranch|) (IF (|has| |t#2| (-845)) (-6 (-845)) |%noBranch|) (IF (|has| |t#2| (-790)) (-6 (-790)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -4002 (|has| |#2| (-1046)) (-12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-614 |#2|) -4002 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-859)) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-859))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1046)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1046))) ((-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| (-1046)) ((-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|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1046))) ((-637 |#2|) |has| |#2| (-1046)) ((-714 |#2|) -4002 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-723) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-788) |has| |#2| (-845)) ((-789) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-790) |has| |#2| (-790)) ((-791) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-792) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-845) |has| |#2| (-845)) ((-847) -4002 (|has| |#2| (-845)) (|has| |#2| (-790))) ((-897 (-1170)) -12 (|has| |#2| (-897 (-1170))) (|has| |#2| (-1046))) ((-1035 #0#) -12 (|has| |#2| (-1035 (-407 (-564)))) (|has| |#2| (-1094))) ((-1035 (-564)) -12 (|has| |#2| (-1035 (-564))) (|has| |#2| (-1094))) ((-1035 |#2|) |has| |#2| (-1094)) ((-1052 |#2|) -4002 (|has| |#2| (-1046)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1052 $) |has| |#2| (-172)) ((-1046) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1053) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-172))) ((-1106) -4002 (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-723)) (|has| |#2| (-172))) ((-1094) -4002 (|has| |#2| (-1094)) (|has| |#2| (-1046)) (|has| |#2| (-845)) (|has| |#2| (-790)) (|has| |#2| (-723)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1046)) ((-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 $) -4005 (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1046))) ((-637 |#1|) |has| |#1| (-1046)) ((-714 #0#) |has| |#1| (-556)) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) |has| |#1| (-556)) ((-723) -4005 (|has| |#1| (-1106)) (|has| |#1| (-1046)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-847) . T) ((-897 (-1170)) |has| |#1| (-1046)) ((-883 (-379)) |has| |#1| (-883 (-379))) ((-883 (-564)) |has| |#1| (-883 (-564))) ((-881 |#1|) . 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T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-906))) -((-4276 (((-641 (-1076)) $) 34)) (-1363 (($ $) 31)) (-4252 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-1317 (($ $) 14)) (-1330 ((|#2| $) 12)) (-2897 ((|#3| $) 10))) -(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -4276 ((-641 (-1076)) |#1|)) (-15 -4252 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4252 (|#1| |#1| (-1076) |#3|)) (-15 -1363 (|#1| |#1|)) (-15 -4252 (|#1| |#2| |#3|)) (-15 -2897 (|#3| |#1|)) (-15 -1317 (|#1| |#1|)) (-15 -1330 (|#2| |#1|))) (-1237 |#2| |#3|) (-1046) (-789)) (T -1236)) -NIL -(-10 -8 (-15 -4276 ((-641 (-1076)) |#1|)) (-15 -4252 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4252 (|#1| |#1| (-1076) |#3|)) (-15 -1363 (|#1| |#1|)) (-15 -4252 (|#1| |#2| |#3|)) (-15 -2897 (|#3| |#1|)) (-15 -1317 (|#1| |#1|)) (-15 -1330 (|#2| |#1|))) -((-3695 (((-112) $ $) 7)) (-2827 (((-112) $) 16)) (-4276 (((-641 (-1076)) $) 77)) (-3822 (((-1170) $) 106)) (-2588 (((-2 (|:| -2336 $) (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-768)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -4002 (|has| |#1| (-1035 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1076)) . T) ((-614 |#1|) . T) ((-614 $) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-859)) . T) ((-172) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1076) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-889 (-379))) -12 (|has| (-1076) (-612 (-889 (-379)))) (|has| |#1| (-612 (-889 (-379))))) ((-612 (-889 (-564))) -12 (|has| (-1076) (-612 (-889 (-564)))) (|has| |#1| (-612 (-889 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -4002 (|has| |#1| (-906)) (|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) -4002 (|has| |#1| (-906)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -4002 (|has| |#1| (-906)) (|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) ((-714 #1#) |has| |#1| (-38 (-407 (-564)))) ((-714 |#1|) |has| |#1| (-172)) ((-714 $) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-723) . T) ((-847) |has| |#1| (-847)) ((-897 #2#) . T) ((-897 (-1170)) |has| |#1| (-897 (-1170))) ((-883 (-379)) -12 (|has| (-1076) (-883 (-379))) (|has| |#1| (-883 (-379)))) ((-883 (-564)) -12 (|has| (-1076) (-883 (-564))) (|has| |#1| (-883 (-564)))) ((-946 |#1| #0# #2#) . T) ((-906) |has| |#1| (-906)) ((-917) |has| |#1| (-363)) ((-1035 (-407 (-564))) |has| |#1| (-1035 (-407 (-564)))) ((-1035 (-564)) |has| |#1| (-1035 (-564))) ((-1035 #2#) . T) ((-1035 |#1|) . T) ((-1052 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1052 |#1|) . T) ((-1052 $) -4002 (|has| |#1| (-906)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1046) . T) ((-1053) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-906))) +((-4170 (((-641 (-1076)) $) 34)) (-4346 (($ $) 31)) (-4145 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-4311 (($ $) 14)) (-4323 ((|#2| $) 12)) (-3344 ((|#3| $) 10))) +(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -4170 ((-641 (-1076)) |#1|)) (-15 -4145 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4145 (|#1| |#1| (-1076) |#3|)) (-15 -4346 (|#1| |#1|)) (-15 -4145 (|#1| |#2| |#3|)) (-15 -3344 (|#3| |#1|)) (-15 -4311 (|#1| |#1|)) (-15 -4323 (|#2| |#1|))) (-1237 |#2| |#3|) (-1046) (-789)) (T -1236)) +NIL +(-10 -8 (-15 -4170 ((-641 (-1076)) |#1|)) (-15 -4145 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -4145 (|#1| |#1| (-1076) |#3|)) (-15 -4346 (|#1| |#1|)) (-15 -4145 (|#1| |#2| |#3|)) (-15 -3344 (|#3| |#1|)) (-15 -4311 (|#1| |#1|)) (-15 -4323 (|#2| |#1|))) +((-1754 (((-112) $ $) 7)) (-3976 (((-112) $) 16)) (-4170 (((-641 (-1076)) $) 77)) (-3657 (((-1170) $) 106)) (-3584 (((-2 (|:| -1950 $) (|:| 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NIL 3178286 NIL) (-1279 3172891 3175005 3175393 "XPBWPOLY" 3176146 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3168794 3171054 3171096 "XF" 3171717 NIL XF (NIL T) -9 NIL 3172117 NIL) (-1277 3168415 3168503 3168672 "XF-" 3168677 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3163741 3165004 3165059 "XFALG" 3167231 NIL XFALG (NIL T T) -9 NIL 3168020 NIL) (-1275 3162874 3162978 3163183 "XEXPPKG" 3163633 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3161010 3162724 3162820 "XDPOLY" 3162825 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159947 3160521 3160564 "XALG" 3160569 NIL XALG (NIL T) -9 NIL 3160680 NIL) (-1272 3153416 3157924 3158418 "WUTSET" 3159539 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3151699 3152468 3152791 "WP" 3153227 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3151328 3151521 3151591 "WHILEAST" 3151651 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3150827 3151045 3151139 "WHEREAST" 3151256 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3149713 3149911 3150206 "WFFINTBS" 3150624 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3147617 3148044 3148506 "WEIER" 3149285 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3146764 3147188 3147230 "VSPACE" 3147366 NIL VSPACE (NIL T) -9 NIL 3147440 NIL) (-1265 3146602 3146629 3146720 "VSPACE-" 3146725 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3146410 3146453 3146521 "VOID" 3146556 T VOID (NIL) -8 NIL NIL NIL) (-1263 3144546 3144905 3145311 "VIEW" 3146026 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140970 3141609 3142346 "VIEWDEF" 3143831 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3130301 3132518 3134691 "VIEW3D" 3138819 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3122579 3124212 3125791 "VIEW2D" 3128744 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117981 3122349 3122441 "VECTOR" 3122522 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3116558 3116817 3117135 "VECTOR2" 3117711 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3110085 3114342 3114385 "VECTCAT" 3115378 NIL VECTCAT (NIL T) -9 NIL 3115964 NIL) (-1256 3109099 3109353 3109743 "VECTCAT-" 3109748 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3108580 3108750 3108870 "VARIABLE" 3109014 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3108513 3108518 3108548 "UTYPE" 3108553 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3107343 3107497 3107759 "UTSODETL" 3108339 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3104783 3105243 3105767 "UTSODE" 3106884 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3096647 3102409 3102898 "UTS" 3104352 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3087882 3093214 3093257 "UTSCAT" 3094369 NIL UTSCAT (NIL T) -9 NIL 3095126 NIL) (-1249 3085230 3085952 3086941 "UTSCAT-" 3086946 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3084857 3084900 3085033 "UTS2" 3085181 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3079130 3081695 3081738 "URAGG" 3083808 NIL URAGG (NIL T) -9 NIL 3084531 NIL) (-1246 3076069 3076932 3078055 "URAGG-" 3078060 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3071785 3074683 3075155 "UPXSSING" 3075733 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3063878 3071032 3071305 "UPXS" 3071570 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056978 3063782 3063854 "UPXSCONS" 3063859 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3047215 3053973 3054035 "UPXSCCA" 3054609 NIL UPXSCCA (NIL T T) -9 NIL 3054842 NIL) (-1241 3046853 3046938 3047112 "UPXSCCA-" 3047117 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036943 3043474 3043517 "UPXSCAT" 3044165 NIL UPXSCAT (NIL T) -9 NIL 3044773 NIL) (-1239 3036373 3036452 3036631 "UPXS2" 3036858 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3035027 3035280 3035631 "UPSQFREE" 3036116 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3028807 3031829 3031884 "UPSCAT" 3033045 NIL UPSCAT (NIL T T) -9 NIL 3033819 NIL) (-1236 3028011 3028218 3028545 "UPSCAT-" 3028550 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3013853 3021859 3021902 "UPOLYC" 3024003 NIL UPOLYC (NIL T) -9 NIL 3025224 NIL) (-1234 3005181 3007607 3010754 "UPOLYC-" 3010759 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3004808 3004851 3004984 "UPOLYC2" 3005132 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2996374 3004491 3004620 "UP" 3004727 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2995713 2995820 2995984 "UPMP" 2996263 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2995266 2995347 2995486 "UPDIVP" 2995626 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2993834 2994083 2994399 "UPDECOMP" 2995015 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2993069 2993181 2993366 "UPCDEN" 2993718 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2992588 2992657 2992806 "UP2" 2992994 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2991103 2991792 2992069 "UNISEG" 2992346 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2990318 2990445 2990650 "UNISEG2" 2990946 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2989378 2989558 2989784 "UNIFACT" 2990134 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2973337 2988555 2988806 "ULS" 2989185 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2961363 2973241 2973313 "ULSCONS" 2973318 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943971 2955921 2955983 "ULSCCAT" 2956621 NIL ULSCCAT (NIL T T) -9 NIL 2956909 NIL) (-1220 2943021 2943266 2943654 "ULSCCAT-" 2943659 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2932888 2939333 2939376 "ULSCAT" 2940239 NIL ULSCAT (NIL T) -9 NIL 2940969 NIL) (-1218 2932318 2932397 2932576 "ULS2" 2932803 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2931435 2931918 2932025 "UINT8" 2932136 T UINT8 (NIL) -8 NIL NIL 2932221) (-1216 2930551 2931034 2931141 "UINT64" 2931252 T UINT64 (NIL) -8 NIL NIL 2931337) (-1215 2929667 2930150 2930257 "UINT32" 2930368 T UINT32 (NIL) -8 NIL NIL 2930453) (-1214 2928783 2929266 2929373 "UINT16" 2929484 T UINT16 (NIL) -8 NIL NIL 2929569) (-1213 2927178 2928109 2928139 "UFD" 2928351 T UFD (NIL) -9 NIL 2928465 NIL) (-1212 2926972 2927018 2927113 "UFD-" 2927118 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2926054 2926237 2926453 "UDVO" 2926778 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2923870 2924279 2924750 "UDPO" 2925618 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2923803 2923808 2923838 "TYPE" 2923843 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2923590 2923758 2923789 "TYPEAST" 2923794 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2922561 2922763 2923003 "TWOFACT" 2923384 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2921632 2921970 2922205 "TUPLE" 2922361 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2919323 2919842 2920381 "TUBETOOL" 2921115 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2918172 2918377 2918618 "TUBE" 2919116 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912928 2917144 2917427 "TS" 2917924 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2901595 2905687 2905784 "TSETCAT" 2911053 NIL TSETCAT (NIL T T T T) -9 NIL 2912584 NIL) (-1201 2896327 2897927 2899818 "TSETCAT-" 2899823 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2890589 2891436 2892378 "TRMANIP" 2895463 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2890030 2890093 2890256 "TRIMAT" 2890521 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2887826 2888063 2888427 "TRIGMNIP" 2889779 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2887346 2887459 2887489 "TRIGCAT" 2887702 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2887015 2887094 2887235 "TRIGCAT-" 2887240 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883908 2885873 2886154 "TREE" 2886769 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2883182 2883710 2883740 "TRANFUN" 2883775 T TRANFUN (NIL) -9 NIL 2883841 NIL) (-1193 2882461 2882652 2882932 "TRANFUN-" 2882937 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2882265 2882297 2882358 "TOPSP" 2882422 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2881613 2881728 2881882 "TOOLSIGN" 2882146 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2880274 2880790 2881029 "TEXTFILE" 2881396 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2878213 2878727 2879156 "TEX" 2879867 T TEX (NIL) -8 NIL NIL NIL) (-1188 2877994 2878025 2878097 "TEX1" 2878176 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2877642 2877705 2877795 "TEMUTL" 2877926 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2875796 2876076 2876401 "TBCMPPK" 2877365 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2867684 2873956 2874012 "TBAGG" 2874412 NIL TBAGG (NIL T T) -9 NIL 2874623 NIL) (-1184 2862754 2864242 2865996 "TBAGG-" 2866001 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862138 2862245 2862390 "TANEXP" 2862643 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2855639 2861995 2862088 "TABLE" 2862093 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855051 2855150 2855288 "TABLEAU" 2855536 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2849659 2850879 2852127 "TABLBUMP" 2853837 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848881 2849028 2849209 "SYSTEM" 2849500 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845340 2846039 2846822 "SYSSOLP" 2848132 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844374 2844852 2844971 "SYSNNI" 2845157 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845242) (-1176 2843671 2844103 2844182 "SYSINT" 2844242 NIL SYSINT (NIL NIL) -8 NIL NIL 2844287) (-1175 2840030 2840949 2841659 "SYNTAX" 2842983 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837188 2837790 2838422 "SYMTAB" 2839420 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2832437 2833339 2834322 "SYMS" 2836227 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2829699 2831895 2832125 "SYMPOLY" 2832242 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829216 2829291 2829414 "SYMFUNC" 2829611 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825262 2826528 2827341 "SYMBOL" 2828425 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818801 2820490 2822210 "SWITCH" 2823564 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812062 2817622 2817925 "SUTS" 2818556 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804155 2811309 2811582 "SUPXS" 2811847 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2795670 2803773 2803899 "SUP" 2804064 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794829 2794956 2795173 "SUPFRACF" 2795538 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2794450 2794509 2794622 "SUP2" 2794764 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792863 2793137 2793500 "SUMRF" 2794149 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792177 2792243 2792442 "SUMFS" 2792784 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776171 2791354 2791605 "SULS" 2791984 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775800 2775993 2776063 "SUCHTAST" 2776123 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775122 2775325 2775465 "SUCH" 2775708 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769016 2770028 2770987 "SUBSPACE" 2774210 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2768446 2768536 2768700 "SUBRESP" 2768904 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761811 2763111 2764422 "STTF" 2767182 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755984 2757104 2758251 "STTFNC" 2760711 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747295 2749166 2750960 "STTAYLOR" 2754225 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2740539 2747159 2747242 "STRTBL" 2747247 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735930 2740494 2740525 "STRING" 2740530 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730818 2735303 2735333 "STRICAT" 2735392 T STRICAT (NIL) -9 NIL 2735454 NIL) (-1150 2723621 2728437 2729048 "STREAM" 2730242 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723131 2723208 2723352 "STREAM3" 2723538 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722113 2722296 2722531 "STREAM2" 2722944 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721801 2721853 2721946 "STREAM1" 2722055 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720817 2720998 2721229 "STINPROD" 2721617 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720395 2720579 2720609 "STEP" 2720689 T STEP (NIL) -9 NIL 2720767 NIL) (-1144 2713938 2720294 2720371 "STBL" 2720376 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709112 2713159 2713202 "STAGG" 2713355 NIL STAGG (NIL T) -9 NIL 2713444 NIL) (-1142 2706814 2707416 2708288 "STAGG-" 2708293 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705009 2706584 2706676 "STACK" 2706757 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697732 2703150 2703606 "SREGSET" 2704639 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690157 2691526 2693039 "SRDCMPK" 2696338 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683124 2687597 2687627 "SRAGG" 2688930 T SRAGG (NIL) -9 NIL 2689538 NIL) (-1137 2682141 2682396 2682775 "SRAGG-" 2682780 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2676628 2681088 2681509 "SQMATRIX" 2681767 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670375 2673346 2674073 "SPLTREE" 2675973 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666365 2667031 2667677 "SPLNODE" 2669801 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665412 2665645 2665675 "SPFCAT" 2666119 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664149 2664359 2664623 "SPECOUT" 2665170 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655801 2657545 2657575 "SPADXPT" 2661967 T SPADXPT (NIL) -9 NIL 2664001 NIL) (-1130 2655562 2655602 2655671 "SPADPRSR" 2655754 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653744 2655517 2655548 "SPADAST" 2655553 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2645715 2647462 2647505 "SPACEC" 2651878 NIL SPACEC (NIL T) -9 NIL 2653694 NIL) (-1127 2643872 2645647 2645696 "SPACE3" 2645701 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2642624 2642795 2643086 "SORTPAK" 2643677 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2640674 2640977 2641396 "SOLVETRA" 2642288 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2639685 2639907 2640181 "SOLVESER" 2640447 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634896 2635786 2636788 "SOLVERAD" 2638737 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2630711 2631320 2632049 "SOLVEFOR" 2634263 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625008 2630060 2630157 "SNTSCAT" 2630162 NIL SNTSCAT (NIL T T T T) -9 NIL 2630232 NIL) (-1120 2619141 2623331 2623722 "SMTS" 2624698 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2613581 2619029 2619106 "SMP" 2619111 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611740 2612041 2612439 "SMITH" 2613278 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2604627 2608791 2608894 "SMATCAT" 2610245 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610795 NIL) (-1116 2601567 2602390 2603568 "SMATCAT-" 2603573 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599280 2600803 2600846 "SKAGG" 2601107 NIL SKAGG (NIL T) -9 NIL 2601242 NIL) (-1114 2595615 2598696 2598891 "SINT" 2599078 T SINT (NIL) -8 NIL NIL 2599251) (-1113 2595387 2595425 2595491 "SIMPAN" 2595571 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2594693 2594922 2595062 "SIG" 2595269 T SIG (NIL) -8 NIL NIL NIL) (-1111 2593531 2593752 2594027 "SIGNRF" 2594452 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592336 2592487 2592778 "SIGNEF" 2593360 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2591669 2591919 2592043 "SIGAST" 2592234 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589359 2589813 2590319 "SHP" 2591210 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583259 2589260 2589336 "SHDP" 2589341 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582858 2583024 2583054 "SGROUP" 2583147 T SGROUP (NIL) -9 NIL 2583209 NIL) (-1105 2582716 2582742 2582815 "SGROUP-" 2582820 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2579551 2580249 2580972 "SGCF" 2582015 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573946 2578998 2579095 "SFRTCAT" 2579100 NIL SFRTCAT (NIL T T T T) -9 NIL 2579139 NIL) (-1102 2567367 2568385 2569521 "SFRGCD" 2572929 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2560494 2561566 2562752 "SFQCMPK" 2566300 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560116 2560205 2560315 "SFORT" 2560435 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559261 2559956 2560077 "SEXOF" 2560082 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558395 2559142 2559210 "SEX" 2559215 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553934 2554623 2554718 "SEXCAT" 2557655 NIL SEXCAT (NIL T T T T T) -9 NIL 2558233 NIL) (-1096 2551114 2553868 2553916 "SET" 2553921 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549365 2549827 2550132 "SETMN" 2550855 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548971 2549097 2549127 "SETCAT" 2549244 T SETCAT (NIL) -9 NIL 2549329 NIL) (-1093 2548751 2548803 2548902 "SETCAT-" 2548907 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545138 2547212 2547255 "SETAGG" 2548125 NIL SETAGG (NIL T) -9 NIL 2548465 NIL) (-1091 2544596 2544712 2544949 "SETAGG-" 2544954 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544066 2544292 2544393 "SEQAST" 2544517 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543265 2543559 2543620 "SEGXCAT" 2543906 NIL SEGXCAT (NIL T T) -9 NIL 2544026 NIL) (-1088 2542319 2542931 2543113 "SEG" 2543118 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541298 2541512 2541555 "SEGCAT" 2542077 NIL SEGCAT (NIL T) -9 NIL 2542298 NIL) (-1086 2540347 2540677 2540877 "SEGBIND" 2541133 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539968 2540027 2540140 "SEGBIND2" 2540282 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2539568 2539769 2539846 "SEGAST" 2539913 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538787 2538913 2539117 "SEG2" 2539412 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538224 2538722 2538769 "SDVAR" 2538774 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2530506 2537994 2538124 "SDPOL" 2538129 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529099 2529365 2529684 "SCPKG" 2530221 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528259 2528432 2528625 "SCOPE" 2528928 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2527479 2527613 2527792 "SCACHE" 2528114 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527151 2527311 2527341 "SASTCAT" 2527346 T SASTCAT (NIL) -9 NIL 2527359 NIL) (-1076 2526665 2526986 2527062 "SAOS" 2527097 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526230 2526265 2526438 "SAERFFC" 2526624 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520196 2526127 2526207 "SAE" 2526212 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519789 2519824 2519983 "SAEFACT" 2520155 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518110 2518424 2518825 "RURPK" 2519455 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516746 2517025 2517337 "RULESET" 2517944 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513933 2514436 2514901 "RULE" 2516427 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2513572 2513727 2513810 "RULECOLD" 2513885 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513070 2513289 2513383 "RSTRCAST" 2513500 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2507918 2508713 2509633 "RSETGCD" 2512269 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497175 2502227 2502324 "RSETCAT" 2506443 NIL RSETCAT (NIL T T T T) -9 NIL 2507540 NIL) (-1065 2495102 2495641 2496465 "RSETCAT-" 2496470 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2487487 2488864 2490384 "RSDCMPK" 2493701 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2485492 2485933 2486007 "RRCC" 2487093 NIL RRCC (NIL T T) -9 NIL 2487437 NIL) (-1062 2484843 2485017 2485296 "RRCC-" 2485301 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484313 2484539 2484640 "RPTAST" 2484764 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458311 2467906 2467973 "RPOLCAT" 2478637 NIL RPOLCAT (NIL T T T) -9 NIL 2481796 NIL) (-1059 2449809 2452149 2455271 "RPOLCAT-" 2455276 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2440856 2448020 2448502 "ROUTINE" 2449349 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2437681 2440482 2440622 "ROMAN" 2440738 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2435952 2436541 2436801 "ROIRC" 2437486 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432337 2434588 2434618 "RNS" 2434922 T RNS (NIL) -9 NIL 2435195 NIL) (-1054 2430846 2431229 2431763 "RNS-" 2431838 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430295 2430677 2430707 "RNG" 2430712 T RNG (NIL) -9 NIL 2430733 NIL) (-1052 2429687 2430049 2430092 "RMODULE" 2430154 NIL RMODULE (NIL T) -9 NIL 2430196 NIL) (-1051 2428523 2428617 2428953 "RMCAT2" 2429588 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425400 2427869 2428166 "RMATRIX" 2428285 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418342 2420576 2420691 "RMATCAT" 2424050 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425032 NIL) (-1048 2417717 2417864 2418171 "RMATCAT-" 2418176 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417284 2417359 2417487 "RINTERP" 2417636 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416403 2416931 2416961 "RING" 2417017 T RING (NIL) -9 NIL 2417109 NIL) (-1045 2416195 2416239 2416336 "RING-" 2416341 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415036 2415273 2415531 "RIDIST" 2415959 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406352 2414504 2414710 "RGCHAIN" 2414884 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2405728 2406108 2406149 "RGBCSPC" 2406207 NIL RGBCSPC (NIL T) -9 NIL 2406259 NIL) (-1041 2404912 