diff options
Diffstat (limited to 'src/share/algebra')
| -rw-r--r-- | src/share/algebra/browse.daase | 636 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1212 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1320 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8896 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 30372 |
5 files changed, 21218 insertions, 21218 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 1ff95bd0..33a5561f 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,5 +1,5 @@ -(2283317 . 3451461726) +(2283317 . 3451578536) (-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 -2308) +(-32 R -2313) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) @@ -88,11 +88,11 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -2308 UP UPUP -3253) +(-40 -2313 UP UPUP -3281) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2797 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2797 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2797 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) -(-41 R -2308) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2750 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2750 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2750 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +(-41 R -2313) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -430) (|devaluate| |#1|))))) @@ -111,7 +111,7 @@ NIL (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) ((-4406 . T) (-4407 . T)) -((-2797 (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|))))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|))))))) +((-2750 (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|))))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -2308) +(-54 |Base| R -2313) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -167,64 +167,64 @@ NIL (-59 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-61 -2446) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-61 -2445) ((|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 -2446) +(-62 -2445) ((|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 -2446) +(-63 -2445) ((|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 -2446) +(-64 -2445) ((|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 -2446) +(-65 -2445) ((|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 -2446) +(-66 -2445) ((|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 -2446) +(-67 -2445) ((|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 -2446) +(-68 -2445) ((|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 -2446) +(-69 -2445) ((|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 -2446) +(-70 -2445) ((|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 -2446) +(-71 -2445) ((|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 -2446) +(-72 -2445) ((|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 -2446) +(-73 -2445) ((|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 -2446) +(-74 -2445) ((|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 -2446) +(-77 -2445) ((|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 -2446) +(-78 -2445) ((|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 -2446) +(-79 -2445) ((|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 -2446) +(-80 -2445) ((|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 -2446) +(-81 -2445) ((|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 -2446) +(-82 -2445) ((|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 -2446) +(-83 -2445) ((|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 -2446) +(-84 -2445) ((|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 -2446) +(-85 -2445) ((|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 -2446) +(-86 -2445) ((|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 -2446) +(-87 -2445) ((|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 -2446) +(-88 -2445) ((|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 -2446) +(-89 -2445) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -295,7 +295,7 @@ NIL (-91 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-92 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -343,7 +343,7 @@ NIL (-103 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-104 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL @@ -363,7 +363,7 @@ NIL (-108) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-109) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -388,7 +388,7 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|Identifier|) (|None|)) "\\spad{setProperty(op,{} p,{} v)} attaches property \\spad{p} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Maybe| (|None|)) $ (|Identifier|)) "\\spad{property(op,{} p)} returns the value of property \\spad{p} if it is attached to \\spad{op},{} otherwise \\spad{nothing}.") (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|Identifier|)) "\\spad{deleteProperty!(op,{} p)} unattaches property \\spad{p} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.") (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|Identifier|)) "\\spad{assert(op,{} p)} attaches property \\spad{p} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|Identifier|)) "\\spad{has?(op,{}p)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|operator| (($ (|Symbol|) (|Arity|)) "\\spad{operator(f,{} a)} makes \\spad{f} into an operator of arity \\spad{a}.") (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}."))) NIL NIL -(-115 -2308 UP) +(-115 -2313 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL @@ -399,7 +399,7 @@ NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2797 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) +((|HasCategory| (-116 |#1|) (QUOTE (-905))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-147))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-116 |#1|) (QUOTE (-1018))) (|HasCategory| (-116 |#1|) (QUOTE (-816))) (-2750 (|HasCategory| (-116 |#1|) (QUOTE (-816))) (|HasCategory| (-116 |#1|) (QUOTE (-846)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-1145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-116 |#1|) (QUOTE (-233))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-307))) (|HasCategory| (-116 |#1|) (QUOTE (-545))) (|HasCategory| (-116 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-116 |#1|) (QUOTE (-905)))) (|HasCategory| (-116 |#1|) (QUOTE (-145))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL @@ -415,7 +415,7 @@ NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL @@ -435,15 +435,15 @@ NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-128) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity \\spad{`n'}. The array can then store up to \\spad{`n'} bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|finiteAggregate| ((|attribute|) "A ByteBuffer object is a finite aggregate")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,{}n)} sets the number of active bytes in the `buf'. Error if \\spad{`n'} is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2797 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) +((-2750 (-12 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-2750 (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-129) (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094)))) (|HasCategory| (-129) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-129) (QUOTE (-1094))) (|HasCategory| (-129) (LIST (QUOTE -309) (QUOTE (-129)))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -468,11 +468,11 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4408 "*") . T)) NIL -(-135 |minix| -2291 S T$) +(-135 |minix| -3490 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-136 |minix| -2291 R) +(-136 |minix| -3490 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -495,7 +495,7 @@ NIL (-141) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) ((-4406 . T) (-4396 . T) (-4407 . T)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2750 (-12 (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-368))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-142 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -520,7 +520,7 @@ NIL ((|constructor| (NIL "Rings of Characteristic Zero."))) ((-4403 . T)) NIL -(-148 -2308 UP UPUP) +(-148 -2313 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 -2308) +(-158 R -2313) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -594,7 +594,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-998))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasCategory| |#2| (QUOTE (-1054))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4402)) (|HasAttribute| |#2| (QUOTE -4405)) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-846)))) (-166 R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#1|) (|:| |phi| |#1|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#1| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#1| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#1| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#1| |#1|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) -((-4399 -2797 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3609 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4399 -2750 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3624 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-167 RR PR) ((|constructor| (NIL "\\indented{1}{Author:} Date Created: Date Last Updated: Basic Functions: Related Constructors: Complex,{} UnivariatePolynomial Also See: AMS Classifications: Keywords: complex,{} polynomial factorization,{} factor References:")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} factorizes the polynomial \\spad{p} with complex coefficients."))) @@ -606,8 +606,8 @@ NIL NIL (-169 R) ((|constructor| (NIL "\\spadtype {Complex(R)} creates the domain of elements of the form \\spad{a + b * i} where \\spad{a} and \\spad{b} come from the ring \\spad{R},{} and \\spad{i} is a new element such that \\spad{i**2 = -1}."))) -((-4399 -2797 (|has| |#1| (-556)) (-12 (|has| |#1| (-307)) (|has| |#1| (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4402 |has| |#1| (-6 -4402)) (-4405 |has| |#1| (-6 -4405)) (-3609 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . 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T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (QUOTE (-349)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (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 -1034) (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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(|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-905)))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-905))))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| |#1| (QUOTE (-1054))) (-12 (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-1194)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-233))) (-12 (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasAttribute| |#1| (QUOTE -4402)) (|HasAttribute| |#1| (QUOTE -4405)) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-349))))) (-170 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -680,7 +680,7 @@ NIL ((|constructor| (NIL "This domain provides implementations for constructors.")) (|findConstructor| (((|Maybe| $) (|Identifier|)) "\\spad{findConstructor(s)} attempts to find a constructor named \\spad{s}. If successful,{} returns that constructor; otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-188 R -2308) +(-188 R -2313) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -788,23 +788,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\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 -2308 UP UPUP R) +(-215 -2313 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 -2308 FP) +(-216 -2313 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-217) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-218) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition \\spad{`d'}.