2405267 2405308 "RGBCMDL" 2405540 NIL RGBCMDL (NIL T) -9 NIL 2405654 NIL) (-1040 2401906 2402520 2403190 "RF" 2404276 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2401552 2401615 2401718 "RFFACTOR" 2401837 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401277 2401312 2401409 "RFFACT" 2401511 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399394 2399758 2400140 "RFDIST" 2400917 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2398847 2398939 2399102 "RETSOL" 2399296 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2398483 2398563 2398606 "RETRACT" 2398739 NIL RETRACT (NIL T) -9 NIL 2398826 NIL) (-1034 2398332 2398357 2398444 "RETRACT-" 2398449 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2397961 2398154 2398224 "RETAST" 2398284 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2390815 2397614 2397741 "RESULT" 2397856 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2389433 2390084 2390283 "RESRING" 2390718 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389069 2389118 2389216 "RESLATC" 2389370 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2388774 2388809 2388916 "REPSQ" 2389028 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386196 2386776 2387378 "REP" 2388194 T REP (NIL) -7 NIL NIL NIL) (-1027 2385893 2385928 2386039 "REPDB" 2386155 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2379793 2381182 2382405 "REP2" 2384705 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376170 2376851 2377659 "REP1" 2379020 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2368893 2374311 2374767 "REGSET" 2375800 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2367706 2368041 2368291 "REF" 2368678 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367083 2367186 2367353 "REDORDER" 2367590 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363078 2366296 2366523 "RECLOS" 2366911 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362130 2362311 2362526 "REALSOLV" 2362885 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2361976 2362017 2362047 "REAL" 2362052 T REAL (NIL) -9 NIL 2362087 NIL) (-1018 2358459 2359261 2360145 "REAL0Q" 2361141 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354060 2355048 2356109 "REAL0" 2357440 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2353558 2353777 2353871 "RDUCEAST" 2353988 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2352963 2353035 2353242 "RDIV" 2353480 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352031 2352205 2352418 "RDIST" 2352785 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2350628 2350915 2351287 "RDETRS" 2351739 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2348440 2348894 2349432 "RDETR" 2350170 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347051 2347329 2347733 "RDEEFS" 2348156 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2345546 2345852 2346284 "RDEEF" 2346739 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2339799 2342682 2342712 "RCFIELD" 2344007 T RCFIELD (NIL) -9 NIL 2344737 NIL) (-1008 2337863 2338367 2339063 "RCFIELD-" 2339138 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334179 2335964 2336007 "RCAGG" 2337091 NIL RCAGG (NIL T) -9 NIL 2337556 NIL) (-1006 2333807 2333901 2334064 "RCAGG-" 2334069 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333142 2333254 2333419 "RATRET" 2333691 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2332695 2332762 2332883 "RATFACT" 2333070 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332003 2332123 2332275 "RANDSRC" 2332565 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2331737 2331781 2331854 "RADUTIL" 2331952 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2324880 2330570 2330880 "RADIX" 2331461 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2316526 2324722 2324852 "RADFF" 2324857 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316178 2316253 2316281 "RADCAT" 2316438 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2315963 2316011 2316108 "RADCAT-" 2316113 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314114 2315738 2315827 "QUEUE" 2315907 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2310682 2314051 2314096 "QUAT" 2314101 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310320 2310363 2310490 "QUATCT2" 2310633 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304059 2307369 2307409 "QUATCAT" 2308189 NIL QUATCAT (NIL T) -9 NIL 2308955 NIL) (-993 2300203 2301240 2302627 "QUATCAT-" 2302721 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2297723 2299287 2299328 "QUAGG" 2299703 NIL QUAGG (NIL T) -9 NIL 2299878 NIL) (-991 2297355 2297548 2297616 "QQUTAST" 2297675 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296280 2296753 2296925 "QFORM" 2297227 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2287484 2292697 2292737 "QFCAT" 2293395 NIL QFCAT (NIL T) -9 NIL 2294396 NIL) (-988 2283056 2284257 2285848 "QFCAT-" 2285942 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2282694 2282737 2282864 "QFCAT2" 2283007 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282154 2282264 2282394 "QEQUAT" 2282584 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275301 2276373 2277557 "QCMPACK" 2281087 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2272877 2273298 2273726 "QALGSET" 2274956 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272122 2272296 2272528 "QALGSET2" 2272697 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2270812 2271036 2271353 "PWFFINTB" 2271895 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2268994 2269162 2269516 "PUSHVAR" 2270626 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2264912 2265966 2266007 "PTRANFN" 2267891 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263314 2263605 2263927 "PTPACK" 2264623 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2262946 2263003 2263112 "PTFUNC2" 2263251 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2257473 2261818 2261859 "PTCAT" 2262155 NIL PTCAT (NIL T) -9 NIL 2262308 NIL) (-976 2257131 2257166 2257290 "PSQFR" 2257432 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2255726 2256024 2256358 "PSEUDLIN" 2256829 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2242489 2244860 2247184 "PSETPK" 2253486 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2235533 2238247 2238343 "PSETCAT" 2241364 NIL PSETCAT (NIL T T T T) -9 NIL 2242178 NIL) (-972 2233369 2234003 2234824 "PSETCAT-" 2234829 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2232718 2232883 2232911 "PSCURVE" 2233179 T PSCURVE (NIL) -9 NIL 2233346 NIL) (-970 2229066 2230556 2230621 "PSCAT" 2231465 NIL PSCAT (NIL T T T) -9 NIL 2231705 NIL) (-969 2228129 2228345 2228745 "PSCAT-" 2228750 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2226861 2227494 2227699 "PRTITION" 2227944 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226363 2226582 2226674 "PRTDAST" 2226789 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2215453 2217667 2219855 "PRS" 2224225 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213311 2214803 2214843 "PRQAGG" 2215026 NIL PRQAGG (NIL T) -9 NIL 2215128 NIL) (-964 2212697 2212926 2212954 "PROPLOG" 2213139 T PROPLOG (NIL) -9 NIL 2213261 NIL) (-963 2209867 2210511 2210975 "PROPFRML" 2212265 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209327 2209437 2209567 "PROPERTY" 2209757 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203412 2207493 2208313 "PRODUCT" 2208553 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2200717 2202870 2203104 "PR" 2203223 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2200513 2200545 2200604 "PRINT" 2200678 T PRINT (NIL) -7 NIL NIL NIL) (-958 2199853 2199970 2200122 "PRIMES" 2200393 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2197918 2198319 2198785 "PRIMELT" 2199432 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2197647 2197696 2197724 "PRIMCAT" 2197848 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2193808 2197585 2197630 "PRIMARR" 2197635 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2192815 2192993 2193221 "PRIMARR2" 2193626 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2192458 2192514 2192625 "PREASSOC" 2192753 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2191933 2192066 2192094 "PPCURVE" 2192299 T PPCURVE (NIL) -9 NIL 2192435 NIL) (-951 2191555 2191728 2191811 "PORTNUM" 2191870 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2188914 2189313 2189905 "POLYROOT" 2191136 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2182851 2188518 2188678 "POLY" 2188787 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182234 2182292 2182526 "POLYLIFT" 2182787 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2178509 2178958 2179587 "POLYCATQ" 2181779 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165318 2170684 2170749 "POLYCAT" 2174263 NIL POLYCAT (NIL T T T) -9 NIL 2176191 NIL) (-945 2158767 2160629 2163013 "POLYCAT-" 2163018 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158354 2158422 2158542 "POLY2UP" 2158693 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2157986 2158043 2158152 "POLY2" 2158291 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2156671 2156910 2157186 "POLUTIL" 2157760 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155026 2155303 2155634 "POLTOPOL" 2156393 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2150543 2154962 2155008 "POINT" 2155013 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2148730 2149087 2149462 "PNTHEORY" 2150188 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147149 2147446 2147858 "PMTOOLS" 2148428 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2146742 2146820 2146937 "PMSYM" 2147065 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146252 2146321 2146495 "PMQFCAT" 2146667 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2145607 2145717 2145873 "PMPRED" 2146129 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145003 2145089 2145250 "PMPREDFS" 2145508 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2143646 2143854 2144239 "PMPLCAT" 2144765 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143178 2143257 2143409 "PMLSAGG" 2143561 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2142653 2142729 2142910 "PMKERNEL" 2143096 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142270 2142345 2142458 "PMINS" 2142572 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2141698 2141767 2141983 "PMFS" 2142195 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2140926 2141044 2141249 "PMDOWN" 2141575 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140089 2140248 2140430 "PMASS" 2140764 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139363 2139474 2139637 "PMASSFS" 2139975 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139018 2139086 2139180 "PLOTTOOL" 2139289 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2133625 2134829 2135977 "PLOT" 2137890 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129429 2130473 2131394 "PLOT3D" 2132724 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128341 2128518 2128753 "PLOT1" 2129233 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2103730 2108407 2113258 "PLEQN" 2123607 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103048 2103170 2103350 "PINTERP" 2103595 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2102741 2102788 2102891 "PINTERPA" 2102995 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2101989 2102510 2102597 "PI" 2102637 T PI (NIL) -8 NIL NIL 2102704) (-917 2100378 2101327 2101355 "PID" 2101537 T PID (NIL) -9 NIL 2101671 NIL) (-916 2100103 2100140 2100228 "PICOERCE" 2100335 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099423 2099562 2099738 "PGROEB" 2099959 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095010 2095824 2096729 "PGE" 2098538 T PGE (NIL) -7 NIL NIL NIL) (-913 2093133 2093380 2093746 "PGCD" 2094727 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2092471 2092574 2092735 "PFRPAC" 2093017 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089139 2091019 2091372 "PFR" 2092150 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2087528 2087772 2088097 "PFOTOOLS" 2088886 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086061 2086300 2086651 "PFOQ" 2087285 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2084534 2084746 2085109 "PFO" 2085845 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081114 2084423 2084492 "PF" 2084497 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2078540 2079785 2079813 "PFECAT" 2080398 T PFECAT (NIL) -9 NIL 2080782 NIL) (-905 2077985 2078139 2078353 "PFECAT-" 2078358 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2076588 2076840 2077141 "PFBRU" 2077734 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2074453 2074806 2075238 "PFBR" 2076239 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070362 2071829 2072505 "PERM" 2073810 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2065623 2066569 2067439 "PERMGRP" 2069525 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2063755 2064686 2064727 "PERMCAT" 2065173 NIL PERMCAT (NIL T) -9 NIL 2065478 NIL) (-899 2063408 2063449 2063573 "PERMAN" 2063708 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2060944 2063073 2063195 "PENDTREE" 2063319 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059029 2059771 2059812 "PDRING" 2060469 NIL PDRING (NIL T) -9 NIL 2060755 NIL) (-896 2058132 2058350 2058712 "PDRING-" 2058717 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055374 2056125 2056793 "PDEPROB" 2057484 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2052919 2053423 2053978 "PDEPACK" 2054839 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2051831 2052021 2052272 "PDECOMP" 2052718 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2049436 2050253 2050281 "PDECAT" 2051068 T PDECAT (NIL) -9 NIL 2051781 NIL) (-891 2049187 2049220 2049310 "PCOMP" 2049397 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047392 2047988 2048285 "PBWLB" 2048916 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2039892 2041465 2042803 "PATTERN" 2046075 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2039524 2039581 2039690 "PATTERN2" 2039829 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037281 2037669 2038126 "PATTERN1" 2039113 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2034676 2035230 2035711 "PATRES" 2036846 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034240 2034307 2034439 "PATRES2" 2034603 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032123 2032528 2032935 "PATMATCH" 2033907 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2031659 2031842 2031883 "PATMAB" 2031990 NIL PATMAB (NIL T) -9 NIL 2032073 NIL) (-882 2030204 2030513 2030771 "PATLRES" 2031464 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2029750 2029873 2029914 "PATAB" 2029919 NIL PATAB (NIL T) -9 NIL 2030091 NIL) (-880 2027231 2027763 2028336 "PARTPERM" 2029197 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2026852 2026915 2027017 "PARSURF" 2027162 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2026484 2026541 2026650 "PARSU2" 2026789 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026248 2026288 2026355 "PARSER" 2026437 T PARSER (NIL) -7 NIL NIL NIL) (-876 2025869 2025932 2026034 "PARSCURV" 2026179 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2025501 2025558 2025667 "PARSC2" 2025806 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025140 2025198 2025295 "PARPCURV" 2025437 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2024772 2024829 2024938 "PARPC2" 2025077 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024292 2024378 2024497 "PAN2EXPR" 2024673 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023096 2023413 2023641 "PALETTE" 2024084 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2021564 2022101 2022461 "PAIR" 2022782 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2015461 2020823 2021017 "PADICRC" 2021419 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2008717 2014807 2014991 "PADICRAT" 2015309 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007059 2008654 2008699 "PADIC" 2008704 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004261 2005799 2005839 "PADICCT" 2006420 NIL PADICCT (NIL NIL) -9 NIL 2006702 NIL) (-865 2003218 2003418 2003686 "PADEPAC" 2004048 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002430 2002563 2002769 "PADE" 2003080 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2000844 2001638 2001918 "OWP" 2002234 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000364 2000550 2000647 "OVERSET" 2000767 T OVERSET (NIL) -8 NIL NIL NIL) (-861 1999437 1999969 2000141 "OVAR" 2000232 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1998701 1998822 1998983 "OUT" 1999296 T OUT (NIL) -7 NIL NIL NIL) (-859 1987599 1989810 1992010 "OUTFORM" 1996521 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1986935 1987196 1987323 "OUTBFILE" 1987492 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986242 1986407 1986435 "OUTBCON" 1986753 T OUTBCON (NIL) -9 NIL 1986919 NIL) (-856 1985843 1985955 1986112 "OUTBCON-" 1986117 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985250 1985572 1985661 "OSI" 1985774 T OSI (NIL) -8 NIL NIL NIL) (-854 1984806 1985118 1985146 "OSGROUP" 1985151 T OSGROUP (NIL) -9 NIL 1985173 NIL) (-853 1983551 1983778 1984063 "ORTHPOL" 1984553 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981129 1983386 1983507 "OREUP" 1983512 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1978559 1980820 1980947 "ORESUP" 1981071 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976087 1976587 1977148 "OREPCTO" 1978048 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1969903 1972078 1972119 "OREPCAT" 1974467 NIL OREPCAT (NIL T) -9 NIL 1975571 NIL) (-848 1967050 1967832 1968890 "OREPCAT-" 1968895 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966227 1966499 1966527 "ORDSET" 1966836 T ORDSET (NIL) -9 NIL 1967000 NIL) (-846 1965746 1965868 1966061 "ORDSET-" 1966066 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964372 1965137 1965165 "ORDRING" 1965367 T ORDRING (NIL) -9 NIL 1965492 NIL) (-844 1964017 1964111 1964255 "ORDRING-" 1964260 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963423 1963860 1963888 "ORDMON" 1963893 T ORDMON (NIL) -9 NIL 1963914 NIL) (-842 1962585 1962732 1962927 "ORDFUNS" 1963272 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1961949 1962342 1962370 "ORDFIN" 1962435 T ORDFIN (NIL) -9 NIL 1962509 NIL) (-840 1958535 1960535 1960944 "ORDCOMP" 1961573 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1957801 1957928 1958114 "ORDCOMP2" 1958395 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954409 1955292 1956106 "OPTPROB" 1957007 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951211 1951850 1952554 "OPTPACK" 1953725 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1948924 1949664 1949692 "OPTCAT" 1950511 T OPTCAT (NIL) -9 NIL 1951161 NIL) (-835 1948367 1948601 1948706 "OPSIG" 1948839 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948135 1948174 1948240 "OPQUERY" 1948321 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945293 1946446 1946950 "OP" 1947664 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1944828 1944999 1945040 "OPERCAT" 1945175 NIL OPERCAT (NIL T) -9 NIL 1945243 NIL) (-831 1944674 1944701 1944787 "OPERCAT-" 1944792 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1941513 1943471 1943840 "ONECOMP" 1944338 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1940818 1940933 1941107 "ONECOMP2" 1941385 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940237 1940343 1940473 "OMSERVER" 1940708 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937125 1939677 1939717 "OMSAGG" 1939778 NIL OMSAGG (NIL T) -9 NIL 1939842 NIL) (-826 1935748 1936011 1936293 "OMPKG" 1936863 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935178 1935281 1935309 "OM" 1935608 T OM (NIL) -9 NIL NIL NIL) (-824 1933752 1934727 1934896 "OMLO" 1935059 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1932677 1932824 1933051 "OMEXPR" 1933578 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1931995 1932223 1932359 "OMERR" 1932561 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931173 1931416 1931576 "OMERRK" 1931855 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1930651 1930850 1930958 "OMENC" 1931085 T OMENC (NIL) -8 NIL NIL NIL) (-819 1924546 1925731 1926902 "OMDEV" 1929500 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1923615 1923786 1923980 "OMCONN" 1924372 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922228 1923178 1923206 "OINTDOM" 1923211 T OINTDOM (NIL) -9 NIL 1923232 NIL) (-816 1918034 1919218 1919934 "OFMONOID" 1921544 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1917472 1917971 1918016 "ODVAR" 1918021 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1914922 1917217 1917372 "ODR" 1917377 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907258 1914698 1914824 "ODPOL" 1914829 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901128 1907130 1907235 "ODP" 1907240 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1899894 1900109 1900384 "ODETOOLS" 1900902 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1896861 1897519 1898235 "ODESYS" 1899227 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1891743 1892651 1893676 "ODERTRIC" 1895936 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891169 1891251 1891445 "ODERED" 1891655 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888057 1888605 1889282 "ODERAT" 1890592 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885014 1885481 1886078 "ODEPRRIC" 1887586 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1882984 1883553 1884039 "ODEPROB" 1884548 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1879504 1879989 1880636 "ODEPRIM" 1882463 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1878753 1878855 1879115 "ODEPAL" 1879396 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1874915 1875706 1876570 "ODEPACK" 1877909 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1873948 1874055 1874284 "ODEINT" 1874804 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868049 1869474 1870921 "ODEIFTBL" 1872521 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863384 1864170 1865129 "ODEEF" 1867208 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1862719 1862808 1863038 "ODECONST" 1863289 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1860870 1861505 1861533 "ODECAT" 1862138 T ODECAT (NIL) -9 NIL 1862669 NIL) (-796 1857769 1860582 1860701 "OCT" 1860783 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857407 1857450 1857577 "OCTCT2" 1857720 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852173 1854581 1854621 "OC" 1855718 NIL OC (NIL T) -9 NIL 1856576 NIL) (-793 1849400 1850148 1851138 "OC-" 1851232 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1848778 1849220 1849248 "OCAMON" 1849253 T OCAMON (NIL) -9 NIL 1849274 NIL) (-791 1848335 1848650 1848678 "OASGP" 1848683 T OASGP (NIL) -9 NIL 1848703 NIL) (-790 1847622 1848085 1848113 "OAMONS" 1848153 T OAMONS (NIL) -9 NIL 1848196 NIL) (-789 1847062 1847469 1847497 "OAMON" 1847502 T OAMON (NIL) -9 NIL 1847522 NIL) (-788 1846366 1846858 1846886 "OAGROUP" 1846891 T OAGROUP (NIL) -9 NIL 1846911 NIL) (-787 1846056 1846106 1846194 "NUMTUBE" 1846310 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1839629 1841147 1842683 "NUMQUAD" 1844540 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835385 1836373 1837398 "NUMODE" 1838624 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1832766 1833620 1833648 "NUMINT" 1834571 T NUMINT (NIL) -9 NIL 1835335 NIL) (-783 1831714 1831911 1832129 "NUMFMT" 1832568 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818073 1821018 1823550 "NUMERIC" 1829221 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1812470 1817522 1817617 "NTSCAT" 1817622 NIL NTSCAT (NIL T T T T) -9 NIL 1817661 NIL) (-780 1811664 1811829 1812022 "NTPOLFN" 1812309 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1799496 1808489 1809301 "NSUP" 1810885 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799128 1799185 1799294 "NSUP2" 1799433 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789111 1798902 1799035 "NSMP" 1799040 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1787543 1787844 1788201 "NREP" 1788799 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786134 1786386 1786744 "NPCOEF" 1787286 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785200 1785315 1785531 "NORMRETR" 1786015 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783241 1783531 1783940 "NORMPK" 1784908 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1782926 1782954 1783078 "NORMMA" 1783207 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1782753 1782883 1782912 "NONE" 1782917 T NONE (NIL) -8 NIL NIL NIL) (-770 1782542 1782571 1782640 "NONE1" 1782717 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782025 1782087 1782273 "NODE1" 1782474 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780295 1781119 1781374 "NNI" 1781721 T NNI (NIL) -8 NIL NIL 1781956) (-767 1778715 1779028 1779392 "NLINSOL" 1779963 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1774983 1775951 1776850 "NIPROB" 1777836 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1773740 1773974 1774276 "NFINTBAS" 1774745 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1772914 1773390 1773431 "NETCLT" 1773603 NIL NETCLT (NIL T) -9 NIL 1773685 NIL) (-763 1771622 1771853 1772134 "NCODIV" 1772682 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771384 1771421 1771496 "NCNTFRAC" 1771579 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1769564 1769928 1770348 "NCEP" 1771009 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1768461 1769208 1769236 "NASRING" 1769346 T NASRING (NIL) -9 NIL 1769426 NIL) (-759 1768256 1768300 1768394 "NASRING-" 1768399 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767409 1767908 1767936 "NARNG" 1768053 T NARNG (NIL) -9 NIL 1768144 NIL) (-757 1767101 1767168 1767302 "NARNG-" 1767307 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1765980 1766187 1766422 "NAGSP" 1766886 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757252 1758936 1760609 "NAGS" 1764327 T NAGS (NIL) -7 NIL NIL NIL) (-754 1755800 1756108 1756439 "NAGF07" 1756941 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750338 1751629 1752936 "NAGF04" 1754513 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743306 1744920 1746553 "NAGF02" 1748725 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1738530 1739630 1740747 "NAGF01" 1742209 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732158 1733724 1735309 "NAGE04" 1736965 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723327 1725448 1727578 "NAGE02" 1730048 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719280 1720227 1721191 "NAGE01" 1722383 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717075 1717609 1718167 "NAGD03" 1718742 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1708825 1710753 1712707 "NAGD02" 1715141 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1702636 1704061 1705501 "NAGD01" 1707405 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1698845 1699667 1700504 "NAGC06" 1701819 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697310 1697642 1697998 "NAGC05" 1698509 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1696686 1696805 1696949 "NAGC02" 1697186 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1695746 1696303 1696343 "NAALG" 1696422 NIL NAALG (NIL T) -9 NIL 1696483 NIL) (-740 1695581 1695610 1695700 "NAALG-" 1695705 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1689531 1690639 1691826 "MULTSQFR" 1694477 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1688850 1688925 1689109 "MULTFACT" 1689443 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1681935 1685813 1685866 "MTSCAT" 1686936 NIL MTSCAT (NIL T T) -9 NIL 1687450 NIL) (-736 1681647 1681701 1681793 "MTHING" 1681875 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1681439 1681472 1681532 "MSYSCMD" 1681607 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1677548 1680194 1680514 "MSET" 1681152 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1674643 1677109 1677150 "MSETAGG" 1677155 NIL MSETAGG (NIL T) -9 NIL 1677189 NIL) (-732 1670511 1672022 1672767 "MRING" 1673943 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670077 1670144 1670275 "MRF2" 1670438 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1669695 1669730 1669874 "MRATFAC" 1670036 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667307 1667602 1668033 "MPRFF" 1669400 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661359 1667161 1667258 "MPOLY" 1667263 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1660849 1660884 1661092 "MPCPF" 1661318 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660363 1660406 1660590 "MPC3" 1660800 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1659558 1659639 1659860 "MPC2" 1660278 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657859 1658196 1658586 "MONOTOOL" 1659218 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657110 1657401 1657429 "MONOID" 1657648 T MONOID (NIL) -9 NIL 1657795 NIL) (-722 1656656 1656775 1656956 "MONOID-" 1656961 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1647507 1653423 1653482 "MONOGEN" 1654156 NIL MONOGEN (NIL T T) -9 NIL 1654612 NIL) (-720 1644725 1645460 1646460 "MONOGEN-" 1646579 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1643584 1644004 1644032 "MONADWU" 1644424 T MONADWU (NIL) -9 NIL 1644662 NIL) (-718 1642956 1643115 1643363 "MONADWU-" 1643368 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642341 1642559 1642587 "MONAD" 1642794 T MONAD (NIL) -9 NIL 1642906 NIL) (-716 1642026 1642104 1642236 "MONAD-" 1642241 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640342 1640939 1641218 "MOEBIUS" 1641779 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1639734 1640112 1640152 "MODULE" 1640157 NIL MODULE (NIL T) -9 NIL 1640183 NIL) (-713 1639302 1639398 1639588 "MODULE-" 1639593 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637009 1637666 1637993 "MODRING" 1639126 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1633980 1635114 1635635 "MODOP" 1636538 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1632595 1633047 1633324 "MODMONOM" 1633843 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622392 1630886 1631300 "MODMON" 1632232 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1619575 1621236 1621512 "MODFIELD" 1622267 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1618579 1618856 1619046 "MMLFORM" 1619405 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618105 1618148 1618327 "MMAP" 1618530 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616314 1617055 1617096 "MLO" 1617519 NIL MLO (NIL T) -9 NIL 1617761 NIL) (-704 1613680 1614196 1614798 "MLIFT" 1615795 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613071 1613155 1613309 "MKUCFUNC" 1613591 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1612670 1612740 1612863 "MKRECORD" 1612994 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1611717 1611879 1612107 "MKFUNC" 1612481 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611105 1611209 1611365 "MKFLCFN" 1611600 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1610648 1611015 1611074 "MKCHSET" 1611079 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1609925 1610027 1610212 "MKBCFUNC" 1610541 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1606659 1609479 1609615 "MINT" 1609809 T MINT (NIL) -8 NIL NIL NIL) (-696 1605471 1605714 1605991 "MHROWRED" 1606414 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1600878 1604006 1604411 "MFLOAT" 1605086 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600235 1600311 1600482 "MFINFACT" 1600790 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1596550 1597398 1598282 "MESH" 1599371 T MESH (NIL) -7 NIL NIL NIL) (-692 1594940 1595252 1595605 "MDDFACT" 1596237 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1591782 1594099 1594140 "MDAGG" 1594395 NIL MDAGG (NIL T) -9 NIL 1594538 NIL) (-690 1581552 1591075 1591282 "MCMPLX" 1591595 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1580693 1580839 1581039 "MCDEN" 1581401 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1578583 1578853 1579233 "MCALCFN" 1580423 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1577508 1577748 1577981 "MAYBE" 1578389 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575120 1575643 1576205 "MATSTOR" 1576979 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571125 1574492 1574740 "MATRIX" 1574905 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1566889 1567598 1568334 "MATLIN" 1570482 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557043 1560181 1560258 "MATCAT" 1565138 NIL MATCAT (NIL T T T) -9 NIL 1566555 NIL) (-682 1553399 1554420 1555776 "MATCAT-" 1555781 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1551993 1552146 1552479 "MATCAT2" 1553234 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550105 1550429 1550813 "MAPPKG3" 1551668 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549086 1549259 1549481 "MAPPKG2" 1549929 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1547585 1547869 1548196 "MAPPKG1" 1548792 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1546691 1546991 1547168 "MAPPAST" 1547428 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546302 1546360 1546483 "MAPHACK3" 1546627 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1545894 1545955 1546069 "MAPHACK2" 1546234 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545331 1545435 1545577 "MAPHACK1" 1545785 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1543437 1544031 1544335 "MAGMA" 1545059 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1542943 1543161 1543252 "MACROAST" 1543366 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539409 1541182 1541643 "M3D" 1542515 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1533563 1537778 1537819 "LZSTAGG" 1538601 NIL LZSTAGG (NIL T) -9 NIL 1538896 NIL) (-669 1529520 1530694 1532151 "LZSTAGG-" 1532156 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1526634 1527411 1527898 "LWORD" 1529065 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526237 1526438 1526513 "LSTAST" 1526579 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519430 1526008 1526142 "LSQM" 1526147 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1518654 1518793 1519021 "LSPP" 1519285 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1516466 1516767 1517223 "LSMP" 1518343 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513245 1513919 1514649 "LSMP1" 1515768 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507170 1512412 1512453 "LSAGG" 1512515 NIL LSAGG (NIL T) -9 NIL 1512593 NIL) (-661 1503865 1504789 1506002 "LSAGG-" 1506007 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1501491 1503009 1503258 "LPOLY" 1503660 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501073 1501158 1501281 "LPEFRAC" 1501400 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499420 1500167 1500420 "LO" 1500905 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499072 1499184 1499212 "LOGIC" 1499323 T LOGIC (NIL) -9 NIL 1499404 NIL) (-656 1498934 1498957 1499028 "LOGIC-" 1499033 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498127 1498267 1498460 "LODOOPS" 1498790 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1495577 1498043 1498109 "LODO" 1498114 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494115 1494350 1494703 "LODOF" 1495324 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1490463 1492868 1492909 "LODOCAT" 1493347 NIL LODOCAT (NIL T) -9 NIL 1493558 NIL) (-651 1490196 1490254 1490381 "LODOCAT-" 1490386 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1487543 1490037 1490155 "LODO2" 1490160 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485005 1487480 1487525 "LODO1" 1487530 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1483865 1484030 1484342 "LODEEF" 1484828 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479151 1481995 1482036 "LNAGG" 1482983 NIL LNAGG (NIL T) -9 NIL 1483427 NIL) (-646 1478298 1478512 1478854 "LNAGG-" 1478859 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1474461 1475223 1475862 "LMOPS" 1477713 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1473856 1474218 1474259 "LMODULE" 1474320 NIL LMODULE (NIL T) -9 NIL 1474362 NIL) (-643 1471102 1473501 1473624 "LMDICT" 1473766 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1470828 1471010 1471070 "LITERAL" 1471075 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464059 1469774 1470072 "LIST" 1470563 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1463584 1463658 1463797 "LIST3" 1463979 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1462591 1462769 1462997 "LIST2" 1463402 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1460725 1461037 1461436 "LIST2MAP" 1462238 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1459447 1460091 1460132 "LINEXP" 1460387 NIL LINEXP (NIL T) -9 NIL 1460536 NIL) (-636 1458094 1458354 1458651 "LINDEP" 1459199 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1454861 1455580 1456357 "LIMITRF" 1457349 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453136 1453432 1453848 "LIMITPS" 1454556 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1447591 1452647 1452875 "LIE" 1452957 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1446640 1447083 1447123 "LIECAT" 1447263 NIL LIECAT (NIL T) -9 NIL 1447414 NIL) (-631 1446481 1446508 1446596 "LIECAT-" 1446601 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439093 1445930 1446095 "LIB" 1446336 T LIB (NIL) -8 NIL NIL NIL) (-629 1434728 1435611 1436546 "LGROBP" 1438210 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1432594 1432868 1433230 "LF" 1434449 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1431434 1432126 1432154 "LFCAT" 1432361 T LFCAT (NIL) -9 NIL 1432500 NIL) (-626 1428336 1428966 1429654 "LEXTRIPK" 1430798 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425107 1425906 1426409 "LEXP" 1427916 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1424610 1424828 1424920 "LETAST" 1425035 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423008 1423321 1423722 "LEADCDET" 1424292 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422198 1422272 1422501 "LAZM3PK" 1422929 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417142 1420275 1420813 "LAUPOL" 1421710 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1416707 1416751 1416919 "LAPLACE" 1417092 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1414673 1415808 1416059 "LA" 1416540 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1413746 1414304 1414345 "LALG" 1414407 NIL LALG (NIL T) -9 NIL 1414466 NIL) (-617 1413460 1413519 1413655 "LALG-" 1413660 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413295 1413319 1413360 "KVTFROM" 1413422 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412095 1412512 1412741 "KTVLOGIC" 1413086 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1411930 1411954 1411995 "KRCFROM" 1412057 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1410834 1411021 1411320 "KOVACIC" 1411730 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1410669 1410693 1410734 "KONVERT" 1410796 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1410504 1410528 1410569 "KOERCE" 1410631 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408238 1408998 1409391 "KERNEL" 1410143 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1407740 1407821 1407951 "KERNEL2" 1408152 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1401591 1406279 1406333 "KDAGG" 1406710 NIL KDAGG (NIL T T) -9 NIL 1406916 NIL) (-607 1401120 1401244 1401449 "KDAGG-" 1401454 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394295 1400781 1400936 "KAFILE" 1400998 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1388750 1393806 1394034 "JORDAN" 1394116 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388156 1388399 1388520 "JOINAST" 1388649 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388002 1388061 1388116 "JAVACODE" 1388121 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384301 1386207 1386261 "IXAGG" 1387190 NIL IXAGG (NIL T T) -9 NIL 1387649 NIL) (-601 1383220 1383526 1383945 "IXAGG-" 1383950 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1378800 1383142 1383201 "IVECTOR" 1383206 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1377566 1377803 1378069 "ITUPLE" 1378567 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376002 1376179 1376485 "ITRIGMNP" 1377388 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1374747 1374951 1375234 "ITFUN3" 1375778 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374379 1374436 1374545 "ITFUN2" 1374684 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372208 1373241 1373540 "ITAYLOR" 1374113 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361180 1366345 1367508 "ISUPS" 1371078 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360284 1360424 1360660 "ISUMP" 1361027 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1355548 1360085 1360164 "ISTRING" 1360237 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355051 1355269 1355361 "ISAST" 1355476 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354261 1354342 1354558 "IRURPK" 1354965 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353197 1353398 1353638 "IRSN" 1354041 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351226 1351581 1352017 "IRRF2F" 1352835 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1350973 1351011 1351087 "IRREDFFX" 1351182 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1349588 1349847 1350146 "IROOT" 1350706 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346219 1347272 1347964 "IR" 1348928 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1343832 1344327 1344893 "IR2" 1345697 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1342904 1343017 1343238 "IR2F" 1343715 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1342695 1342729 1342789 "IPRNTPK" 1342864 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339302 1342584 1342653 "IPF" 1342658 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1337656 1339227 1339284 "IPADIC" 1339289 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1336995 1337216 1337346 "IP4ADDR" 1337546 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1336495 1336699 1336809 "IOMODE" 1336905 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1335568 1336092 1336219 "IOBFILE" 1336388 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335056 1335472 1335500 "IOBCON" 1335505 T IOBCON (NIL) -9 NIL 1335526 NIL) (-575 1334553 1334611 1334801 "INVLAPLA" 1334992 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324201 1326555 1328941 "INTTR" 1332217 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1320545 1321287 1322151 "INTTOOLS" 1323386 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320131 1320222 1320339 "INTSLPE" 1320448 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318112 1320054 1320113 "INTRVL" 1320118 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1315714 1316226 1316801 "INTRF" 1317597 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315125 1315222 1315364 "INTRET" 1315612 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313122 1313511 1313981 "INTRAT" 1314733 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310350 1310933 1311559 "INTPM" 1312607 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307052 1307652 1308397 "INTPAF" 1309736 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302231 1303193 1304244 "INTPACK" 1306021 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299135 1301960 1302087 "INT" 1302124 T INT (NIL) -8 NIL NIL NIL) (-563 1298387 1298539 1298747 "INTHERTR" 1298977 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1297826 1297906 1298094 "INTHERAL" 1298301 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1295672 1296115 1296572 "INTHEORY" 1297389 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1286980 1288601 1290380 "INTG0" 1294024 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1267553 1272343 1277153 "INTFTBL" 1282190 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1266802 1266940 1267113 "INTFACT" 1267412 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264187 1264633 1265197 "INTEF" 1266356 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1262646 1263359 1263387 "INTDOM" 1263688 T INTDOM (NIL) -9 NIL 1263895 NIL) (-555 1262015 1262189 1262431 "INTDOM-" 1262436 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1258502 1260399 1260453 "INTCAT" 1261252 NIL INTCAT (NIL T) -9 NIL 1261572 NIL) (-553 1257974 1258077 1258205 "INTBIT" 1258394 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1256645 1256799 1257113 "INTALG" 1257819 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256102 1256192 1256362 "INTAF" 1256549 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1249556 1255912 1256052 "INTABL" 1256057 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1248887 1249326 1249391 "INT8" 1249425 T INT8 (NIL) -8 NIL NIL 1249470) (-548 1248217 1248656 1248721 "INT64" 1248755 T INT64 (NIL) -8 NIL NIL 1248800) (-547 1247547 1247986 1248051 "INT32" 1248085 T INT32 (NIL) -8 NIL NIL 1248130) (-546 1246877 1247316 1247381 "INT16" 1247415 T INT16 (NIL) -8 NIL NIL 1247460) (-545 1241884 1244566 1244594 "INS" 1245528 T INS (NIL) -9 NIL 1246193 NIL) (-544 1239124 1239895 1240869 "INS-" 1240942 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237899 1238126 1238424 "INPSIGN" 1238877 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237017 1237134 1237331 "INPRODPF" 1237779 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1235911 1236028 1236265 "INPRODFF" 1236897 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1234911 1235063 1235323 "INNMFACT" 1235747 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234108 1234205 1234393 "INMODGCD" 1234810 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232616 1232861 1233185 "INFSP" 1233853 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231800 1231917 1232100 "INFPROD0" 1232496 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228682 1229865 1230380 "INFORM" 1231293 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228292 1228352 1228450 "INFORM1" 1228617 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227815 1227904 1228018 "INFINITY" 1228198 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1226991 1227535 1227636 "INETCLTS" 1227734 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225607 1225857 1226178 "INEP" 1226739 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224883 1225504 1225569 "INDE" 1225574 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224447 1224515 1224632 "INCRMAPS" 1224810 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223265 1223716 1223922 "INBFILE" 1224261 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218565 1219501 1220445 "INBFF" 1222353 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217473 1217742 1217770 "INBCON" 1218283 T INBCON (NIL) -9 NIL 1218549 NIL) (-526 1216725 1216948 1217224 "INBCON-" 1217229 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216231 1216449 1216540 "INAST" 1216654 T INAST (NIL) -8 NIL NIL NIL) (-524 1215685 1215910 1216016 "IMPTAST" 1216145 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212179 1215529 1215633 "IMATRIX" 1215638 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210891 1211014 1211329 "IMATQF" 1212035 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209111 1209338 1209675 "IMATLIN" 1210647 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203737 1209035 1209093 "ILIST" 1209098 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201690 1203597 1203710 "IIARRAY2" 1203715 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197115 1201601 1201665 "IFF" 1201670 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196489 1196732 1196848 "IFAST" 1197019 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191532 1195781 1195969 "IFARRAY" 1196346 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190739 1191436 1191509 "IFAMON" 1191514 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190323 1190388 1190442 "IEVALAB" 1190649 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1189998 1190066 1190226 "IEVALAB-" 1190231 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189656 1189912 1189975 "IDPO" 1189980 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1188933 1189545 1189620 "IDPOAMS" 1189625 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188267 1188822 1188897 "IDPOAM" 1188902 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187352 1187602 1187655 "IDPC" 1188068 NIL IDPC (NIL T T) -9 NIL 1188217 NIL) (-508 1186848 1187244 1187317 "IDPAM" 1187322 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186251 1186740 1186813 "IDPAG" 1186818 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186019 1186166 1186216 "IDENT" 1186221 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182274 1183122 1184017 "IDECOMP" 1185176 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175138 1176197 1177244 "IDEAL" 1181310 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174302 1174414 1174613 "ICDEN" 1175022 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173400 1173782 1173929 "ICARD" 1174175 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171460 1171773 1172178 "IBPTOOLS" 1173077 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167094 1171080 1171193 "IBITS" 1171379 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163817 1164393 1165088 "IBATOOL" 1166511 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161596 1162058 1162591 "IBACHIN" 1163352 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159473 1161442 1161545 "IARRAY2" 1161550 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155626 1159399 1159456 "IARRAY1" 1159461 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149610 1154038 1154519 "IAN" 1155165 T IAN (NIL) -8 NIL NIL NIL) (-494 1149121 1149178 1149351 "IALGFACT" 1149547 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148649 1148762 1148790 "HYPCAT" 1148997 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148187 1148304 1148490 "HYPCAT-" 1148495 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147809 1147982 1148065 "HOSTNAME" 1148124 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147654 1147691 1147732 "HOMOTOP" 1147737 NIL HOMOTOP (NIL T) -9 NIL 1147770 NIL) (-489 1144333 1145664 1145705 "HOAGG" 1146686 NIL HOAGG (NIL T) -9 NIL 1147365 NIL) (-488 1142927 1143326 1143852 "HOAGG-" 1143857 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136958 1142522 1142671 "HEXADEC" 1142798 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135706 1135928 1136191 "HEUGCD" 1136735 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134809 1135543 1135673 "HELLFDIV" 1135678 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133036 1134586 1134674 "HEAP" 1134753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132326 1132588 1132722 "HEADAST" 1132922 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126240 1132241 1132303 "HDP" 1132308 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119983 1125875 1126027 "HDMP" 1126141 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119307 1119447 1119611 "HB" 1119839 T HB (NIL) -7 NIL NIL NIL) (-479 1112804 1119153 1119257 "HASHTBL" 1119262 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112307 1112525 1112617 "HASAST" 1112732 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110112 1111929 1112111 "HACKPI" 1112145 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105807 1109965 1110078 "GTSET" 1110083 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099333 1105685 1105783 "GSTBL" 1105788 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091638 1098364 1098629 "GSERIES" 1099124 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090805 1091196 1091224 "GROUP" 1091427 T GROUP (NIL) -9 NIL 1091561 NIL) (-472 1090171 1090330 1090581 "GROUP-" 1090586 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088538 1088859 1089246 "GROEBSOL" 1089848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087478 1087740 1087791 "GRMOD" 1088320 NIL GRMOD (NIL T T) -9 NIL 1088488 NIL) (-469 1087246 1087282 1087410 "GRMOD-" 1087415 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082563 1083600 1084600 "GRIMAGE" 1086266 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081029 1081290 1081614 "GRDEF" 1082259 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080473 1080589 1080730 "GRAY" 1080908 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079686 1080066 1080117 "GRALG" 1080270 NIL GRALG (NIL T T) -9 NIL 1080363 NIL) (-464 1079347 1079420 1079583 "GRALG-" 1079588 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076151 1078932 1079110 "GPOLSET" 1079254 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075505 1075562 1075820 "GOSPER" 1076088 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071264 1071943 1072469 "GMODPOL" 1075204 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070269 1070453 1070691 "GHENSEL" 1071076 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064320 1065163 1066190 "GENUPS" 1069353 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064017 1064068 1064157 "GENUFACT" 1064263 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063429 1063506 1063671 "GENPGCD" 1063935 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062903 1062938 1063151 "GENMFACT" 1063388 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061469 1061726 1062033 "GENEEZ" 1062646 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055370 1061080 1061242 "GDMP" 1061392 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044739 1049141 1050247 "GCNAALG" 1054353 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043158 1043994 1044022 "GCDDOM" 1044277 T GCDDOM (NIL) -9 NIL 1044434 NIL) (-451 1042628 1042755 1042970 "GCDDOM-" 1042975 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041300 1041485 1041789 "GB" 1042407 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029916 1032246 1034638 "GBINTERN" 1038991 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027753 1028045 1028466 "GBF" 1029591 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026534 1026699 1026966 "GBEUCLID" 1027569 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025883 1026008 1026157 "GAUSSFAC" 1026405 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024250 1024552 1024866 "GALUTIL" 1025602 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022558 1022832 1023156 "GALPOLYU" 1023977 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019923 1020213 1020620 "GALFACTU" 1022255 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011729 1013228 1014836 "GALFACT" 1018355 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009117 1009775 1009803 "FVFUN" 1010959 T FVFUN (NIL) -9 NIL 1011679 NIL) (-440 1008383 1008565 1008593 "FVC" 1008884 T FVC (NIL) -9 NIL 1009067 NIL) (-439 1008053 1008208 1008276 "FUNDESC" 1008335 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007695 1007850 1007931 "FUNCTION" 1008005 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005466 1006017 1006483 "FT" 1007249 T FT (NIL) -8 NIL NIL NIL) (-436 1004284 1004767 1004970 "FTEM" 1005283 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002540 1002829 1003233 "FSUPFACT" 1003975 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000937 1001226 1001558 "FST" 1002228 T FST (NIL) -8 NIL NIL NIL) (-433 1000108 1000214 1000409 "FSRED" 1000819 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998786 999042 999396 "FSPRMELT" 999823 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995871 996309 996808 "FSPECF" 998349 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977925 986374 986414 "FS" 990262 NIL FS (NIL T) -9 NIL 992551 NIL) (-429 966572 969565 973621 "FS-" 973918 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966086 966140 966317 "FSINT" 966513 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964405 965079 965382 "FSERIES" 965865 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963419 963535 963766 "FSCINT" 964285 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959653 962363 962404 "FSAGG" 962774 NIL FSAGG (NIL T) -9 NIL 963033 NIL) (-424 957415 958016 958812 "FSAGG-" 958907 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956457 956600 956827 "FSAGG2" 957268 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954111 954391 954945 "FS2UPS" 956175 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953693 953736 953891 "FS2" 954062 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952550 952721 953030 "FS2EXPXP" 953518 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951976 952091 952243 "FRUTIL" 952430 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943416 947471 948829 "FR" 950650 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938491 941134 941174 "FRNAALG" 942570 NIL FRNAALG (NIL T) -9 NIL 943177 NIL) (-416 934164 935240 936515 "FRNAALG-" 937265 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933802 933845 933972 "FRNAAF2" 934115 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932209 932656 932951 "FRMOD" 933614 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929987 930592 930909 "FRIDEAL" 932000 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929182 929269 929558 "FRIDEAL2" 929894 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928315 928729 928770 "FRETRCT" 928775 NIL FRETRCT (NIL T) -9 NIL 928951 NIL) (-410 927427 927658 928009 "FRETRCT-" 928014 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924631 925815 925874 "FRAMALG" 926756 NIL FRAMALG (NIL T T) -9 NIL 927048 NIL) (-408 922765 923220 923850 "FRAMALG-" 924073 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916713 922240 922516 "FRAC" 922521 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916349 916406 916513 "FRAC2" 916650 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915985 916042 916149 "FR2" 916286 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910650 913510 913538 "FPS" 914657 T FPS (NIL) -9 NIL 915214 NIL) (-403 910099 910208 910372 "FPS-" 910518 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907545 909188 909216 "FPC" 909441 T FPC (NIL) -9 NIL 909583 NIL) (-401 907338 907378 907475 "FPC-" 907480 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906216 906826 906867 "FPATMAB" 906872 NIL FPATMAB (NIL T) -9 NIL 907024 NIL) (-399 903916 904392 904818 "FPARFRAC" 905853 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899309 899808 900490 "FORTRAN" 903348 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897025 897525 898064 "FORT" 898790 T FORT (NIL) -7 NIL NIL NIL) (-396 894701 895263 895291 "FORTFN" 896351 T FORTFN (NIL) -9 NIL 896975 NIL) (-395 894465 894515 894543 "FORTCAT" 894602 T FORTCAT (NIL) -9 NIL 894664 NIL) (-394 892598 893081 893471 "FORMULA" 894095 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892386 892416 892485 "FORMULA1" 892562 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891909 891961 892134 "FORDER" 892328 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891005 891169 891362 "FOP" 891736 T FOP (NIL) -7 NIL NIL NIL) (-390 889613 890285 890459 "FNLA" 890887 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888368 888757 888785 "FNCAT" 889245 T FNCAT (NIL) -9 NIL 889505 NIL) (-388 887934 888327 888355 "FNAME" 888360 T FNAME (NIL) -8 NIL NIL NIL) (-387 886589 887526 887554 "FMTC" 887559 T FMTC (NIL) -9 NIL 887595 NIL) (-386 882949 884112 884741 "FMONOID" 885993 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882168 882691 882840 "FM" 882845 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879592 880238 880266 "FMFUN" 881410 T FMFUN (NIL) -9 NIL 882118 NIL) (-383 878861 879042 879070 "FMC" 879360 T FMC (NIL) -9 NIL 879542 NIL) (-382 876055 876889 876943 "FMCAT" 878138 NIL FMCAT (NIL T T) -9 NIL 878633 NIL) (-381 874948 875821 875921 "FM1" 876000 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872722 873138 873632 "FLOATRP" 874499 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866323 870451 871072 "FLOAT" 872121 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863761 864261 864839 "FLOATCP" 865790 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862562 863374 863415 "FLINEXP" 863420 NIL FLINEXP (NIL T) -9 NIL 863513 NIL) (-376 861716 861951 862279 "FLINEXP-" 862284 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860792 860936 861160 "FLASORT" 861568 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858009 858851 858903 "FLALG" 860130 NIL FLALG (NIL T T) -9 NIL 860597 NIL) (-373 851793 855495 855536 "FLAGG" 856798 NIL FLAGG (NIL T) -9 NIL 857450 NIL) (-372 850519 850858 851348 "FLAGG-" 851353 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849561 849704 849931 "FLAGG2" 850372 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846528 847510 847569 "FINRALG" 848697 NIL FINRALG (NIL T T) -9 NIL 849205 NIL) (-369 845688 845917 846256 "FINRALG-" 846261 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845094 845307 845335 "FINITE" 845531 T FINITE (NIL) -9 NIL 845638 NIL) (-367 837552 839713 839753 "FINAALG" 843420 NIL FINAALG (NIL T) -9 NIL 844873 NIL) (-366 832884 833934 835078 "FINAALG-" 836457 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832279 832639 832742 "FILE" 832814 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830963 831275 831329 "FILECAT" 832013 NIL FILECAT (NIL T T) -9 NIL 832229 NIL) (-363 828823 830325 830353 "FIELD" 830393 T FIELD (NIL) -9 NIL 830473 NIL) (-362 827443 827828 828339 "FIELD-" 828344 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825320 826078 826425 "FGROUP" 827129 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824410 824574 824794 "FGLMICPK" 825152 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820269 824335 824392 "FFX" 824397 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819870 819931 820066 "FFSLPE" 820202 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815859 816642 817438 "FFPOLY" 819106 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815363 815399 815608 "FFPOLY2" 815817 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811233 815282 815345 "FFP" 815350 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806658 811144 811208 "FF" 811213 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801811 806001 806191 "FFNBX" 806512 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796767 800946 801204 "FFNBP" 801665 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791427 796051 796262 "FFNB" 796600 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790259 790457 790772 "FFINTBAS" 791224 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786479 788666 788694 "FFIELDC" 789314 T FFIELDC (NIL) -9 NIL 789690 NIL) (-348 785141 785512 786009 "FFIELDC-" 786014 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784710 784756 784880 "FFHOM" 785083 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782405 782892 783409 "FFF" 784225 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778050 782147 782248 "FFCGX" 782348 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773698 777782 777889 "FFCGP" 777993 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768908 773425 773533 "FFCG" 773634 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750733 759779 759865 "FFCAT" 765030 NIL FFCAT (NIL T T T) -9 NIL 766481 NIL) (-341 745931 746978 748292 "FFCAT-" 749522 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745342 745385 745620 "FFCAT2" 745882 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734539 738314 739534 "FEXPR" 744194 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733539 733974 734015 "FEVALAB" 734099 NIL FEVALAB (NIL T) -9 NIL 734360 NIL) (-337 732698 732908 733246 "FEVALAB-" 733251 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731291 732081 732284 "FDIV" 732597 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728357 729072 729187 "FDIVCAT" 730755 NIL FDIVCAT (NIL T T T T) -9 NIL 731192 NIL) (-334 728119 728146 728316 "FDIVCAT-" 728321 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727339 727426 727703 "FDIV2" 728026 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726025 726284 726573 "FCPAK1" 727070 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725151 725525 725666 "FCOMP" 725916 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708880 712301 715839 "FC" 721633 T FC (NIL) -8 NIL NIL NIL) (-329 701451 705444 705484 "FAXF" 707286 NIL FAXF (NIL T) -9 NIL 707978 NIL) (-328 698727 699385 700210 "FAXF-" 700675 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693827 698103 698279 "FARRAY" 698584 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689072 691112 691165 "FAMR" 692188 NIL FAMR (NIL T T) -9 NIL 692648 NIL) (-325 687962 688264 688699 "FAMR-" 688704 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687158 687884 687937 "FAMONOID" 687942 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684970 685654 685707 "FAMONC" 686648 NIL FAMONC (NIL T T) -9 NIL 687034 NIL) (-322 683662 684724 684861 "FAGROUP" 684866 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681457 681776 682179 "FACUTIL" 683343 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680556 680741 680963 "FACTFUNC" 681267 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672953 679807 680019 "EXPUPXS" 680412 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670436 670976 671562 "EXPRTUBE" 672387 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666630 667222 667959 "EXPRODE" 669775 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651996 665285 665713 "EXPR" 666234 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646403 646990 647803 "EXPR2UPS" 651294 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646039 646096 646203 "EXPR2" 646340 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637436 645171 645468 "EXPEXPAN" 645876 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637263 637393 637422 "EXIT" 637427 T EXIT (NIL) -8 NIL NIL NIL) (-311 636770 636987 637078 "EXITAST" 637192 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636397 636459 636572 "EVALCYC" 636702 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635938 636056 636097 "EVALAB" 636267 NIL EVALAB (NIL T) -9 NIL 636371 NIL) (-308 635419 635541 635762 "EVALAB-" 635767 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632879 634155 634183 "EUCDOM" 634738 T EUCDOM (NIL) -9 NIL 635088 NIL) (-306 631284 631726 632316 "EUCDOM-" 632321 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618822 621582 624332 "ESTOOLS" 628554 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618454 618511 618620 "ESTOOLS2" 618759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618205 618247 618327 "ESTOOLS1" 618406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612110 613838 613866 "ES" 616634 T ES (NIL) -9 NIL 618043 NIL) (-301 607057 608344 610161 "ES-" 610325 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603431 604192 604972 "ESCONT" 606297 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603176 603208 603290 "ESCONT1" 603393 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602851 602901 603001 "ES2" 603120 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602481 602539 602648 "ES1" 602787 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601697 601826 602002 "ERROR" 602325 T ERROR (NIL) -7 NIL NIL NIL) (-295 595200 601556 601647 "EQTBL" 601652 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587751 590514 591963 "EQ" 593784 NIL -3307 (NIL T) -8 NIL NIL NIL) (-293 587383 587440 587549 "EQ2" 587688 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582672 583721 584814 "EP" 586322 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581250 581547 581859 "ENV" 582380 T ENV (NIL) -8 NIL NIL NIL) (-290 580421 580949 580977 "ENTIRER" 580982 T ENTIRER (NIL) -9 NIL 581028 NIL) (-289 576915 578376 578746 "EMR" 580220 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576059 576244 576298 "ELTAGG" 576678 NIL ELTAGG (NIL T T) -9 NIL 576889 NIL) (-287 575778 575840 575981 "ELTAGG-" 575986 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575567 575596 575650 "ELTAB" 575734 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574693 574839 575038 "ELFUTS" 575418 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574435 574491 574519 "ELEMFUN" 574624 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574305 574326 574394 "ELEMFUN-" 574399 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569196 572405 572446 "ELAGG" 573386 NIL ELAGG (NIL T) -9 NIL 573849 NIL) (-281 567481 567915 568578 "ELAGG-" 568583 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566146 566424 566717 "ELABEXPR" 567208 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559010 560813 561640 "EFUPXS" 565422 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552460 554261 555071 "EFULS" 558286 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549882 550240 550719 "EFSTRUC" 552092 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538953 540519 542079 "EF" 548397 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538054 538438 538587 "EAB" 538824 T EAB (NIL) -8 NIL NIL NIL) (-274 537263 538013 538041 "E04UCFA" 538046 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536472 537222 537250 "E04NAFA" 537255 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535681 536431 536459 "E04MBFA" 536464 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534890 535640 535668 "E04JAFA" 535673 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534101 534849 534877 "E04GCFA" 534882 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533312 534060 534088 "E04FDFA" 534093 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532521 533271 533299 "E04DGFA" 533304 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526694 528046 529410 "E04AGNT" 531177 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525400 525880 525920 "DVARCAT" 526395 NIL DVARCAT (NIL T) -9 NIL 526594 NIL) (-265 524604 524816 525130 "DVARCAT-" 525135 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517496 524403 524532 "DSMP" 524537 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512305 513441 514509 "DROPT" 516448 T DROPT (NIL) -8 NIL NIL NIL) (-262 511970 512029 512127 "DROPT1" 512240 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507085 508211 509348 "DROPT0" 510853 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505430 505755 506141 "DRAWPT" 506719 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500017 500940 502019 "DRAW" 504404 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499650 499703 499821 "DRAWHACK" 499958 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498381 498650 498941 "DRAWCX" 499379 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497896 497965 498116 "DRAWCURV" 498307 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488364 490326 492441 "DRAWCFUN" 495801 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485177 487059 487100 "DQAGG" 487729 NIL DQAGG (NIL T) -9 NIL 488002 NIL) (-253 473448 480155 480238 "DPOLCAT" 482090 NIL DPOLCAT (NIL T T T T) -9 NIL 482635 NIL) (-252 468284 469633 471591 "DPOLCAT-" 471596 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461433 468145 468243 "DPMO" 468248 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454485 461213 461380 "DPMM" 461385 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454117 454404 454452 "DOMCTOR" 454457 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453412 453639 453776 "DOMAIN" 454000 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447155 453047 453199 "DMP" 453313 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446755 446811 446955 "DLP" 447093 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440625 446082 446272 "DLIST" 446597 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437469 439478 439519 "DLAGG" 440069 NIL DLAGG (NIL T) -9 NIL 440299 NIL) (-243 436274 436912 436940 "DIVRING" 437032 T DIVRING (NIL) -9 NIL 437115 NIL) (-242 435511 435701 436001 "DIVRING-" 436006 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433613 433970 434376 "DISPLAY" 435125 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427549 433527 433590 "DIRPROD" 433595 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426397 426600 426865 "DIRPROD2" 427342 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415654 421612 421665 "DIRPCAT" 422075 NIL DIRPCAT (NIL NIL T) -9 NIL 422915 NIL) (-237 412980 413622 414503 "DIRPCAT-" 414840 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412267 412427 412613 "DIOSP" 412814 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408969 411179 411220 "DIOPS" 411654 NIL DIOPS (NIL T) -9 NIL 411883 NIL) (-234 408518 408632 408823 "DIOPS-" 408828 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407402 408004 408032 "DIFRING" 408219 T DIFRING (NIL) -9 NIL 408329 NIL) (-232 407048 407125 407277 "DIFRING-" 407282 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404845 406091 406132 "DIFEXT" 406495 NIL DIFEXT (NIL T) -9 NIL 406789 NIL) (-230 403130 403558 404224 "DIFEXT-" 404229 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400452 402662 402703 "DIAGG" 402708 NIL DIAGG (NIL T) -9 NIL 402728 NIL) (-228 399836 399993 400245 "DIAGG-" 400250 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395301 398795 399072 "DHMATRIX" 399605 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390913 391822 392832 "DFSFUN" 394311 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386018 389844 390156 "DFLOAT" 390621 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384246 384527 384923 "DFINTTLS" 385726 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381302 382267 382667 "DERHAM" 383912 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379151 381077 381166 "DEQUEUE" 381246 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378366 378499 378695 "DEGRED" 379013 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374761 375506 376359 "DEFINTRF" 377594 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372288 372757 373356 "DEFINTEF" 374280 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371665 371908 372023 "DEFAST" 372193 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365696 371260 371409 "DECIMAL" 371536 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363206 363666 364172 "DDFACT" 365240 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362802 362845 362996 "DBLRESP" 363157 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360701 361035 361395 "DBASE" 362569 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359970 360181 360327 "DATAARY" 360600 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359103 359929 359957 "D03FAFA" 359962 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358237 359062 359090 "D03EEFA" 359095 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356187 356653 357142 "D03AGNT" 357768 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355503 356146 356174 "D02EJFA" 356179 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354819 355462 355490 "D02CJFA" 355495 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354135 354778 354806 "D02BHFA" 354811 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353451 354094 354122 "D02BBFA" 354127 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346648 348237 349843 "D02AGNT" 351865 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344416 344939 345485 "D01WGTS" 346122 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343510 344375 344403 "D01TRNS" 344408 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342605 343469 343497 "D01GBFA" 343502 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341700 342564 342592 "D01FCFA" 342597 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340795 341659 341687 "D01ASFA" 341692 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339890 340754 340782 "D01AQFA" 340787 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338985 339849 339877 "D01APFA" 339882 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338080 338944 338972 "D01ANFA" 338977 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337175 338039 338067 "D01AMFA" 338072 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336270 337134 337162 "D01ALFA" 337167 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335365 336229 336257 "D01AKFA" 336262 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334460 335324 335352 "D01AJFA" 335357 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327755 329308 330869 "D01AGNT" 332919 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327092 327220 327372 "CYCLOTOM" 327623 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323827 324540 325267 "CYCLES" 326385 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323139 323273 323444 "CVMP" 323688 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320910 321168 321544 "CTRIGMNP" 322867 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320401 320701 320775 "CTOR" 320856 T CTOR (NIL) -8 NIL NIL NIL) (-186 319937 320132 320233 "CTORKIND" 320320 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319285 319544 319572 "CTORCAT" 319754 T CTORCAT (NIL) -9 NIL 319867 NIL) (-184 318883 318994 319153 "CTORCAT-" 319158 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318399 318586 318684 "CTORCALL" 318805 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317773 317872 318025 "CSTTOOLS" 318296 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313572 314229 314987 "CRFP" 317085 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313074 313293 313385 "CRCEAST" 313500 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312121 312306 312534 "CRAPACK" 312878 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311505 311606 311810 "CPMATCH" 311997 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311230 311258 311364 "CPIMA" 311471 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307594 308266 308984 "COORDSYS" 310565 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307002 307124 307267 "CONTOUR" 307471 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302920 305005 305497 "CONTFRAC" 306542 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302800 302821 302849 "CONDUIT" 302886 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301965 302493 302521 "COMRING" 302526 T COMRING (NIL) -9 NIL 302578 NIL) (-171 301046 301323 301507 "COMPPROP" 301801 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 300707 300742 300870 "COMPLPAT" 301005 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 290756 300516 300625 "COMPLEX" 300630 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 290392 290449 290556 "COMPLEX2" 290693 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290110 290145 290243 "COMPFACT" 290351 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274264 284492 284532 "COMPCAT" 285536 NIL COMPCAT (NIL T) -9 NIL 286932 NIL) (-165 263775 266703 270330 "COMPCAT-" 270686 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 263504 263532 263635 "COMMUPC" 263741 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263299 263332 263391 "COMMONOP" 263465 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 262882 263050 263137 "COMM" 263232 T COMM (NIL) -8 NIL NIL NIL) (-161 262485 262686 262761 "COMMAAST" 262827 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 261734 261928 261956 "COMBOPC" 262294 T COMBOPC (NIL) -9 NIL 262469 NIL) (-159 260630 260840 261082 "COMBINAT" 261524 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 256827 257401 258041 "COMBF" 260052 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 255612 255943 256178 "COLOR" 256612 T COLOR (NIL) -8 NIL NIL NIL) (-156 255115 255333 255425 "COLONAST" 255540 T COLONAST (NIL) -8 NIL NIL NIL) (-155 254755 254802 254927 "CMPLXRT" 255062 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254230 254455 254554 "CLLCTAST" 254676 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 249730 250760 251840 "CLIP" 253170 T CLIP (NIL) -7 NIL NIL NIL) (-152 248103 248836 249075 "CLIF" 249557 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244325 246249 246290 "CLAGG" 247219 NIL CLAGG (NIL T) -9 NIL 247755 NIL) (-150 242747 243204 243787 "CLAGG-" 243792 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242291 242376 242516 "CINTSLPE" 242656 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 239792 240263 240811 "CHVAR" 241819 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239027 239555 239583 "CHARZ" 239588 T CHARZ (NIL) -9 NIL 239603 NIL) (-146 238781 238821 238899 "CHARPOL" 238981 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 237900 238461 238489 "CHARNZ" 238536 T CHARNZ (NIL) -9 NIL 238592 NIL) (-144 235889 236590 236925 "CHAR" 237585 T CHAR (NIL) -8 NIL NIL NIL) (-143 235615 235676 235704 "CFCAT" 235815 T CFCAT (NIL) -9 NIL NIL NIL) (-142 234860 234971 235153 "CDEN" 235499 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 230852 234013 234293 "CCLASS" 234600 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230159 230302 230465 "CATEGORY" 230709 T -10 (NIL) -8 NIL NIL NIL) (-139 229791 230078 230126 "CATCTOR" 230131 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229269 229494 229592 "CATAST" 229713 T CATAST (NIL) -8 NIL NIL NIL) (-137 228772 228990 229082 "CASEAST" 229197 T CASEAST (NIL) -8 NIL NIL NIL) (-136 223808 224801 225554 "CARTEN" 228075 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 222916 223064 223285 "CARTEN2" 223655 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221258 222066 222323 "CARD" 222679 T CARD (NIL) -8 NIL NIL NIL) (-133 220861 221062 221137 "CAPSLAST" 221203 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220233 220561 220589 "CACHSET" 220721 T CACHSET (NIL) -9 NIL 220798 NIL) (-131 219729 220025 220053 "CABMON" 220103 T CABMON (NIL) -9 NIL 220159 NIL) (-130 219229 219433 219543 "BYTEORD" 219639 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218232 218763 218905 "BYTE" 219068 T BYTE (NIL) -8 NIL NIL 219190) (-128 213632 217737 217909 "BYTEBUF" 218080 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211189 213324 213431 "BTREE" 213558 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208686 210837 210959 "BTOURN" 211099 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206103 208156 208197 "BTCAT" 208265 NIL BTCAT (NIL T) -9 NIL 208342 NIL) (-124 205770 205850 205999 "BTCAT-" 206004 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201062 204913 204941 "BTAGG" 205163 T BTAGG (NIL) -9 NIL 205324 NIL) (-122 200552 200677 200883 "BTAGG-" 200888 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197595 199830 200045 "BSTREE" 200369 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196733 196859 197043 "BRILL" 197451 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193432 195459 195500 "BRAGG" 196149 NIL BRAGG (NIL T) -9 NIL 196407 NIL) (-118 191961 192367 192922 "BRAGG-" 192927 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185217 191307 191491 "BPADICRT" 191809 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183559 185154 185199 "BPADIC" 185204 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183257 183287 183401 "BOUNDZRO" 183523 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178772 179863 180730 "BOP" 182410 T BOP (NIL) -8 NIL NIL NIL) (-113 176393 176837 177357 "BOP1" 178285 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175095 175817 176010 "BOOLEAN" 176220 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174457 174835 174889 "BMODULE" 174894 NIL BMODULE (NIL T T) -9 NIL 174959 NIL) (-110 170285 174255 174328 "BITS" 174404 T BITS (NIL) -8 NIL NIL NIL) (-109 169697 169819 169961 "BINDING" 170163 T BINDING (NIL) -8 NIL NIL NIL) (-108 163731 169294 169442 "BINARY" 169569 T BINARY (NIL) -8 NIL NIL NIL) (-107 161558 162986 163027 "BGAGG" 163287 NIL BGAGG (NIL T) -9 NIL 163424 NIL) (-106 161389 161421 161512 "BGAGG-" 161517 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160487 160773 160978 "BFUNCT" 161204 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159177 159355 159643 "BEZOUT" 160311 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155694 158029 158359 "BBTREE" 158880 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155428 155481 155509 "BASTYPE" 155628 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155281 155309 155382 "BASTYPE-" 155387 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154715 154791 154943 "BALFACT" 155192 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153598 154130 154316 "AUTOMOR" 154560 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153324 153329 153355 "ATTREG" 153360 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151603 152021 152373 "ATTRBUT" 152990 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151238 151431 151497 "ATTRAST" 151555 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150774 150887 150913 "ATRIG" 151114 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150583 150624 150711 "ATRIG-" 150716 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150254 150414 150440 "ASTCAT" 150445 T ASTCAT (NIL) -9 NIL 150475 NIL) (-92 149981 150040 150159 "ASTCAT-" 150164 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148178 149757 149845 "ASTACK" 149924 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146683 146980 147345 "ASSOCEQ" 147860 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145715 146342 146466 "ASP9" 146590 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145478 145663 145702 "ASP8" 145707 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144346 145083 145225 "ASP80" 145367 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143244 143981 144113 "ASP7" 144245 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142198 142921 143039 "ASP78" 143157 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141167 141878 141995 "ASP77" 142112 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140079 140805 140936 "ASP74" 141067 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138979 139714 139846 "ASP73" 139978 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138083 138805 138905 "ASP6" 138910 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137027 137760 137878 "ASP55" 137996 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 135976 136701 136820 "ASP50" 136939 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135064 135677 135787 "ASP4" 135897 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134152 134765 134875 "ASP49" 134985 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 132936 133691 133859 "ASP42" 134041 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131712 132469 132639 "ASP41" 132823 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130662 131389 131507 "ASP35" 131625 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130427 130610 130649 "ASP34" 130654 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130164 130231 130307 "ASP33" 130382 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129057 129799 129931 "ASP31" 130063 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 128822 129005 129044 "ASP30" 129049 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128557 128626 128702 "ASP29" 128777 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128322 128505 128544 "ASP28" 128549 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128087 128270 128309 "ASP27" 128314 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127171 127785 127896 "ASP24" 128007 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126247 126973 127085 "ASP20" 127090 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125335 125948 126058 "ASP1" 126168 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124277 125009 125128 "ASP19" 125247 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124014 124081 124157 "ASP12" 124232 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 122866 123613 123757 "ASP10" 123901 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 120765 122710 122801 "ARRAY2" 122806 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116579 120413 120527 "ARRAY1" 120682 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115611 115784 116005 "ARRAY12" 116402 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 109970 111841 111916 "ARR2CAT" 114546 NIL ARR2CAT (NIL T T T) -9 NIL 115304 NIL) (-56 107404 108148 109102 "ARR2CAT-" 109107 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107231 107310 "ARITY" 107343 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 3199892 3199897 3199902 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3199877 3199882 3199887 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3199862 3199867 3199872 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3199847 3199852 3199857 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3199016 3199722 3199799 "ZMOD" 3199804 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3198126 3198290 3198499 "ZLINDEP" 3198848 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3187426 3189194 3191166 "ZDSOLVE" 3196256 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3186672 3186813 3187002 "YSTREAM" 3187272 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3184473 3185973 3186177 "XRPOLY" 3186515 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3181053 3182344 3182919 "XPR" 3183945 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3178801 3180384 3180588 "XPOLY" 3180884 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3176584 3177926 3177981 "XPOLYC" 3178269 NIL XPOLYC (NIL T T) -9 NIL 3178382 NIL) (-1279 3172987 3175101 3175489 "XPBWPOLY" 3176242 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3168890 3171150 3171192 "XF" 3171813 NIL XF (NIL T) -9 NIL 3172213 NIL) (-1277 3168511 3168599 3168768 "XF-" 3168773 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3163837 3165100 3165155 "XFALG" 3167327 NIL XFALG (NIL T T) -9 NIL 3168116 NIL) (-1275 3162970 3163074 3163279 "XEXPPKG" 3163729 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3161106 3162820 3162916 "XDPOLY" 3162921 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3160043 3160617 3160660 "XALG" 3160665 NIL XALG (NIL T) -9 NIL 3160776 NIL) (-1272 3153512 3158020 3158514 "WUTSET" 3159635 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3151795 3152564 3152887 "WP" 3153323 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3151424 3151617 3151687 "WHILEAST" 3151747 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3150923 3151141 3151235 "WHEREAST" 3151352 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3149809 3150007 3150302 "WFFINTBS" 3150720 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3147713 3148140 3148602 "WEIER" 3149381 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3146860 3147284 3147326 "VSPACE" 3147462 NIL VSPACE (NIL T) -9 NIL 3147536 NIL) (-1265 3146698 3146725 3146816 "VSPACE-" 3146821 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3146506 3146549 3146617 "VOID" 3146652 T VOID (NIL) -8 NIL NIL NIL) (-1263 3144642 3145001 3145407 "VIEW" 3146122 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3141066 3141705 3142442 "VIEWDEF" 3143927 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3130397 3132614 3134787 "VIEW3D" 3138915 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3122675 3124308 3125887 "VIEW2D" 3128840 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3118077 3122445 3122537 "VECTOR" 3122618 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3116654 3116913 3117231 "VECTOR2" 3117807 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3110181 3114438 3114481 "VECTCAT" 3115474 NIL VECTCAT (NIL T) -9 NIL 3116060 NIL) (-1256 3109195 3109449 3109839 "VECTCAT-" 3109844 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3108676 3108846 3108966 "VARIABLE" 3109110 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3108609 3108614 3108644 "UTYPE" 3108649 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3107439 3107593 3107855 "UTSODETL" 3108435 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3104879 3105339 3105863 "UTSODE" 3106980 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3096743 3102505 3102994 "UTS" 3104448 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3087978 3093310 3093353 "UTSCAT" 3094465 NIL UTSCAT (NIL T) -9 NIL 3095222 NIL) (-1249 3085326 3086048 3087037 "UTSCAT-" 3087042 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3084953 3084996 3085129 "UTS2" 3085277 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3079226 3081791 3081834 "URAGG" 3083904 NIL URAGG (NIL T) -9 NIL 3084627 NIL) (-1246 3076165 3077028 3078151 "URAGG-" 3078156 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3071881 3074779 3075251 "UPXSSING" 3075829 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3063974 3071128 3071401 "UPXS" 3071666 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3057074 3063878 3063950 "UPXSCONS" 3063955 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3047311 3054069 3054131 "UPXSCCA" 3054705 NIL UPXSCCA (NIL T T) -9 NIL 3054938 NIL) (-1241 3046949 3047034 3047208 "UPXSCCA-" 3047213 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3037039 3043570 3043613 "UPXSCAT" 3044261 NIL UPXSCAT (NIL T) -9 NIL 3044869 NIL) (-1239 3036469 3036548 3036727 "UPXS2" 3036954 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3035123 3035376 3035727 "UPSQFREE" 3036212 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3028903 3031925 3031980 "UPSCAT" 3033141 NIL UPSCAT (NIL T T) -9 NIL 3033915 NIL) (-1236 3028107 3028314 3028641 "UPSCAT-" 3028646 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3013949 3021955 3021998 "UPOLYC" 3024099 NIL UPOLYC (NIL T) -9 NIL 3025320 NIL) (-1234 3005277 3007703 3010850 "UPOLYC-" 3010855 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3004904 3004947 3005080 "UPOLYC2" 3005228 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2996470 3004587 3004716 "UP" 3004823 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2995809 2995916 2996080 "UPMP" 2996359 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2995362 2995443 2995582 "UPDIVP" 2995722 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2993930 2994179 2994495 "UPDECOMP" 2995111 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2993165 2993277 2993462 "UPCDEN" 2993814 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2992684 2992753 2992902 "UP2" 2993090 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2991199 2991888 2992165 "UNISEG" 2992442 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2990414 2990541 2990746 "UNISEG2" 2991042 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2989474 2989654 2989880 "UNIFACT" 2990230 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2973433 2988651 2988902 "ULS" 2989281 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2961459 2973337 2973409 "ULSCONS" 2973414 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2944067 2956017 2956079 "ULSCCAT" 2956717 NIL ULSCCAT (NIL T T) -9 NIL 2957005 NIL) (-1220 2943117 2943362 2943750 "ULSCCAT-" 2943755 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2932984 2939429 2939472 "ULSCAT" 2940335 NIL ULSCAT (NIL T) -9 NIL 2941065 NIL) (-1218 2932414 2932493 2932672 "ULS2" 2932899 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2931531 2932014 2932121 "UINT8" 2932232 T UINT8 (NIL) -8 NIL NIL 2932317) (-1216 2930647 2931130 2931237 "UINT64" 2931348 T UINT64 (NIL) -8 NIL NIL 2931433) (-1215 2929763 2930246 2930353 "UINT32" 2930464 T UINT32 (NIL) -8 NIL NIL 2930549) (-1214 2928879 2929362 2929469 "UINT16" 2929580 T UINT16 (NIL) -8 NIL NIL 2929665) (-1213 2927274 2928205 2928235 "UFD" 2928447 T UFD (NIL) -9 NIL 2928561 NIL) (-1212 2927068 2927114 2927209 "UFD-" 2927214 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2926150 2926333 2926549 "UDVO" 2926874 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2923966 2924375 2924846 "UDPO" 2925714 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2923899 2923904 2923934 "TYPE" 2923939 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2923686 2923854 2923885 "TYPEAST" 2923890 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2922657 2922859 2923099 "TWOFACT" 2923480 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2921728 2922066 2922301 "TUPLE" 2922457 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2919419 2919938 2920477 "TUBETOOL" 2921211 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2918268 2918473 2918714 "TUBE" 2919212 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2913024 2917240 2917523 "TS" 2918020 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2901691 2905783 2905880 "TSETCAT" 2911149 NIL TSETCAT (NIL T T T T) -9 NIL 2912680 NIL) (-1201 2896423 2898023 2899914 "TSETCAT-" 2899919 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2890685 2891532 2892474 "TRMANIP" 2895559 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2890126 2890189 2890352 "TRIMAT" 2890617 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2887922 2888159 2888523 "TRIGMNIP" 2889875 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2887442 2887555 2887585 "TRIGCAT" 2887798 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2887111 2887190 2887331 "TRIGCAT-" 2887336 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2884004 2885969 2886250 "TREE" 2886865 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2883278 2883806 2883836 "TRANFUN" 2883871 T TRANFUN (NIL) -9 NIL 2883937 NIL) (-1193 2882557 2882748 2883028 "TRANFUN-" 2883033 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2882361 2882393 2882454 "TOPSP" 2882518 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2881709 2881824 2881978 "TOOLSIGN" 2882242 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2880370 2880886 2881125 "TEXTFILE" 2881492 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2878309 2878823 2879252 "TEX" 2879963 T TEX (NIL) -8 NIL NIL NIL) (-1188 2878090 2878121 2878193 "TEX1" 2878272 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2877738 2877801 2877891 "TEMUTL" 2878022 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2875892 2876172 2876497 "TBCMPPK" 2877461 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2867780 2874052 2874108 "TBAGG" 2874508 NIL TBAGG (NIL T T) -9 NIL 2874719 NIL) (-1184 2862850 2864338 2866092 "TBAGG-" 2866097 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2862234 2862341 2862486 "TANEXP" 2862739 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2855735 2862091 2862184 "TABLE" 2862189 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2855147 2855246 2855384 "TABLEAU" 2855632 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2849755 2850975 2852223 "TABLBUMP" 2853933 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2848977 2849124 2849305 "SYSTEM" 2849596 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2845436 2846135 2846918 "SYSSOLP" 2848228 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2844470 2844948 2845067 "SYSNNI" 2845253 NIL SYSNNI (NIL NIL) -8 NIL NIL 2845338) (-1176 2843767 2844199 2844278 "SYSINT" 2844338 NIL SYSINT (NIL NIL) -8 NIL NIL 2844383) (-1175 2840126 2841045 2841755 "SYNTAX" 2843079 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2837284 2837886 2838518 "SYMTAB" 2839516 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2832533 2833435 2834418 "SYMS" 2836323 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2829795 2831991 2832221 "SYMPOLY" 2832338 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2829312 2829387 2829510 "SYMFUNC" 2829707 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2825358 2826624 2827437 "SYMBOL" 2828521 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2818897 2820586 2822306 "SWITCH" 2823660 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2812158 2817718 2818021 "SUTS" 2818652 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2804251 2811405 2811678 "SUPXS" 2811943 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2795766 2803869 2803995 "SUP" 2804160 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2794925 2795052 2795269 "SUPFRACF" 2795634 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2794546 2794605 2794718 "SUP2" 2794860 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2792959 2793233 2793596 "SUMRF" 2794245 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2792273 2792339 2792538 "SUMFS" 2792880 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2776267 2791450 2791701 "SULS" 2792080 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2775896 2776089 2776159 "SUCHTAST" 2776219 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2775218 2775421 2775561 "SUCH" 2775804 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2769112 2770124 2771083 "SUBSPACE" 2774306 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2768542 2768632 2768796 "SUBRESP" 2769000 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2761907 2763207 2764518 "STTF" 2767278 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2756080 2757200 2758347 "STTFNC" 2760807 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2747391 2749262 2751056 "STTAYLOR" 2754321 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2740635 2747255 2747338 "STRTBL" 2747343 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2736026 2740590 2740621 "STRING" 2740626 T STRING (NIL) -8 NIL NIL NIL) (-1151 2730914 2735399 2735429 "STRICAT" 2735488 T STRICAT (NIL) -9 NIL 2735550 NIL) (-1150 2723717 2728533 2729144 "STREAM" 2730338 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2723227 2723304 2723448 "STREAM3" 2723634 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2722209 2722392 2722627 "STREAM2" 2723040 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2721897 2721949 2722042 "STREAM1" 2722151 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2720913 2721094 2721325 "STINPROD" 2721713 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2720491 2720675 2720705 "STEP" 2720785 T STEP (NIL) -9 NIL 2720863 NIL) (-1144 2714034 2720390 2720467 "STBL" 2720472 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2709208 2713255 2713298 "STAGG" 2713451 NIL STAGG (NIL T) -9 NIL 2713540 NIL) (-1142 2706910 2707512 2708384 "STAGG-" 2708389 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2705105 2706680 2706772 "STACK" 2706853 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2697828 2703246 2703702 "SREGSET" 2704735 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2690253 2691622 2693135 "SRDCMPK" 2696434 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2683220 2687693 2687723 "SRAGG" 2689026 T SRAGG (NIL) -9 NIL 2689634 NIL) (-1137 2682237 2682492 2682871 "SRAGG-" 2682876 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2676724 2681184 2681605 "SQMATRIX" 2681863 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2670471 2673442 2674169 "SPLTREE" 2676069 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2666461 2667127 2667773 "SPLNODE" 2669897 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2665508 2665741 2665771 "SPFCAT" 2666215 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2664245 2664455 2664719 "SPECOUT" 2665266 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2655897 2657641 2657671 "SPADXPT" 2662063 T SPADXPT (NIL) -9 NIL 2664097 NIL) (-1130 2655658 2655698 2655767 "SPADPRSR" 2655850 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2653840 2655613 2655644 "SPADAST" 2655649 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2645811 2647558 2647601 "SPACEC" 2651974 NIL SPACEC (NIL T) -9 NIL 2653790 NIL) (-1127 2643968 2645743 2645792 "SPACE3" 2645797 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2642720 2642891 2643182 "SORTPAK" 2643773 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2640770 2641073 2641492 "SOLVETRA" 2642384 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2639781 2640003 2640277 "SOLVESER" 2640543 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2634992 2635882 2636884 "SOLVERAD" 2638833 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2630807 2631416 2632145 "SOLVEFOR" 2634359 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2625104 2630156 2630253 "SNTSCAT" 2630258 NIL SNTSCAT (NIL T T T T) -9 NIL 2630328 NIL) (-1120 2619237 2623427 2623818 "SMTS" 2624794 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2613677 2619125 2619202 "SMP" 2619207 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2611836 2612137 2612535 "SMITH" 2613374 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2604723 2608887 2608990 "SMATCAT" 2610341 NIL SMATCAT (NIL NIL T T T) -9 NIL 2610891 NIL) (-1116 2601663 2602486 2603664 "SMATCAT-" 2603669 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2599376 2600899 2600942 "SKAGG" 2601203 NIL SKAGG (NIL T) -9 NIL 2601338 NIL) (-1114 2595711 2598792 2598987 "SINT" 2599174 T SINT (NIL) -8 NIL NIL 2599347) (-1113 2595483 2595521 2595587 "SIMPAN" 2595667 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2594789 2595018 2595158 "SIG" 2595365 T SIG (NIL) -8 NIL NIL NIL) (-1111 2593627 2593848 2594123 "SIGNRF" 2594548 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2592432 2592583 2592874 "SIGNEF" 2593456 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2591765 2592015 2592139 "SIGAST" 2592330 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2589455 2589909 2590415 "SHP" 2591306 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2583355 2589356 2589432 "SHDP" 2589437 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2582954 2583120 2583150 "SGROUP" 2583243 T SGROUP (NIL) -9 NIL 2583305 NIL) (-1105 2582812 2582838 2582911 "SGROUP-" 2582916 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2579647 2580345 2581068 "SGCF" 2582111 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2574042 2579094 2579191 "SFRTCAT" 2579196 NIL SFRTCAT (NIL T T T T) -9 NIL 2579235 NIL) (-1102 2567463 2568481 2569617 "SFRGCD" 2573025 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2560590 2561662 2562848 "SFQCMPK" 2566396 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2560212 2560301 2560411 "SFORT" 2560531 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2559357 2560052 2560173 "SEXOF" 2560178 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2558491 2559238 2559306 "SEX" 2559311 T SEX (NIL) -8 NIL NIL NIL) (-1097 2554030 2554719 2554814 "SEXCAT" 2557751 NIL SEXCAT (NIL T T T T T) -9 NIL 2558329 NIL) (-1096 2551210 2553964 2554012 "SET" 2554017 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2549461 2549923 2550228 "SETMN" 2550951 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2549067 2549193 2549223 "SETCAT" 2549340 T SETCAT (NIL) -9 NIL 2549425 NIL) (-1093 2548847 2548899 2548998 "SETCAT-" 2549003 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2545234 2547308 2547351 "SETAGG" 2548221 NIL SETAGG (NIL T) -9 NIL 2548561 NIL) (-1091 2544692 2544808 2545045 "SETAGG-" 2545050 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2544162 2544388 2544489 "SEQAST" 2544613 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2543361 2543655 2543716 "SEGXCAT" 2544002 NIL SEGXCAT (NIL T T) -9 NIL 2544122 NIL) (-1088 2542415 2543027 2543209 "SEG" 2543214 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2541394 2541608 2541651 "SEGCAT" 2542173 NIL SEGCAT (NIL T) -9 NIL 2542394 NIL) (-1086 2540443 2540773 2540973 "SEGBIND" 2541229 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2540064 2540123 2540236 "SEGBIND2" 2540378 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2539664 2539865 2539942 "SEGAST" 2540009 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2538883 2539009 2539213 "SEG2" 2539508 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2538320 2538818 2538865 "SDVAR" 2538870 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2530602 2538090 2538220 "SDPOL" 2538225 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2529195 2529461 2529780 "SCPKG" 2530317 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2528355 2528528 2528721 "SCOPE" 2529024 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2527575 2527709 2527888 "SCACHE" 2528210 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2527247 2527407 2527437 "SASTCAT" 2527442 T SASTCAT (NIL) -9 NIL 2527455 NIL) (-1076 2526761 2527082 2527158 "SAOS" 2527193 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2526326 2526361 2526534 "SAERFFC" 2526720 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2520292 2526223 2526303 "SAE" 2526308 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2519885 2519920 2520079 "SAEFACT" 2520251 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2518206 2518520 2518921 "RURPK" 2519551 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2516842 2517121 2517433 "RULESET" 2518040 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2514029 2514532 2514997 "RULE" 2516523 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2513668 2513823 2513906 "RULECOLD" 2513981 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2513166 2513385 2513479 "RSTRCAST" 2513596 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1067 2508014 2508809 2509729 "RSETGCD" 2512365 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1066 2497271 2502323 2502420 "RSETCAT" 2506539 NIL RSETCAT (NIL T T T T) -9 NIL 2507636 NIL) (-1065 2495198 2495737 2496561 "RSETCAT-" 2496566 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1064 2487583 2488960 2490480 "RSDCMPK" 2493797 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1063 2485588 2486029 2486103 "RRCC" 2487189 NIL RRCC (NIL T T) -9 NIL 2487533 NIL) (-1062 2484939 2485113 2485392 "RRCC-" 2485397 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1061 2484409 2484635 2484736 "RPTAST" 2484860 T RPTAST (NIL) -8 NIL NIL NIL) (-1060 2458407 2468002 2468069 "RPOLCAT" 2478733 NIL RPOLCAT (NIL T T T) -9 NIL 2481892 NIL) (-1059 2449905 2452245 2455367 "RPOLCAT-" 2455372 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1058 2440952 2448116 2448598 "ROUTINE" 2449445 T ROUTINE (NIL) -8 NIL NIL NIL) (-1057 2437777 2440578 2440718 "ROMAN" 2440834 T ROMAN (NIL) -8 NIL NIL NIL) (-1056 2436048 2436637 2436897 "ROIRC" 2437582 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1055 2432433 2434684 2434714 "RNS" 2435018 T RNS (NIL) -9 NIL 2435291 NIL) (-1054 2430942 2431325 2431859 "RNS-" 2431934 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1053 2430391 2430773 2430803 "RNG" 2430808 T RNG (NIL) -9 NIL 2430829 NIL) (-1052 2429783 2430145 2430188 "RMODULE" 2430250 NIL RMODULE (NIL T) -9 NIL 2430292 NIL) (-1051 2428619 2428713 2429049 "RMCAT2" 2429684 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1050 2425496 2427965 2428262 "RMATRIX" 2428381 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1049 2418438 2420672 2420787 "RMATCAT" 2424146 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2425128 NIL) (-1048 2417813 2417960 2418267 "RMATCAT-" 2418272 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1047 2417380 2417455 2417583 "RINTERP" 2417732 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1046 2416499 2417027 2417057 "RING" 2417113 T RING (NIL) -9 NIL 2417205 NIL) (-1045 2416291 2416335 2416432 "RING-" 2416437 NIL RING- (NIL T) -8 NIL NIL NIL) (-1044 2415132 2415369 2415627 "RIDIST" 2416055 T RIDIST (NIL) -7 NIL NIL NIL) (-1043 2406448 2414600 2414806 "RGCHAIN" 2414980 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1042 2405824 2406204 2406245 "RGBCSPC" 2406303 NIL RGBCSPC (NIL T) -9 NIL 2406355 NIL) (-1041 2405008 2405363 2405404 "RGBCMDL" 2405636 NIL RGBCMDL (NIL T) -9 NIL 2405750 NIL) (-1040 2402002 2402616 2403286 "RF" 2404372 NIL RF (NIL T) -7 NIL NIL NIL) (-1039 2401648 2401711 2401814 "RFFACTOR" 2401933 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1038 2401373 2401408 2401505 "RFFACT" 2401607 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1037 2399490 2399854 2400236 "RFDIST" 2401013 T RFDIST (NIL) -7 NIL NIL NIL) (-1036 2398943 2399035 2399198 "RETSOL" 2399392 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1035 2398579 2398659 2398702 "RETRACT" 2398835 NIL RETRACT (NIL T) -9 NIL 2398922 NIL) (-1034 2398428 2398453 2398540 "RETRACT-" 2398545 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1033 2398057 2398250 2398320 "RETAST" 2398380 T RETAST (NIL) -8 NIL NIL NIL) (-1032 2390911 2397710 2397837 "RESULT" 2397952 T RESULT (NIL) -8 NIL NIL NIL) (-1031 2389529 2390180 2390379 "RESRING" 2390814 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1030 2389165 2389214 2389312 "RESLATC" 2389466 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1029 2388870 2388905 2389012 "REPSQ" 2389124 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1028 2386292 2386872 2387474 "REP" 2388290 T REP (NIL) -7 NIL NIL NIL) (-1027 2385989 2386024 2386135 "REPDB" 2386251 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1026 2379889 2381278 2382501 "REP2" 2384801 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1025 2376266 2376947 2377755 "REP1" 2379116 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1024 2368989 2374407 2374863 "REGSET" 2375896 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1023 2367802 2368137 2368387 "REF" 2368774 NIL REF (NIL T) -8 NIL NIL NIL) (-1022 2367179 2367282 2367449 "REDORDER" 2367686 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1021 2363174 2366392 2366619 "RECLOS" 2367007 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1020 2362226 2362407 2362622 "REALSOLV" 2362981 T REALSOLV (NIL) -7 NIL NIL NIL) (-1019 2362072 2362113 2362143 "REAL" 2362148 T REAL (NIL) -9 NIL 2362183 NIL) (-1018 2358555 2359357 2360241 "REAL0Q" 2361237 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1017 2354156 2355144 2356205 "REAL0" 2357536 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1016 2353654 2353873 2353967 "RDUCEAST" 2354084 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1015 2353059 2353131 2353338 "RDIV" 2353576 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1014 2352127 2352301 2352514 "RDIST" 2352881 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1013 2350724 2351011 2351383 "RDETRS" 2351835 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1012 2348536 2348990 2349528 "RDETR" 2350266 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1011 2347147 2347425 2347829 "RDEEFS" 2348252 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1010 2345642 2345948 2346380 "RDEEF" 2346835 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1009 2339895 2342778 2342808 "RCFIELD" 2344103 T RCFIELD (NIL) -9 NIL 2344833 NIL) (-1008 2337959 2338463 2339159 "RCFIELD-" 2339234 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1007 2334275 2336060 2336103 "RCAGG" 2337187 NIL RCAGG (NIL T) -9 NIL 2337652 NIL) (-1006 2333903 2333997 2334160 "RCAGG-" 2334165 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1005 2333238 2333350 2333515 "RATRET" 2333787 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1004 2332791 2332858 2332979 "RATFACT" 2333166 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1003 2332099 2332219 2332371 "RANDSRC" 2332661 T RANDSRC (NIL) -7 NIL NIL NIL) (-1002 2331833 2331877 2331950 "RADUTIL" 2332048 T RADUTIL (NIL) -7 NIL NIL NIL) (-1001 2324976 2330666 2330976 "RADIX" 2331557 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-1000 2316622 2324818 2324948 "RADFF" 2324953 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-999 2316274 2316349 2316377 "RADCAT" 2316534 T RADCAT (NIL) -9 NIL NIL NIL) (-998 2316059 2316107 2316204 "RADCAT-" 2316209 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-997 2314210 2315834 2315923 "QUEUE" 2316003 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-996 2310778 2314147 2314192 "QUAT" 2314197 NIL QUAT (NIL T) -8 NIL NIL NIL) (-995 2310416 2310459 2310586 "QUATCT2" 2310729 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-994 2304155 2307465 2307505 "QUATCAT" 2308285 NIL QUATCAT (NIL T) -9 NIL 2309051 NIL) (-993 2300299 2301336 2302723 "QUATCAT-" 2302817 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-992 2297819 2299383 2299424 "QUAGG" 2299799 NIL QUAGG (NIL T) -9 NIL 2299974 NIL) (-991 2297451 2297644 2297712 "QQUTAST" 2297771 T QQUTAST (NIL) -8 NIL NIL NIL) (-990 2296376 2296849 2297021 "QFORM" 2297323 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-989 2287580 2292793 2292833 "QFCAT" 2293491 NIL QFCAT (NIL T) -9 NIL 2294492 NIL) (-988 2283152 2284353 2285944 "QFCAT-" 2286038 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-987 2282790 2282833 2282960 "QFCAT2" 2283103 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-986 2282250 2282360 2282490 "QEQUAT" 2282680 T QEQUAT (NIL) -8 NIL NIL NIL) (-985 2275397 2276469 2277653 "QCMPACK" 2281183 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-984 2272973 2273394 2273822 "QALGSET" 2275052 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-983 2272218 2272392 2272624 "QALGSET2" 2272793 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-982 2270908 2271132 2271449 "PWFFINTB" 2271991 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-981 2269090 2269258 2269612 "PUSHVAR" 2270722 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-980 2265008 2266062 2266103 "PTRANFN" 2267987 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-979 2263410 2263701 2264023 "PTPACK" 2264719 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-978 2263042 2263099 2263208 "PTFUNC2" 2263347 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-977 2257569 2261914 2261955 "PTCAT" 2262251 NIL PTCAT (NIL T) -9 NIL 2262404 NIL) (-976 2257227 2257262 2257386 "PSQFR" 2257528 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-975 2255822 2256120 2256454 "PSEUDLIN" 2256925 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-974 2242585 2244956 2247280 "PSETPK" 2253582 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-973 2235629 2238343 2238439 "PSETCAT" 2241460 NIL PSETCAT (NIL T T T T) -9 NIL 2242274 NIL) (-972 2233465 2234099 2234920 "PSETCAT-" 2234925 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-971 2232814 2232979 2233007 "PSCURVE" 2233275 T PSCURVE (NIL) -9 NIL 2233442 NIL) (-970 2229162 2230652 2230717 "PSCAT" 2231561 NIL PSCAT (NIL T T T) -9 NIL 2231801 NIL) (-969 2228225 2228441 2228841 "PSCAT-" 2228846 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-968 2226957 2227590 2227795 "PRTITION" 2228040 T PRTITION (NIL) -8 NIL NIL NIL) (-967 2226459 2226678 2226770 "PRTDAST" 2226885 T PRTDAST (NIL) -8 NIL NIL NIL) (-966 2215549 2217763 2219951 "PRS" 2224321 NIL PRS (NIL T T) -7 NIL NIL NIL) (-965 2213407 2214899 2214939 "PRQAGG" 2215122 NIL PRQAGG (NIL T) -9 NIL 2215224 NIL) (-964 2212793 2213022 2213050 "PROPLOG" 2213235 T PROPLOG (NIL) -9 NIL 2213357 NIL) (-963 2209963 2210607 2211071 "PROPFRML" 2212361 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-962 2209423 2209533 2209663 "PROPERTY" 2209853 T PROPERTY (NIL) -8 NIL NIL NIL) (-961 2203508 2207589 2208409 "PRODUCT" 2208649 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-960 2200813 2202966 2203200 "PR" 2203319 NIL PR (NIL T T) -8 NIL NIL NIL) (-959 2200609 2200641 2200700 "PRINT" 2200774 T PRINT (NIL) -7 NIL NIL NIL) (-958 2199949 2200066 2200218 "PRIMES" 2200489 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-957 2198014 2198415 2198881 "PRIMELT" 2199528 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-956 2197743 2197792 2197820 "PRIMCAT" 2197944 T PRIMCAT (NIL) -9 NIL NIL NIL) (-955 2193904 2197681 2197726 "PRIMARR" 2197731 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-954 2192911 2193089 2193317 "PRIMARR2" 2193722 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-953 2192554 2192610 2192721 "PREASSOC" 2192849 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-952 2192029 2192162 2192190 "PPCURVE" 2192395 T PPCURVE (NIL) -9 NIL 2192531 NIL) (-951 2191651 2191824 2191907 "PORTNUM" 2191966 T PORTNUM (NIL) -8 NIL NIL NIL) (-950 2189010 2189409 2190001 "POLYROOT" 2191232 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-949 2182947 2188614 2188774 "POLY" 2188883 NIL POLY (NIL T) -8 NIL NIL NIL) (-948 2182330 2182388 2182622 "POLYLIFT" 2182883 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-947 2178605 2179054 2179683 "POLYCATQ" 2181875 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-946 2165414 2170780 2170845 "POLYCAT" 2174359 NIL POLYCAT (NIL T T T) -9 NIL 2176287 NIL) (-945 2158863 2160725 2163109 "POLYCAT-" 2163114 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-944 2158450 2158518 2158638 "POLY2UP" 2158789 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-943 2158082 2158139 2158248 "POLY2" 2158387 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-942 2156767 2157006 2157282 "POLUTIL" 2157856 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-941 2155122 2155399 2155730 "POLTOPOL" 2156489 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-940 2150639 2155058 2155104 "POINT" 2155109 NIL POINT (NIL T) -8 NIL NIL NIL) (-939 2148826 2149183 2149558 "PNTHEORY" 2150284 T PNTHEORY (NIL) -7 NIL NIL NIL) (-938 2147245 2147542 2147954 "PMTOOLS" 2148524 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-937 2146838 2146916 2147033 "PMSYM" 2147161 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-936 2146348 2146417 2146591 "PMQFCAT" 2146763 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-935 2145703 2145813 2145969 "PMPRED" 2146225 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-934 2145099 2145185 2145346 "PMPREDFS" 2145604 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-933 2143742 2143950 2144335 "PMPLCAT" 2144861 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-932 2143274 2143353 2143505 "PMLSAGG" 2143657 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-931 2142749 2142825 2143006 "PMKERNEL" 2143192 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-930 2142366 2142441 2142554 "PMINS" 2142668 NIL PMINS (NIL T) -7 NIL NIL NIL) (-929 2141794 2141863 2142079 "PMFS" 2142291 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-928 2141022 2141140 2141345 "PMDOWN" 2141671 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-927 2140185 2140344 2140526 "PMASS" 2140860 T PMASS (NIL) -7 NIL NIL NIL) (-926 2139459 2139570 2139733 "PMASSFS" 2140071 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-925 2139114 2139182 2139276 "PLOTTOOL" 2139385 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-924 2133721 2134925 2136073 "PLOT" 2137986 T PLOT (NIL) -8 NIL NIL NIL) (-923 2129525 2130569 2131490 "PLOT3D" 2132820 T PLOT3D (NIL) -8 NIL NIL NIL) (-922 2128437 2128614 2128849 "PLOT1" 2129329 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-921 2103826 2108503 2113354 "PLEQN" 2123703 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-920 2103144 2103266 2103446 "PINTERP" 2103691 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-919 2102837 2102884 2102987 "PINTERPA" 2103091 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-918 2102085 2102606 2102693 "PI" 2102733 T PI (NIL) -8 NIL NIL 2102800) (-917 2100474 2101423 2101451 "PID" 2101633 T PID (NIL) -9 NIL 2101767 NIL) (-916 2100199 2100236 2100324 "PICOERCE" 2100431 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-915 2099519 2099658 2099834 "PGROEB" 2100055 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-914 2095106 2095920 2096825 "PGE" 2098634 T PGE (NIL) -7 NIL NIL NIL) (-913 2093229 2093476 2093842 "PGCD" 2094823 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-912 2092567 2092670 2092831 "PFRPAC" 2093113 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-911 2089235 2091115 2091468 "PFR" 2092246 NIL PFR (NIL T) -8 NIL NIL NIL) (-910 2087624 2087868 2088193 "PFOTOOLS" 2088982 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-909 2086157 2086396 2086747 "PFOQ" 2087381 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-908 2084630 2084842 2085205 "PFO" 2085941 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-907 2081210 2084519 2084588 "PF" 2084593 NIL PF (NIL NIL) -8 NIL NIL NIL) (-906 2078636 2079881 2079909 "PFECAT" 2080494 T PFECAT (NIL) -9 NIL 2080878 NIL) (-905 2078081 2078235 2078449 "PFECAT-" 2078454 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-904 2076684 2076936 2077237 "PFBRU" 2077830 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-903 2074549 2074902 2075334 "PFBR" 2076335 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-902 2070458 2071925 2072601 "PERM" 2073906 NIL PERM (NIL T) -8 NIL NIL NIL) (-901 2065719 2066665 2067535 "PERMGRP" 2069621 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-900 2063851 2064782 2064823 "PERMCAT" 2065269 NIL PERMCAT (NIL T) -9 NIL 2065574 NIL) (-899 2063504 2063545 2063669 "PERMAN" 2063804 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-898 2061040 2063169 2063291 "PENDTREE" 2063415 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-897 2059125 2059867 2059908 "PDRING" 2060565 NIL PDRING (NIL T) -9 NIL 2060851 NIL) (-896 2058228 2058446 2058808 "PDRING-" 2058813 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-895 2055470 2056221 2056889 "PDEPROB" 2057580 T PDEPROB (NIL) -8 NIL NIL NIL) (-894 2053015 2053519 2054074 "PDEPACK" 2054935 T PDEPACK (NIL) -7 NIL NIL NIL) (-893 2051927 2052117 2052368 "PDECOMP" 2052814 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-892 2049532 2050349 2050377 "PDECAT" 2051164 T PDECAT (NIL) -9 NIL 2051877 NIL) (-891 2049283 2049316 2049406 "PCOMP" 2049493 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-890 2047488 2048084 2048381 "PBWLB" 2049012 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-889 2039988 2041561 2042899 "PATTERN" 2046171 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-888 2039620 2039677 2039786 "PATTERN2" 2039925 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-887 2037377 2037765 2038222 "PATTERN1" 2039209 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-886 2034772 2035326 2035807 "PATRES" 2036942 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-885 2034336 2034403 2034535 "PATRES2" 2034699 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-884 2032219 2032624 2033031 "PATMATCH" 2034003 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-883 2031755 2031938 2031979 "PATMAB" 2032086 NIL PATMAB (NIL T) -9 NIL 2032169 NIL) (-882 2030300 2030609 2030867 "PATLRES" 2031560 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-881 2029846 2029969 2030010 "PATAB" 2030015 NIL PATAB (NIL T) -9 NIL 2030187 NIL) (-880 2027327 2027859 2028432 "PARTPERM" 2029293 T PARTPERM (NIL) -7 NIL NIL NIL) (-879 2026948 2027011 2027113 "PARSURF" 2027258 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-878 2026580 2026637 2026746 "PARSU2" 2026885 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-877 2026344 2026384 2026451 "PARSER" 2026533 T PARSER (NIL) -7 NIL NIL NIL) (-876 2025965 2026028 2026130 "PARSCURV" 2026275 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-875 2025597 2025654 2025763 "PARSC2" 2025902 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-874 2025236 2025294 2025391 "PARPCURV" 2025533 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-873 2024868 2024925 2025034 "PARPC2" 2025173 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-872 2024388 2024474 2024593 "PAN2EXPR" 2024769 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-871 2023192 2023509 2023737 "PALETTE" 2024180 T PALETTE (NIL) -8 NIL NIL NIL) (-870 2021660 2022197 2022557 "PAIR" 2022878 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-869 2015557 2020919 2021113 "PADICRC" 2021515 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-868 2008813 2014903 2015087 "PADICRAT" 2015405 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-867 2007155 2008750 2008795 "PADIC" 2008800 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-866 2004357 2005895 2005935 "PADICCT" 2006516 NIL PADICCT (NIL NIL) -9 NIL 2006798 NIL) (-865 2003314 2003514 2003782 "PADEPAC" 2004144 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-864 2002526 2002659 2002865 "PADE" 2003176 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-863 2000940 2001734 2002014 "OWP" 2002330 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-862 2000460 2000646 2000743 "OVERSET" 2000863 T OVERSET (NIL) -8 NIL NIL NIL) (-861 1999533 2000065 2000237 "OVAR" 2000328 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-860 1998797 1998918 1999079 "OUT" 1999392 T OUT (NIL) -7 NIL NIL NIL) (-859 1987695 1989906 1992106 "OUTFORM" 1996617 T OUTFORM (NIL) -8 NIL NIL NIL) (-858 1987031 1987292 1987419 "OUTBFILE" 1987588 T OUTBFILE (NIL) -8 NIL NIL NIL) (-857 1986338 1986503 1986531 "OUTBCON" 1986849 T OUTBCON (NIL) -9 NIL 1987015 NIL) (-856 1985939 1986051 1986208 "OUTBCON-" 1986213 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-855 1985346 1985668 1985757 "OSI" 1985870 T OSI (NIL) -8 NIL NIL NIL) (-854 1984902 1985214 1985242 "OSGROUP" 1985247 T OSGROUP (NIL) -9 NIL 1985269 NIL) (-853 1983647 1983874 1984159 "ORTHPOL" 1984649 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-852 1981225 1983482 1983603 "OREUP" 1983608 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-851 1978655 1980916 1981043 "ORESUP" 1981167 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-850 1976183 1976683 1977244 "OREPCTO" 1978144 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-849 1969999 1972174 1972215 "OREPCAT" 1974563 NIL OREPCAT (NIL T) -9 NIL 1975667 NIL) (-848 1967146 1967928 1968986 "OREPCAT-" 1968991 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-847 1966323 1966595 1966623 "ORDSET" 1966932 T ORDSET (NIL) -9 NIL 1967096 NIL) (-846 1965842 1965964 1966157 "ORDSET-" 1966162 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-845 1964468 1965233 1965261 "ORDRING" 1965463 T ORDRING (NIL) -9 NIL 1965588 NIL) (-844 1964113 1964207 1964351 "ORDRING-" 1964356 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-843 1963519 1963956 1963984 "ORDMON" 1963989 T ORDMON (NIL) -9 NIL 1964010 NIL) (-842 1962681 1962828 1963023 "ORDFUNS" 1963368 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-841 1962045 1962438 1962466 "ORDFIN" 1962531 T ORDFIN (NIL) -9 NIL 1962605 NIL) (-840 1958631 1960631 1961040 "ORDCOMP" 1961669 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-839 1957897 1958024 1958210 "ORDCOMP2" 1958491 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-838 1954505 1955388 1956202 "OPTPROB" 1957103 T OPTPROB (NIL) -8 NIL NIL NIL) (-837 1951307 1951946 1952650 "OPTPACK" 1953821 T OPTPACK (NIL) -7 NIL NIL NIL) (-836 1949020 1949760 1949788 "OPTCAT" 1950607 T OPTCAT (NIL) -9 NIL 1951257 NIL) (-835 1948463 1948697 1948802 "OPSIG" 1948935 T OPSIG (NIL) -8 NIL NIL NIL) (-834 1948231 1948270 1948336 "OPQUERY" 1948417 T OPQUERY (NIL) -7 NIL NIL NIL) (-833 1945389 1946542 1947046 "OP" 1947760 NIL OP (NIL T) -8 NIL NIL NIL) (-832 1944924 1945095 1945136 "OPERCAT" 1945271 NIL OPERCAT (NIL T) -9 NIL 1945339 NIL) (-831 1944770 1944797 1944883 "OPERCAT-" 1944888 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-830 1941609 1943567 1943936 "ONECOMP" 1944434 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-829 1940914 1941029 1941203 "ONECOMP2" 1941481 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-828 1940333 1940439 1940569 "OMSERVER" 1940804 T OMSERVER (NIL) -7 NIL NIL NIL) (-827 1937221 1939773 1939813 "OMSAGG" 1939874 NIL OMSAGG (NIL T) -9 NIL 1939938 NIL) (-826 1935844 1936107 1936389 "OMPKG" 1936959 T OMPKG (NIL) -7 NIL NIL NIL) (-825 1935274 1935377 1935405 "OM" 1935704 T OM (NIL) -9 NIL NIL NIL) (-824 1933848 1934823 1934992 "OMLO" 1935155 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-823 1932773 1932920 1933147 "OMEXPR" 1933674 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-822 1932091 1932319 1932455 "OMERR" 1932657 T OMERR (NIL) -8 NIL NIL NIL) (-821 1931269 1931512 1931672 "OMERRK" 1931951 T OMERRK (NIL) -8 NIL NIL NIL) (-820 1930747 1930946 1931054 "OMENC" 1931181 T OMENC (NIL) -8 NIL NIL NIL) (-819 1924642 1925827 1926998 "OMDEV" 1929596 T OMDEV (NIL) -8 NIL NIL NIL) (-818 1923711 1923882 1924076 "OMCONN" 1924468 T OMCONN (NIL) -8 NIL NIL NIL) (-817 1922324 1923274 1923302 "OINTDOM" 1923307 T OINTDOM (NIL) -9 NIL 1923328 NIL) (-816 1918130 1919314 1920030 "OFMONOID" 1921640 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-815 1917568 1918067 1918112 "ODVAR" 1918117 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-814 1915018 1917313 1917468 "ODR" 1917473 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-813 1907354 1914794 1914920 "ODPOL" 1914925 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-812 1901224 1907226 1907331 "ODP" 1907336 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-811 1899990 1900205 1900480 "ODETOOLS" 1900998 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-810 1896957 1897615 1898331 "ODESYS" 1899323 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-809 1891839 1892747 1893772 "ODERTRIC" 1896032 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-808 1891265 1891347 1891541 "ODERED" 1891751 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-807 1888153 1888701 1889378 "ODERAT" 1890688 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-806 1885110 1885577 1886174 "ODEPRRIC" 1887682 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-805 1883080 1883649 1884135 "ODEPROB" 1884644 T ODEPROB (NIL) -8 NIL NIL NIL) (-804 1879600 1880085 1880732 "ODEPRIM" 1882559 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-803 1878849 1878951 1879211 "ODEPAL" 1879492 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-802 1875011 1875802 1876666 "ODEPACK" 1878005 T ODEPACK (NIL) -7 NIL NIL NIL) (-801 1874044 1874151 1874380 "ODEINT" 1874900 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-800 1868145 1869570 1871017 "ODEIFTBL" 1872617 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-799 1863480 1864266 1865225 "ODEEF" 1867304 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-798 1862815 1862904 1863134 "ODECONST" 1863385 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-797 1860966 1861601 1861629 "ODECAT" 1862234 T ODECAT (NIL) -9 NIL 1862765 NIL) (-796 1857865 1860678 1860797 "OCT" 1860879 NIL OCT (NIL T) -8 NIL NIL NIL) (-795 1857503 1857546 1857673 "OCTCT2" 1857816 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-794 1852269 1854677 1854717 "OC" 1855814 NIL OC (NIL T) -9 NIL 1856672 NIL) (-793 1849496 1850244 1851234 "OC-" 1851328 NIL OC- (NIL T T) -8 NIL NIL NIL) (-792 1848874 1849316 1849344 "OCAMON" 1849349 T OCAMON (NIL) -9 NIL 1849370 NIL) (-791 1848431 1848746 1848774 "OASGP" 1848779 T OASGP (NIL) -9 NIL 1848799 NIL) (-790 1847718 1848181 1848209 "OAMONS" 1848249 T OAMONS (NIL) -9 NIL 1848292 NIL) (-789 1847158 1847565 1847593 "OAMON" 1847598 T OAMON (NIL) -9 NIL 1847618 NIL) (-788 1846462 1846954 1846982 "OAGROUP" 1846987 T OAGROUP (NIL) -9 NIL 1847007 NIL) (-787 1846152 1846202 1846290 "NUMTUBE" 1846406 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-786 1839725 1841243 1842779 "NUMQUAD" 1844636 T NUMQUAD (NIL) -7 NIL NIL NIL) (-785 1835481 1836469 1837494 "NUMODE" 1838720 T NUMODE (NIL) -7 NIL NIL NIL) (-784 1832862 1833716 1833744 "NUMINT" 1834667 T NUMINT (NIL) -9 NIL 1835431 NIL) (-783 1831810 1832007 1832225 "NUMFMT" 1832664 T NUMFMT (NIL) -7 NIL NIL NIL) (-782 1818169 1821114 1823646 "NUMERIC" 1829317 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-781 1812566 1817618 1817713 "NTSCAT" 1817718 NIL NTSCAT (NIL T T T T) -9 NIL 1817757 NIL) (-780 1811760 1811925 1812118 "NTPOLFN" 1812405 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-779 1799592 1808585 1809397 "NSUP" 1810981 NIL NSUP (NIL T) -8 NIL NIL NIL) (-778 1799224 1799281 1799390 "NSUP2" 1799529 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-777 1789207 1798998 1799131 "NSMP" 1799136 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-776 1787639 1787940 1788297 "NREP" 1788895 NIL NREP (NIL T) -7 NIL NIL NIL) (-775 1786230 1786482 1786840 "NPCOEF" 1787382 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-774 1785296 1785411 1785627 "NORMRETR" 1786111 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-773 1783337 1783627 1784036 "NORMPK" 1785004 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-772 1783022 1783050 1783174 "NORMMA" 1783303 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-771 1782849 1782979 1783008 "NONE" 1783013 T NONE (NIL) -8 NIL NIL NIL) (-770 1782638 1782667 1782736 "NONE1" 1782813 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-769 1782121 1782183 1782369 "NODE1" 1782570 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-768 1780391 1781215 1781470 "NNI" 1781817 T NNI (NIL) -8 NIL NIL 1782052) (-767 1778811 1779124 1779488 "NLINSOL" 1780059 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-766 1775079 1776047 1776946 "NIPROB" 1777932 T NIPROB (NIL) -8 NIL NIL NIL) (-765 1773836 1774070 1774372 "NFINTBAS" 1774841 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-764 1773010 1773486 1773527 "NETCLT" 1773699 NIL NETCLT (NIL T) -9 NIL 1773781 NIL) (-763 1771718 1771949 1772230 "NCODIV" 1772778 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-762 1771480 1771517 1771592 "NCNTFRAC" 1771675 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-761 1769660 1770024 1770444 "NCEP" 1771105 NIL NCEP (NIL T) -7 NIL NIL NIL) (-760 1768557 1769304 1769332 "NASRING" 1769442 T NASRING (NIL) -9 NIL 1769522 NIL) (-759 1768352 1768396 1768490 "NASRING-" 1768495 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-758 1767505 1768004 1768032 "NARNG" 1768149 T NARNG (NIL) -9 NIL 1768240 NIL) (-757 1767197 1767264 1767398 "NARNG-" 1767403 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-756 1766076 1766283 1766518 "NAGSP" 1766982 T NAGSP (NIL) -7 NIL NIL NIL) (-755 1757348 1759032 1760705 "NAGS" 1764423 T NAGS (NIL) -7 NIL NIL NIL) (-754 1755896 1756204 1756535 "NAGF07" 1757037 T NAGF07 (NIL) -7 NIL NIL NIL) (-753 1750434 1751725 1753032 "NAGF04" 1754609 T NAGF04 (NIL) -7 NIL NIL NIL) (-752 1743402 1745016 1746649 "NAGF02" 1748821 T NAGF02 (NIL) -7 NIL NIL NIL) (-751 1738626 1739726 1740843 "NAGF01" 1742305 T NAGF01 (NIL) -7 NIL NIL NIL) (-750 1732254 1733820 1735405 "NAGE04" 1737061 T NAGE04 (NIL) -7 NIL NIL NIL) (-749 1723423 1725544 1727674 "NAGE02" 1730144 T NAGE02 (NIL) -7 NIL NIL NIL) (-748 1719376 1720323 1721287 "NAGE01" 1722479 T NAGE01 (NIL) -7 NIL NIL NIL) (-747 1717171 1717705 1718263 "NAGD03" 1718838 T NAGD03 (NIL) -7 NIL NIL NIL) (-746 1708921 1710849 1712803 "NAGD02" 1715237 T NAGD02 (NIL) -7 NIL NIL NIL) (-745 1702732 1704157 1705597 "NAGD01" 1707501 T NAGD01 (NIL) -7 NIL NIL NIL) (-744 1698941 1699763 1700600 "NAGC06" 1701915 T NAGC06 (NIL) -7 NIL NIL NIL) (-743 1697406 1697738 1698094 "NAGC05" 1698605 T NAGC05 (NIL) -7 NIL NIL NIL) (-742 1696782 1696901 1697045 "NAGC02" 1697282 T NAGC02 (NIL) -7 NIL NIL NIL) (-741 1695842 1696399 1696439 "NAALG" 1696518 NIL NAALG (NIL T) -9 NIL 1696579 NIL) (-740 1695677 1695706 1695796 "NAALG-" 1695801 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-739 1689627 1690735 1691922 "MULTSQFR" 1694573 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-738 1688946 1689021 1689205 "MULTFACT" 1689539 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-737 1682031 1685909 1685962 "MTSCAT" 1687032 NIL MTSCAT (NIL T T) -9 NIL 1687546 NIL) (-736 1681743 1681797 1681889 "MTHING" 1681971 NIL MTHING (NIL T) -7 NIL NIL NIL) (-735 1681535 1681568 1681628 "MSYSCMD" 1681703 T MSYSCMD (NIL) -7 NIL NIL NIL) (-734 1677644 1680290 1680610 "MSET" 1681248 NIL MSET (NIL T) -8 NIL NIL NIL) (-733 1674739 1677205 1677246 "MSETAGG" 1677251 NIL MSETAGG (NIL T) -9 NIL 1677285 NIL) (-732 1670607 1672118 1672863 "MRING" 1674039 NIL MRING (NIL T T) -8 NIL NIL NIL) (-731 1670173 1670240 1670371 "MRF2" 1670534 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-730 1669791 1669826 1669970 "MRATFAC" 1670132 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-729 1667403 1667698 1668129 "MPRFF" 1669496 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-728 1661455 1667257 1667354 "MPOLY" 1667359 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-727 1660945 1660980 1661188 "MPCPF" 1661414 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-726 1660459 1660502 1660686 "MPC3" 1660896 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-725 1659654 1659735 1659956 "MPC2" 1660374 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1657955 1658292 1658682 "MONOTOOL" 1659314 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-723 1657206 1657497 1657525 "MONOID" 1657744 T MONOID (NIL) -9 NIL 1657891 NIL) (-722 1656752 1656871 1657052 "MONOID-" 1657057 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-721 1647603 1653519 1653578 "MONOGEN" 1654252 NIL MONOGEN (NIL T T) -9 NIL 1654708 NIL) (-720 1644821 1645556 1646556 "MONOGEN-" 1646675 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-719 1643680 1644100 1644128 "MONADWU" 1644520 T MONADWU (NIL) -9 NIL 1644758 NIL) (-718 1643052 1643211 1643459 "MONADWU-" 1643464 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-717 1642437 1642655 1642683 "MONAD" 1642890 T MONAD (NIL) -9 NIL 1643002 NIL) (-716 1642122 1642200 1642332 "MONAD-" 1642337 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-715 1640438 1641035 1641314 "MOEBIUS" 1641875 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-714 1639830 1640208 1640248 "MODULE" 1640253 NIL MODULE (NIL T) -9 NIL 1640279 NIL) (-713 1639398 1639494 1639684 "MODULE-" 1639689 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-712 1637105 1637762 1638089 "MODRING" 1639222 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-711 1634076 1635210 1635731 "MODOP" 1636634 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-710 1632691 1633143 1633420 "MODMONOM" 1633939 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-709 1622488 1630982 1631396 "MODMON" 1632328 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-708 1619671 1621332 1621608 "MODFIELD" 1622363 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-707 1618675 1618952 1619142 "MMLFORM" 1619501 T MMLFORM (NIL) -8 NIL NIL NIL) (-706 1618201 1618244 1618423 "MMAP" 1618626 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-705 1616410 1617151 1617192 "MLO" 1617615 NIL MLO (NIL T) -9 NIL 1617857 NIL) (-704 1613776 1614292 1614894 "MLIFT" 1615891 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-703 1613167 1613251 1613405 "MKUCFUNC" 1613687 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-702 1612766 1612836 1612959 "MKRECORD" 1613090 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-701 1611813 1611975 1612203 "MKFUNC" 1612577 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-700 1611201 1611305 1611461 "MKFLCFN" 1611696 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-699 1610744 1611111 1611170 "MKCHSET" 1611175 NIL MKCHSET (NIL T) -8 NIL NIL NIL) (-698 1610021 1610123 1610308 "MKBCFUNC" 1610637 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1606755 1609575 1609711 "MINT" 1609905 T MINT (NIL) -8 NIL NIL NIL) (-696 1605567 1605810 1606087 "MHROWRED" 1606510 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1600974 1604102 1604507 "MFLOAT" 1605182 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600331 1600407 1600578 "MFINFACT" 1600886 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1596646 1597494 1598378 "MESH" 1599467 T MESH (NIL) -7 NIL NIL NIL) (-692 1595036 1595348 1595701 "MDDFACT" 1596333 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1591878 1594195 1594236 "MDAGG" 1594491 NIL MDAGG (NIL T) -9 NIL 1594634 NIL) (-690 1581648 1591171 1591378 "MCMPLX" 1591691 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1580789 1580935 1581135 "MCDEN" 1581497 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1578679 1578949 1579329 "MCALCFN" 1580519 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1577604 1577844 1578077 "MAYBE" 1578485 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575216 1575739 1576301 "MATSTOR" 1577075 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571221 1574588 1574836 "MATRIX" 1575001 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1566985 1567694 1568430 "MATLIN" 1570578 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557139 1560277 1560354 "MATCAT" 1565234 NIL MATCAT (NIL T T T) -9 NIL 1566651 NIL) (-682 1553495 1554516 1555872 "MATCAT-" 1555877 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552089 1552242 1552575 "MATCAT2" 1553330 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550201 1550525 1550909 "MAPPKG3" 1551764 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549182 1549355 1549577 "MAPPKG2" 1550025 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1547681 1547965 1548292 "MAPPKG1" 1548888 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1546787 1547087 1547264 "MAPPAST" 1547524 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1546398 1546456 1546579 "MAPHACK3" 1546723 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1545990 1546051 1546165 "MAPHACK2" 1546330 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1545427 1545531 1545673 "MAPHACK1" 1545881 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1543533 1544127 1544431 "MAGMA" 1545155 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543039 1543257 1543348 "MACROAST" 1543462 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1539505 1541278 1541739 "M3D" 1542611 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1533659 1537874 1537915 "LZSTAGG" 1538697 NIL LZSTAGG (NIL T) -9 NIL 1538992 NIL) (-669 1529616 1530790 1532247 "LZSTAGG-" 1532252 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1526730 1527507 1527994 "LWORD" 1529161 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526333 1526534 1526609 "LSTAST" 1526675 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1519526 1526104 1526238 "LSQM" 1526243 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1518750 1518889 1519117 "LSPP" 1519381 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1516562 1516863 1517319 "LSMP" 1518439 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513341 1514015 1514745 "LSMP1" 1515864 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507266 1512508 1512549 "LSAGG" 1512611 NIL LSAGG (NIL T) -9 NIL 1512689 NIL) (-661 1503961 1504885 1506098 "LSAGG-" 1506103 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1501587 1503105 1503354 "LPOLY" 1503756 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501169 1501254 1501377 "LPEFRAC" 1501496 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1499516 1500263 1500516 "LO" 1501001 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499168 1499280 1499308 "LOGIC" 1499419 T LOGIC (NIL) -9 NIL 1499500 NIL) (-656 1499030 1499053 1499124 "LOGIC-" 1499129 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498223 1498363 1498556 "LODOOPS" 1498886 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1495673 1498139 1498205 "LODO" 1498210 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494211 1494446 1494799 "LODOF" 1495420 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1490559 1492964 1493005 "LODOCAT" 1493443 NIL LODOCAT (NIL T) -9 NIL 1493654 NIL) (-651 1490292 1490350 1490477 "LODOCAT-" 1490482 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1487639 1490133 1490251 "LODO2" 1490256 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485101 1487576 1487621 "LODO1" 1487626 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1483961 1484126 1484438 "LODEEF" 1484924 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479247 1482091 1482132 "LNAGG" 1483079 NIL LNAGG (NIL T) -9 NIL 1483523 NIL) (-646 1478394 1478608 1478950 "LNAGG-" 1478955 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1474557 1475319 1475958 "LMOPS" 1477809 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1473952 1474314 1474355 "LMODULE" 1474416 NIL LMODULE (NIL T) -9 NIL 1474458 NIL) (-643 1471198 1473597 1473720 "LMDICT" 1473862 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1470924 1471106 1471166 "LITERAL" 1471171 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464155 1469870 1470168 "LIST" 1470659 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1463680 1463754 1463893 "LIST3" 1464075 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1462687 1462865 1463093 "LIST2" 1463498 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1460821 1461133 1461532 "LIST2MAP" 1462334 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1459543 1460187 1460228 "LINEXP" 1460483 NIL LINEXP (NIL T) -9 NIL 1460632 NIL) (-636 1458190 1458450 1458747 "LINDEP" 1459295 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1454957 1455676 1456453 "LIMITRF" 1457445 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453232 1453528 1453944 "LIMITPS" 1454652 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1447687 1452743 1452971 "LIE" 1453053 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1446736 1447179 1447219 "LIECAT" 1447359 NIL LIECAT (NIL T) -9 NIL 1447510 NIL) (-631 1446577 1446604 1446692 "LIECAT-" 1446697 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439189 1446026 1446191 "LIB" 1446432 T LIB (NIL) -8 NIL NIL NIL) (-629 1434824 1435707 1436642 "LGROBP" 1438306 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1432690 1432964 1433326 "LF" 1434545 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1431530 1432222 1432250 "LFCAT" 1432457 T LFCAT (NIL) -9 NIL 1432596 NIL) (-626 1428432 1429062 1429750 "LEXTRIPK" 1430894 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425203 1426002 1426505 "LEXP" 1428012 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1424706 1424924 1425016 "LETAST" 1425131 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423104 1423417 1423818 "LEADCDET" 1424388 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422294 1422368 1422597 "LAZM3PK" 1423025 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417238 1420371 1420909 "LAUPOL" 1421806 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1416803 1416847 1417015 "LAPLACE" 1417188 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1414769 1415904 1416155 "LA" 1416636 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1413842 1414400 1414441 "LALG" 1414503 NIL LALG (NIL T) -9 NIL 1414562 NIL) (-617 1413556 1413615 1413751 "LALG-" 1413756 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413391 1413415 1413456 "KVTFROM" 1413518 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412191 1412608 1412837 "KTVLOGIC" 1413182 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412026 1412050 1412091 "KRCFROM" 1412153 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1410930 1411117 1411416 "KOVACIC" 1411826 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1410765 1410789 1410830 "KONVERT" 1410892 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1410600 1410624 1410665 "KOERCE" 1410727 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408334 1409094 1409487 "KERNEL" 1410239 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1407836 1407917 1408047 "KERNEL2" 1408248 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1401687 1406375 1406429 "KDAGG" 1406806 NIL KDAGG (NIL T T) -9 NIL 1407012 NIL) (-607 1401216 1401340 1401545 "KDAGG-" 1401550 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394391 1400877 1401032 "KAFILE" 1401094 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1388846 1393902 1394130 "JORDAN" 1394212 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388252 1388495 1388616 "JOINAST" 1388745 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388098 1388157 1388212 "JAVACODE" 1388217 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1384397 1386303 1386357 "IXAGG" 1387286 NIL IXAGG (NIL T T) -9 NIL 1387745 NIL) (-601 1383316 1383622 1384041 "IXAGG-" 1384046 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1378896 1383238 1383297 "IVECTOR" 1383302 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1377662 1377899 1378165 "ITUPLE" 1378663 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376098 1376275 1376581 "ITRIGMNP" 1377484 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1374843 1375047 1375330 "ITFUN3" 1375874 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1374475 1374532 1374641 "ITFUN2" 1374780 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372304 1373337 1373636 "ITAYLOR" 1374209 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361276 1366441 1367604 "ISUPS" 1371174 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360380 1360520 1360756 "ISUMP" 1361123 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1355644 1360181 1360260 "ISTRING" 1360333 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355147 1355365 1355457 "ISAST" 1355572 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354357 1354438 1354654 "IRURPK" 1355061 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353293 1353494 1353734 "IRSN" 1354137 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351322 1351677 1352113 "IRRF2F" 1352931 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351069 1351107 1351183 "IRREDFFX" 1351278 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1349684 1349943 1350242 "IROOT" 1350802 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346315 1347368 1348060 "IR" 1349024 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1343928 1344423 1344989 "IR2" 1345793 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343000 1343113 1343334 "IR2F" 1343811 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1342791 1342825 1342885 "IPRNTPK" 1342960 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1339398 1342680 1342749 "IPF" 1342754 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1337752 1339323 1339380 "IPADIC" 1339385 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337091 1337312 1337442 "IP4ADDR" 1337642 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1336591 1336795 1336905 "IOMODE" 1337001 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1335664 1336188 1336315 "IOBFILE" 1336484 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335152 1335568 1335596 "IOBCON" 1335601 T IOBCON (NIL) -9 NIL 1335622 NIL) (-575 1334649 1334707 1334897 "INVLAPLA" 1335088 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324297 1326651 1329037 "INTTR" 1332313 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1320641 1321383 1322247 "INTTOOLS" 1323482 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320227 1320318 1320435 "INTSLPE" 1320544 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318208 1320150 1320209 "INTRVL" 1320214 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1315810 1316322 1316897 "INTRF" 1317693 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315221 1315318 1315460 "INTRET" 1315708 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313218 1313607 1314077 "INTRAT" 1314829 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1310446 1311029 1311655 "INTPM" 1312703 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307148 1307748 1308493 "INTPAF" 1309832 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302327 1303289 1304340 "INTPACK" 1306117 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299231 1302056 1302183 "INT" 1302220 T INT (NIL) -8 NIL NIL NIL) (-563 1298483 1298635 1298843 "INTHERTR" 1299073 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1297922 1298002 1298190 "INTHERAL" 1298397 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1295768 1296211 1296668 "INTHEORY" 1297485 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287076 1288697 1290476 "INTG0" 1294120 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1267649 1272439 1277249 "INTFTBL" 1282286 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1266898 1267036 1267209 "INTFACT" 1267508 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264283 1264729 1265293 "INTEF" 1266452 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1262742 1263455 1263483 "INTDOM" 1263784 T INTDOM (NIL) -9 NIL 1263991 NIL) (-555 1262111 1262285 1262527 "INTDOM-" 1262532 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1258598 1260495 1260549 "INTCAT" 1261348 NIL INTCAT (NIL T) -9 NIL 1261668 NIL) (-553 1258070 1258173 1258301 "INTBIT" 1258490 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1256741 1256895 1257209 "INTALG" 1257915 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256198 1256288 1256458 "INTAF" 1256645 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1249652 1256008 1256148 "INTABL" 1256153 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1248983 1249422 1249487 "INT8" 1249521 T INT8 (NIL) -8 NIL NIL 1249566) (-548 1248313 1248752 1248817 "INT64" 1248851 T INT64 (NIL) -8 NIL NIL 1248896) (-547 1247643 1248082 1248147 "INT32" 1248181 T INT32 (NIL) -8 NIL NIL 1248226) (-546 1246973 1247412 1247477 "INT16" 1247511 T INT16 (NIL) -8 NIL NIL 1247556) (-545 1241980 1244662 1244690 "INS" 1245624 T INS (NIL) -9 NIL 1246289 NIL) (-544 1239220 1239991 1240965 "INS-" 1241038 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1237995 1238222 1238520 "INPSIGN" 1238973 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237113 1237230 1237427 "INPRODPF" 1237875 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236007 1236124 1236361 "INPRODFF" 1236993 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235007 1235159 1235419 "INNMFACT" 1235843 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234204 1234301 1234489 "INMODGCD" 1234906 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1232712 1232957 1233281 "INFSP" 1233949 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1231896 1232013 1232196 "INFPROD0" 1232592 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1228778 1229961 1230476 "INFORM" 1231389 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228388 1228448 1228546 "INFORM1" 1228713 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1227911 1228000 1228114 "INFINITY" 1228294 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227087 1227631 1227732 "INETCLTS" 1227830 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1225703 1225953 1226274 "INEP" 1226835 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1224979 1225600 1225665 "INDE" 1225670 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1224543 1224611 1224728 "INCRMAPS" 1224906 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223361 1223812 1224018 "INBFILE" 1224357 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1218661 1219597 1220541 "INBFF" 1222449 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1217569 1217838 1217866 "INBCON" 1218379 T INBCON (NIL) -9 NIL 1218645 NIL) (-526 1216821 1217044 1217320 "INBCON-" 1217325 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216327 1216545 1216636 "INAST" 1216750 T INAST (NIL) -8 NIL NIL NIL) (-524 1215781 1216006 1216112 "IMPTAST" 1216241 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212275 1215625 1215729 "IMATRIX" 1215734 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1210987 1211110 1211425 "IMATQF" 1212131 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209207 1209434 1209771 "IMATLIN" 1210743 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1203833 1209131 1209189 "ILIST" 1209194 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1201786 1203693 1203806 "IIARRAY2" 1203811 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197211 1201697 1201761 "IFF" 1201766 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1196585 1196828 1196944 "IFAST" 1197115 T IFAST (NIL) -8 NIL NIL NIL) (-516 1191628 1195877 1196065 "IFARRAY" 1196442 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1190835 1191532 1191605 "IFAMON" 1191610 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1190419 1190484 1190538 "IEVALAB" 1190745 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190094 1190162 1190322 "IEVALAB-" 1190327 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1189752 1190008 1190071 "IDPO" 1190076 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189029 1189641 1189716 "IDPOAMS" 1189721 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188363 1188918 1188993 "IDPOAM" 1188998 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1187448 1187698 1187751 "IDPC" 1188164 NIL IDPC (NIL T T) -9 NIL 1188313 NIL) (-508 1186944 1187340 1187413 "IDPAM" 1187418 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186347 1186836 1186909 "IDPAG" 1186914 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186019 1186183 1186258 "IDENT" 1186292 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182274 1183122 1184017 "IDECOMP" 1185176 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175138 1176197 1177244 "IDEAL" 1181310 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174302 1174414 1174613 "ICDEN" 1175022 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1173400 1173782 1173929 "ICARD" 1174175 T ICARD (NIL) -8 NIL NIL NIL) (-501 1171460 1171773 1172178 "IBPTOOLS" 1173077 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167094 1171080 1171193 "IBITS" 1171379 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1163817 1164393 1165088 "IBATOOL" 1166511 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1161596 1162058 1162591 "IBACHIN" 1163352 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1159473 1161442 1161545 "IARRAY2" 1161550 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1155626 1159399 1159456 "IARRAY1" 1159461 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1149610 1154038 1154519 "IAN" 1155165 T IAN (NIL) -8 NIL NIL NIL) (-494 1149121 1149178 1149351 "IALGFACT" 1149547 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1148649 1148762 1148790 "HYPCAT" 1148997 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148187 1148304 1148490 "HYPCAT-" 1148495 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1147809 1147982 1148065 "HOSTNAME" 1148124 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1147654 1147691 1147732 "HOMOTOP" 1147737 NIL HOMOTOP (NIL T) -9 NIL 1147770 NIL) (-489 1144333 1145664 1145705 "HOAGG" 1146686 NIL HOAGG (NIL T) -9 NIL 1147365 NIL) (-488 1142927 1143326 1143852 "HOAGG-" 1143857 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1136958 1142522 1142671 "HEXADEC" 1142798 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1135706 1135928 1136191 "HEUGCD" 1136735 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1134809 1135543 1135673 "HELLFDIV" 1135678 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133036 1134586 1134674 "HEAP" 1134753 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132326 1132588 1132722 "HEADAST" 1132922 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126240 1132241 1132303 "HDP" 1132308 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1119983 1125875 1126027 "HDMP" 1126141 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119307 1119447 1119611 "HB" 1119839 T HB (NIL) -7 NIL NIL NIL) (-479 1112804 1119153 1119257 "HASHTBL" 1119262 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112307 1112525 1112617 "HASAST" 1112732 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110112 1111929 1112111 "HACKPI" 1112145 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1105807 1109965 1110078 "GTSET" 1110083 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099333 1105685 1105783 "GSTBL" 1105788 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1091638 1098364 1098629 "GSERIES" 1099124 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1090805 1091196 1091224 "GROUP" 1091427 T GROUP (NIL) -9 NIL 1091561 NIL) (-472 1090171 1090330 1090581 "GROUP-" 1090586 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1088538 1088859 1089246 "GROEBSOL" 1089848 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1087478 1087740 1087791 "GRMOD" 1088320 NIL GRMOD (NIL T T) -9 NIL 1088488 NIL) (-469 1087246 1087282 1087410 "GRMOD-" 1087415 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1082563 1083600 1084600 "GRIMAGE" 1086266 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081029 1081290 1081614 "GRDEF" 1082259 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1080473 1080589 1080730 "GRAY" 1080908 T GRAY (NIL) -7 NIL NIL NIL) (-465 1079686 1080066 1080117 "GRALG" 1080270 NIL GRALG (NIL T T) -9 NIL 1080363 NIL) (-464 1079347 1079420 1079583 "GRALG-" 1079588 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076151 1078932 1079110 "GPOLSET" 1079254 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1075505 1075562 1075820 "GOSPER" 1076088 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071264 1071943 1072469 "GMODPOL" 1075204 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070269 1070453 1070691 "GHENSEL" 1071076 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064320 1065163 1066190 "GENUPS" 1069353 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064017 1064068 1064157 "GENUFACT" 1064263 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1063429 1063506 1063671 "GENPGCD" 1063935 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1062903 1062938 1063151 "GENMFACT" 1063388 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1061469 1061726 1062033 "GENEEZ" 1062646 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055370 1061080 1061242 "GDMP" 1061392 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1044739 1049141 1050247 "GCNAALG" 1054353 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043158 1043994 1044022 "GCDDOM" 1044277 T GCDDOM (NIL) -9 NIL 1044434 NIL) (-451 1042628 1042755 1042970 "GCDDOM-" 1042975 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041300 1041485 1041789 "GB" 1042407 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1029916 1032246 1034638 "GBINTERN" 1038991 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1027753 1028045 1028466 "GBF" 1029591 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1026534 1026699 1026966 "GBEUCLID" 1027569 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1025883 1026008 1026157 "GAUSSFAC" 1026405 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024250 1024552 1024866 "GALUTIL" 1025602 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1022558 1022832 1023156 "GALPOLYU" 1023977 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1019923 1020213 1020620 "GALFACTU" 1022255 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1011729 1013228 1014836 "GALFACT" 1018355 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009117 1009775 1009803 "FVFUN" 1010959 T FVFUN (NIL) -9 NIL 1011679 NIL) (-440 1008383 1008565 1008593 "FVC" 1008884 T FVC (NIL) -9 NIL 1009067 NIL) (-439 1008053 1008208 1008276 "FUNDESC" 1008335 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1007695 1007850 1007931 "FUNCTION" 1008005 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1005466 1006017 1006483 "FT" 1007249 T FT (NIL) -8 NIL NIL NIL) (-436 1004284 1004767 1004970 "FTEM" 1005283 T FTEM (NIL) -8 NIL NIL NIL) (-435 1002540 1002829 1003233 "FSUPFACT" 1003975 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1000937 1001226 1001558 "FST" 1002228 T FST (NIL) -8 NIL NIL NIL) (-433 1000108 1000214 1000409 "FSRED" 1000819 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 998786 999042 999396 "FSPRMELT" 999823 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 995871 996309 996808 "FSPECF" 998349 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 977925 986374 986414 "FS" 990262 NIL FS (NIL T) -9 NIL 992551 NIL) (-429 966572 969565 973621 "FS-" 973918 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966086 966140 966317 "FSINT" 966513 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 964405 965079 965382 "FSERIES" 965865 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 963419 963535 963766 "FSCINT" 964285 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 959653 962363 962404 "FSAGG" 962774 NIL FSAGG (NIL T) -9 NIL 963033 NIL) (-424 957415 958016 958812 "FSAGG-" 958907 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 956457 956600 956827 "FSAGG2" 957268 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954111 954391 954945 "FS2UPS" 956175 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 953693 953736 953891 "FS2" 954062 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 952550 952721 953030 "FS2EXPXP" 953518 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 951976 952091 952243 "FRUTIL" 952430 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 943416 947471 948829 "FR" 950650 NIL FR (NIL T) -8 NIL NIL NIL) (-417 938491 941134 941174 "FRNAALG" 942570 NIL FRNAALG (NIL T) -9 NIL 943177 NIL) (-416 934164 935240 936515 "FRNAALG-" 937265 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 933802 933845 933972 "FRNAAF2" 934115 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932209 932656 932951 "FRMOD" 933614 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 929987 930592 930909 "FRIDEAL" 932000 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929182 929269 929558 "FRIDEAL2" 929894 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928315 928729 928770 "FRETRCT" 928775 NIL FRETRCT (NIL T) -9 NIL 928951 NIL) (-410 927427 927658 928009 "FRETRCT-" 928014 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 924631 925815 925874 "FRAMALG" 926756 NIL FRAMALG (NIL T T) -9 NIL 927048 NIL) (-408 922765 923220 923850 "FRAMALG-" 924073 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 916713 922240 922516 "FRAC" 922521 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916349 916406 916513 "FRAC2" 916650 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 915985 916042 916149 "FR2" 916286 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 910650 913510 913538 "FPS" 914657 T FPS (NIL) -9 NIL 915214 NIL) (-403 910099 910208 910372 "FPS-" 910518 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 907545 909188 909216 "FPC" 909441 T FPC (NIL) -9 NIL 909583 NIL) (-401 907338 907378 907475 "FPC-" 907480 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906216 906826 906867 "FPATMAB" 906872 NIL FPATMAB (NIL T) -9 NIL 907024 NIL) (-399 903916 904392 904818 "FPARFRAC" 905853 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899309 899808 900490 "FORTRAN" 903348 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897025 897525 898064 "FORT" 898790 T FORT (NIL) -7 NIL NIL NIL) (-396 894701 895263 895291 "FORTFN" 896351 T FORTFN (NIL) -9 NIL 896975 NIL) (-395 894465 894515 894543 "FORTCAT" 894602 T FORTCAT (NIL) -9 NIL 894664 NIL) (-394 892598 893081 893471 "FORMULA" 894095 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892386 892416 892485 "FORMULA1" 892562 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 891909 891961 892134 "FORDER" 892328 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891005 891169 891362 "FOP" 891736 T FOP (NIL) -7 NIL NIL NIL) (-390 889613 890285 890459 "FNLA" 890887 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888368 888757 888785 "FNCAT" 889245 T FNCAT (NIL) -9 NIL 889505 NIL) (-388 887934 888327 888355 "FNAME" 888360 T FNAME (NIL) -8 NIL NIL NIL) (-387 886589 887526 887554 "FMTC" 887559 T FMTC (NIL) -9 NIL 887595 NIL) (-386 882949 884112 884741 "FMONOID" 885993 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882168 882691 882840 "FM" 882845 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 879592 880238 880266 "FMFUN" 881410 T FMFUN (NIL) -9 NIL 882118 NIL) (-383 878861 879042 879070 "FMC" 879360 T FMC (NIL) -9 NIL 879542 NIL) (-382 876055 876889 876943 "FMCAT" 878138 NIL FMCAT (NIL T T) -9 NIL 878633 NIL) (-381 874948 875821 875921 "FM1" 876000 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 872722 873138 873632 "FLOATRP" 874499 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866323 870451 871072 "FLOAT" 872121 T FLOAT (NIL) -8 NIL NIL NIL) (-378 863761 864261 864839 "FLOATCP" 865790 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 862562 863374 863415 "FLINEXP" 863420 NIL FLINEXP (NIL T) -9 NIL 863513 NIL) (-376 861716 861951 862279 "FLINEXP-" 862284 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 860792 860936 861160 "FLASORT" 861568 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858009 858851 858903 "FLALG" 860130 NIL FLALG (NIL T T) -9 NIL 860597 NIL) (-373 851793 855495 855536 "FLAGG" 856798 NIL FLAGG (NIL T) -9 NIL 857450 NIL) (-372 850519 850858 851348 "FLAGG-" 851353 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 849561 849704 849931 "FLAGG2" 850372 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 846528 847510 847569 "FINRALG" 848697 NIL FINRALG (NIL T T) -9 NIL 849205 NIL) (-369 845688 845917 846256 "FINRALG-" 846261 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845094 845307 845335 "FINITE" 845531 T FINITE (NIL) -9 NIL 845638 NIL) (-367 837552 839713 839753 "FINAALG" 843420 NIL FINAALG (NIL T) -9 NIL 844873 NIL) (-366 832884 833934 835078 "FINAALG-" 836457 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832279 832639 832742 "FILE" 832814 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 830963 831275 831329 "FILECAT" 832013 NIL FILECAT (NIL T T) -9 NIL 832229 NIL) (-363 828823 830325 830353 "FIELD" 830393 T FIELD (NIL) -9 NIL 830473 NIL) (-362 827443 827828 828339 "FIELD-" 828344 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825320 826078 826425 "FGROUP" 827129 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 824410 824574 824794 "FGLMICPK" 825152 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820269 824335 824392 "FFX" 824397 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 819870 819931 820066 "FFSLPE" 820202 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 815859 816642 817438 "FFPOLY" 819106 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815363 815399 815608 "FFPOLY2" 815817 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811233 815282 815345 "FFP" 815350 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 806658 811144 811208 "FF" 811213 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 801811 806001 806191 "FFNBX" 806512 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 796767 800946 801204 "FFNBP" 801665 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 791427 796051 796262 "FFNB" 796600 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790259 790457 790772 "FFINTBAS" 791224 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 786479 788666 788694 "FFIELDC" 789314 T FFIELDC (NIL) -9 NIL 789690 NIL) (-348 785141 785512 786009 "FFIELDC-" 786014 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 784710 784756 784880 "FFHOM" 785083 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 782405 782892 783409 "FFF" 784225 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778050 782147 782248 "FFCGX" 782348 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 773698 777782 777889 "FFCGP" 777993 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 768908 773425 773533 "FFCG" 773634 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 750733 759779 759865 "FFCAT" 765030 NIL FFCAT (NIL T T T) -9 NIL 766481 NIL) (-341 745931 746978 748292 "FFCAT-" 749522 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745342 745385 745620 "FFCAT2" 745882 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 734539 738314 739534 "FEXPR" 744194 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 733539 733974 734015 "FEVALAB" 734099 NIL FEVALAB (NIL T) -9 NIL 734360 NIL) (-337 732698 732908 733246 "FEVALAB-" 733251 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731291 732081 732284 "FDIV" 732597 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728357 729072 729187 "FDIVCAT" 730755 NIL FDIVCAT (NIL T T T T) -9 NIL 731192 NIL) (-334 728119 728146 728316 "FDIVCAT-" 728321 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727339 727426 727703 "FDIV2" 728026 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726025 726284 726573 "FCPAK1" 727070 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725151 725525 725666 "FCOMP" 725916 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 708880 712301 715839 "FC" 721633 T FC (NIL) -8 NIL NIL NIL) (-329 701451 705444 705484 "FAXF" 707286 NIL FAXF (NIL T) -9 NIL 707978 NIL) (-328 698727 699385 700210 "FAXF-" 700675 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 693827 698103 698279 "FARRAY" 698584 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689072 691112 691165 "FAMR" 692188 NIL FAMR (NIL T T) -9 NIL 692648 NIL) (-325 687962 688264 688699 "FAMR-" 688704 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687158 687884 687937 "FAMONOID" 687942 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 684970 685654 685707 "FAMONC" 686648 NIL FAMONC (NIL T T) -9 NIL 687034 NIL) (-322 683662 684724 684861 "FAGROUP" 684866 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 681457 681776 682179 "FACUTIL" 683343 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 680556 680741 680963 "FACTFUNC" 681267 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 672953 679807 680019 "EXPUPXS" 680412 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 670436 670976 671562 "EXPRTUBE" 672387 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 666630 667222 667959 "EXPRODE" 669775 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 651996 665285 665713 "EXPR" 666234 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 646403 646990 647803 "EXPR2UPS" 651294 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646039 646096 646203 "EXPR2" 646340 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 637436 645171 645468 "EXPEXPAN" 645876 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637263 637393 637422 "EXIT" 637427 T EXIT (NIL) -8 NIL NIL NIL) (-311 636770 636987 637078 "EXITAST" 637192 T EXITAST (NIL) -8 NIL NIL NIL) (-310 636397 636459 636572 "EVALCYC" 636702 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 635938 636056 636097 "EVALAB" 636267 NIL EVALAB (NIL T) -9 NIL 636371 NIL) (-308 635419 635541 635762 "EVALAB-" 635767 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 632879 634155 634183 "EUCDOM" 634738 T EUCDOM (NIL) -9 NIL 635088 NIL) (-306 631284 631726 632316 "EUCDOM-" 632321 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 618822 621582 624332 "ESTOOLS" 628554 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 618454 618511 618620 "ESTOOLS2" 618759 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618205 618247 618327 "ESTOOLS1" 618406 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612110 613838 613866 "ES" 616634 T ES (NIL) -9 NIL 618043 NIL) (-301 607057 608344 610161 "ES-" 610325 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 603431 604192 604972 "ESCONT" 606297 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603176 603208 603290 "ESCONT1" 603393 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 602851 602901 603001 "ES2" 603120 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 602481 602539 602648 "ES1" 602787 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 601697 601826 602002 "ERROR" 602325 T ERROR (NIL) -7 NIL NIL NIL) (-295 595200 601556 601647 "EQTBL" 601652 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 587751 590514 591963 "EQ" 593784 NIL -3205 (NIL T) -8 NIL NIL NIL) (-293 587383 587440 587549 "EQ2" 587688 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 582672 583721 584814 "EP" 586322 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581250 581547 581859 "ENV" 582380 T ENV (NIL) -8 NIL NIL NIL) (-290 580421 580949 580977 "ENTIRER" 580982 T ENTIRER (NIL) -9 NIL 581028 NIL) (-289 576915 578376 578746 "EMR" 580220 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576059 576244 576298 "ELTAGG" 576678 NIL ELTAGG (NIL T T) -9 NIL 576889 NIL) (-287 575778 575840 575981 "ELTAGG-" 575986 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 575567 575596 575650 "ELTAB" 575734 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 574693 574839 575038 "ELFUTS" 575418 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 574435 574491 574519 "ELEMFUN" 574624 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574305 574326 574394 "ELEMFUN-" 574399 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569196 572405 572446 "ELAGG" 573386 NIL ELAGG (NIL T) -9 NIL 573849 NIL) (-281 567481 567915 568578 "ELAGG-" 568583 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566146 566424 566717 "ELABEXPR" 567208 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559010 560813 561640 "EFUPXS" 565422 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 552460 554261 555071 "EFULS" 558286 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 549882 550240 550719 "EFSTRUC" 552092 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 538953 540519 542079 "EF" 548397 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538054 538438 538587 "EAB" 538824 T EAB (NIL) -8 NIL NIL NIL) (-274 537263 538013 538041 "E04UCFA" 538046 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 536472 537222 537250 "E04NAFA" 537255 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 535681 536431 536459 "E04MBFA" 536464 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 534890 535640 535668 "E04JAFA" 535673 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534101 534849 534877 "E04GCFA" 534882 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533312 534060 534088 "E04FDFA" 534093 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 532521 533271 533299 "E04DGFA" 533304 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 526694 528046 529410 "E04AGNT" 531177 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 525400 525880 525920 "DVARCAT" 526395 NIL DVARCAT (NIL T) -9 NIL 526594 NIL) (-265 524604 524816 525130 "DVARCAT-" 525135 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 517496 524403 524532 "DSMP" 524537 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512305 513441 514509 "DROPT" 516448 T DROPT (NIL) -8 NIL NIL NIL) (-262 511970 512029 512127 "DROPT1" 512240 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507085 508211 509348 "DROPT0" 510853 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 505430 505755 506141 "DRAWPT" 506719 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500017 500940 502019 "DRAW" 504404 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 499650 499703 499821 "DRAWHACK" 499958 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 498381 498650 498941 "DRAWCX" 499379 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 497896 497965 498116 "DRAWCURV" 498307 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488364 490326 492441 "DRAWCFUN" 495801 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485177 487059 487100 "DQAGG" 487729 NIL DQAGG (NIL T) -9 NIL 488002 NIL) (-253 473448 480155 480238 "DPOLCAT" 482090 NIL DPOLCAT (NIL T T T T) -9 NIL 482635 NIL) (-252 468284 469633 471591 "DPOLCAT-" 471596 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 461433 468145 468243 "DPMO" 468248 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 454485 461213 461380 "DPMM" 461385 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454117 454404 454452 "DOMCTOR" 454457 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 453412 453639 453776 "DOMAIN" 454000 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447155 453047 453199 "DMP" 453313 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 446755 446811 446955 "DLP" 447093 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 440625 446082 446272 "DLIST" 446597 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 437469 439478 439519 "DLAGG" 440069 NIL DLAGG (NIL T) -9 NIL 440299 NIL) (-243 436274 436912 436940 "DIVRING" 437032 T DIVRING (NIL) -9 NIL 437115 NIL) (-242 435511 435701 436001 "DIVRING-" 436006 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 433613 433970 434376 "DISPLAY" 435125 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 427549 433527 433590 "DIRPROD" 433595 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 426397 426600 426865 "DIRPROD2" 427342 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 415654 421612 421665 "DIRPCAT" 422075 NIL DIRPCAT (NIL NIL T) -9 NIL 422915 NIL) (-237 412980 413622 414503 "DIRPCAT-" 414840 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412267 412427 412613 "DIOSP" 412814 T DIOSP (NIL) -7 NIL NIL NIL) (-235 408969 411179 411220 "DIOPS" 411654 NIL DIOPS (NIL T) -9 NIL 411883 NIL) (-234 408518 408632 408823 "DIOPS-" 408828 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 407402 408004 408032 "DIFRING" 408219 T DIFRING (NIL) -9 NIL 408329 NIL) (-232 407048 407125 407277 "DIFRING-" 407282 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 404845 406091 406132 "DIFEXT" 406495 NIL DIFEXT (NIL T) -9 NIL 406789 NIL) (-230 403130 403558 404224 "DIFEXT-" 404229 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 400452 402662 402703 "DIAGG" 402708 NIL DIAGG (NIL T) -9 NIL 402728 NIL) (-228 399836 399993 400245 "DIAGG-" 400250 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395301 398795 399072 "DHMATRIX" 399605 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 390913 391822 392832 "DFSFUN" 394311 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386018 389844 390156 "DFLOAT" 390621 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384246 384527 384923 "DFINTTLS" 385726 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381302 382267 382667 "DERHAM" 383912 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379151 381077 381166 "DEQUEUE" 381246 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378366 378499 378695 "DEGRED" 379013 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 374761 375506 376359 "DEFINTRF" 377594 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372288 372757 373356 "DEFINTEF" 374280 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 371665 371908 372023 "DEFAST" 372193 T DEFAST (NIL) -8 NIL NIL NIL) (-217 365696 371260 371409 "DECIMAL" 371536 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363206 363666 364172 "DDFACT" 365240 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 362802 362845 362996 "DBLRESP" 363157 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 360701 361035 361395 "DBASE" 362569 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 359970 360181 360327 "DATAARY" 360600 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359103 359929 359957 "D03FAFA" 359962 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358237 359062 359090 "D03EEFA" 359095 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356187 356653 357142 "D03AGNT" 357768 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 355503 356146 356174 "D02EJFA" 356179 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 354819 355462 355490 "D02CJFA" 355495 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354135 354778 354806 "D02BHFA" 354811 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 353451 354094 354122 "D02BBFA" 354127 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 346648 348237 349843 "D02AGNT" 351865 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 344416 344939 345485 "D01WGTS" 346122 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 343510 344375 344403 "D01TRNS" 344408 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 342605 343469 343497 "D01GBFA" 343502 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 341700 342564 342592 "D01FCFA" 342597 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 340795 341659 341687 "D01ASFA" 341692 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 339890 340754 340782 "D01AQFA" 340787 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 338985 339849 339877 "D01APFA" 339882 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338080 338944 338972 "D01ANFA" 338977 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337175 338039 338067 "D01AMFA" 338072 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336270 337134 337162 "D01ALFA" 337167 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335365 336229 336257 "D01AKFA" 336262 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 334460 335324 335352 "D01AJFA" 335357 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 327755 329308 330869 "D01AGNT" 332919 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327092 327220 327372 "CYCLOTOM" 327623 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 323827 324540 325267 "CYCLES" 326385 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323139 323273 323444 "CVMP" 323688 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 320910 321168 321544 "CTRIGMNP" 322867 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 320401 320701 320775 "CTOR" 320856 T CTOR (NIL) -8 NIL NIL NIL) (-186 319937 320132 320233 "CTORKIND" 320320 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319285 319544 319572 "CTORCAT" 319754 T CTORCAT (NIL) -9 NIL 319867 NIL) (-184 318883 318994 319153 "CTORCAT-" 319158 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 318399 318586 318684 "CTORCALL" 318805 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 317773 317872 318025 "CSTTOOLS" 318296 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 313572 314229 314987 "CRFP" 317085 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313074 313293 313385 "CRCEAST" 313500 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312121 312306 312534 "CRAPACK" 312878 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 311505 311606 311810 "CPMATCH" 311997 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311230 311258 311364 "CPIMA" 311471 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 307594 308266 308984 "COORDSYS" 310565 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307002 307124 307267 "CONTOUR" 307471 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 302920 305005 305497 "CONTFRAC" 306542 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 302800 302821 302849 "CONDUIT" 302886 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 301965 302493 302521 "COMRING" 302526 T COMRING (NIL) -9 NIL 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(-133 220861 221062 221137 "CAPSLAST" 221203 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220233 220561 220589 "CACHSET" 220721 T CACHSET (NIL) -9 NIL 220798 NIL) (-131 219729 220025 220053 "CABMON" 220103 T CABMON (NIL) -9 NIL 220159 NIL) (-130 219229 219433 219543 "BYTEORD" 219639 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218232 218763 218905 "BYTE" 219068 T BYTE (NIL) -8 NIL NIL 219190) (-128 213632 217737 217909 "BYTEBUF" 218080 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211189 213324 213431 "BTREE" 213558 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 208686 210837 210959 "BTOURN" 211099 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206103 208156 208197 "BTCAT" 208265 NIL BTCAT (NIL T) -9 NIL 208342 NIL) (-124 205770 205850 205999 "BTCAT-" 206004 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201062 204913 204941 "BTAGG" 205163 T BTAGG (NIL) -9 NIL 205324 NIL) (-122 200552 200677 200883 "BTAGG-" 200888 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 197595 199830 200045 "BSTREE" 200369 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 196733 196859 197043 "BRILL" 197451 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 193432 195459 195500 "BRAGG" 196149 NIL BRAGG (NIL T) -9 NIL 196407 NIL) (-118 191961 192367 192922 "BRAGG-" 192927 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185217 191307 191491 "BPADICRT" 191809 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 183559 185154 185199 "BPADIC" 185204 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183257 183287 183401 "BOUNDZRO" 183523 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 178772 179863 180730 "BOP" 182410 T BOP (NIL) -8 NIL NIL NIL) (-113 176393 176837 177357 "BOP1" 178285 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175095 175817 176010 "BOOLEAN" 176220 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174457 174835 174889 "BMODULE" 174894 NIL BMODULE (NIL T T) -9 NIL 174959 NIL) (-110 170285 174255 174328 "BITS" 174404 T BITS (NIL) -8 NIL NIL NIL) (-109 169697 169819 169961 "BINDING" 170163 T BINDING (NIL) -8 NIL NIL NIL) (-108 163731 169294 169442 "BINARY" 169569 T BINARY (NIL) -8 NIL NIL NIL) (-107 161558 162986 163027 "BGAGG" 163287 NIL BGAGG (NIL T) -9 NIL 163424 NIL) (-106 161389 161421 161512 "BGAGG-" 161517 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160487 160773 160978 "BFUNCT" 161204 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159177 159355 159643 "BEZOUT" 160311 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155694 158029 158359 "BBTREE" 158880 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155428 155481 155509 "BASTYPE" 155628 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155281 155309 155382 "BASTYPE-" 155387 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154715 154791 154943 "BALFACT" 155192 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153598 154130 154316 "AUTOMOR" 154560 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153324 153329 153355 "ATTREG" 153360 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151603 152021 152373 "ATTRBUT" 152990 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151238 151431 151497 "ATTRAST" 151555 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 150774 150887 150913 "ATRIG" 151114 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150583 150624 150711 "ATRIG-" 150716 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150254 150414 150440 "ASTCAT" 150445 T ASTCAT (NIL) -9 NIL 150475 NIL) (-92 149981 150040 150159 "ASTCAT-" 150164 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148178 149757 149845 "ASTACK" 149924 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146683 146980 147345 "ASSOCEQ" 147860 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145715 146342 146466 "ASP9" 146590 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145478 145663 145702 "ASP8" 145707 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144346 145083 145225 "ASP80" 145367 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143244 143981 144113 "ASP7" 144245 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142198 142921 143039 "ASP78" 143157 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141167 141878 141995 "ASP77" 142112 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140079 140805 140936 "ASP74" 141067 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 138979 139714 139846 "ASP73" 139978 NIL ASP73 (NIL 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"ARR2CAT-" 109107 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106996 107231 107310 "ARITY" 107343 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 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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 6dd8ed34..b9bc2cb0 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,72 +1,84 @@ -(735963 . 3449460963) -(((*1 *2 *1 *3) - (-12 (-5 *3 (-564)) (-4 *1 (-323 *4 *2)) (-4 *4 (-1094)) - (-4 *2 (-131))))) -(((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-108)))) - ((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-217)))) - ((*1 *2 *1) (-12 (-5 *2 (-407 (-564))) (-5 *1 (-487)))) - ((*1 *1 *1) (-12 (-4 *1 (-989 *2)) (-4 *2 (-556)) (-4 *2 (-307)))) - ((*1 *2 *1) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-1001 *3)) (-14 *3 (-564)))) - ((*1 *1 *1) (-4 *1 (-1055)))) -(((*1 *2 *1) (-12 (-5 *2 (-819)) (-5 *1 (-818))))) +(735988 . 3449600532) +(((*1 *2 *3) + (-12 (-4 *3 (-1235 (-407 (-564)))) + (-5 *2 (-2 (|:| |den| (-564)) (|:| |gcdnum| (-564)))) + (-5 *1 (-910 *3 *4)) (-4 *4 (-1235 (-407 *3))))) + ((*1 *2 *3) + (-12 (-4 *4 (-1235 (-407 *2))) (-5 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"failed")) + (-5 *4 (-3 (-2 (|:| -2745 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -1993 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2745 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -12277,7 +12736,7 @@ (-4 *8 (-1046)) (-4 *6 (-790)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -1846 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-768)))))) + (-10 -8 (-15 -1771 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-768)))))) (-5 *1 (-948 *6 *7 *8 *5 *2)) (-4 *5 (-946 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-955 *5)) (-4 *5 (-1209)) @@ -12290,8 +12749,8 @@ (-4 *2 (-946 (-949 *4) *5 *6)) (-4 *5 (-790)) (-4 *6 (-13 (-847) - (-10 -8 (-15 -2374 ((-1170) $)) - (-15 -3822 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -2127 ((-1170) $)) + (-15 -3657 ((-3 $ "failed") (-1170)))))) (-5 *1 (-981 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-556)) (-4 *6 (-556)) @@ -12378,397 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