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-219 R -2308) +(-219 R -2313) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -819,18 +819,18 @@ NIL (-222 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-223 |CoefRing| |listIndVar|) ((|constructor| (NIL "The deRham complex of Euclidean space,{} that is,{} the class of differential forms of arbitary degree over a coefficient ring. See Flanders,{} Harley,{} Differential Forms,{} With Applications to the Physical Sciences,{} New York,{} Academic Press,{} 1963.")) (|exteriorDifferential| (($ $) "\\spad{exteriorDifferential(df)} returns the exterior derivative (gradient,{} curl,{} divergence,{} ...) of the differential form \\spad{df}.")) (|totalDifferential| (($ (|Expression| |#1|)) "\\spad{totalDifferential(x)} returns the total differential (gradient) form for element \\spad{x}.")) (|map| (($ (|Mapping| (|Expression| |#1|) (|Expression| |#1|)) $) "\\spad{map(f,{}df)} replaces each coefficient \\spad{x} of differential form \\spad{df} by \\spad{f(x)}.")) (|degree| (((|Integer|) $) "\\spad{degree(df)} returns the homogeneous degree of differential form \\spad{df}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(df)} tests if differential form \\spad{df} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{df}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(df)} tests if all of the terms of differential form \\spad{df} have the same degree.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th basis term for a differential form.")) (|coefficient| (((|Expression| |#1|) $ $) "\\spad{coefficient(df,{}u)},{} where \\spad{df} is a differential form,{} returns the coefficient of \\spad{df} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise.")) (|reductum| (($ $) "\\spad{reductum(df)},{} where \\spad{df} is a differential form,{} returns \\spad{df} minus the leading term of \\spad{df} if \\spad{df} has two or more terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(df)} returns the leading basis term of differential form \\spad{df}.")) (|leadingCoefficient| (((|Expression| |#1|) $) "\\spad{leadingCoefficient(df)} returns the leading coefficient of differential form \\spad{df}."))) ((-4403 . T)) NIL -(-224 R -2308) +(-224 R -2313) ((|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}."))) -((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-226) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -839,7 +839,7 @@ NIL (-227 R) ((|constructor| (NIL "\\indented{1}{A Denavit-Hartenberg Matrix is a 4x4 Matrix of the form:} \\indented{1}{\\spad{nx ox ax px}} \\indented{1}{\\spad{ny oy ay py}} \\indented{1}{\\spad{nz oz az pz}} \\indented{2}{\\spad{0\\space{2}0\\space{2}0\\space{2}1}} (\\spad{n},{} \\spad{o},{} and a are the direction cosines)")) (|translate| (($ |#1| |#1| |#1|) "\\spad{translate(X,{}Y,{}Z)} returns a dhmatrix for translation by \\spad{X},{} \\spad{Y},{} and \\spad{Z}")) (|scale| (($ |#1| |#1| |#1|) "\\spad{scale(sx,{}sy,{}sz)} returns a dhmatrix for scaling in the \\spad{X},{} \\spad{Y} and \\spad{Z} directions")) (|rotatez| (($ |#1|) "\\spad{rotatez(r)} returns a dhmatrix for rotation about axis \\spad{Z} for \\spad{r} degrees")) (|rotatey| (($ |#1|) "\\spad{rotatey(r)} returns a dhmatrix for rotation about axis \\spad{Y} for \\spad{r} degrees")) (|rotatex| (($ |#1|) "\\spad{rotatex(r)} returns a dhmatrix for rotation about axis \\spad{X} for \\spad{r} degrees")) (|identity| (($) "\\spad{identity()} create the identity dhmatrix")) (* (((|Point| |#1|) $ (|Point| |#1|)) "\\spad{t*p} applies the dhmatrix \\spad{t} to point \\spad{p}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-228 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL @@ -876,22 +876,22 @@ NIL ((|constructor| (NIL "any solution of a homogeneous linear Diophantine equation can be represented as a sum of minimal solutions,{} which form a \"basis\" (a minimal solution cannot be represented as a nontrivial sum of solutions) in the case of an inhomogeneous linear Diophantine equation,{} each solution is the sum of a inhomogeneous solution and any number of homogeneous solutions therefore,{} it suffices to compute two sets: \\indented{3}{1. all minimal inhomogeneous solutions} \\indented{3}{2. all minimal homogeneous solutions} the algorithm implemented is a completion procedure,{} which enumerates all solutions in a recursive depth-first-search it can be seen as finding monotone paths in a graph for more details see Reference")) (|dioSolve| (((|Record| (|:| |varOrder| (|List| (|Symbol|))) (|:| |inhom| (|Union| (|List| (|Vector| (|NonNegativeInteger|))) "failed")) (|:| |hom| (|List| (|Vector| (|NonNegativeInteger|))))) (|Equation| (|Polynomial| (|Integer|)))) "\\spad{dioSolve(u)} computes a basis of all minimal solutions for linear homogeneous Diophantine equation \\spad{u},{} then all minimal solutions of inhomogeneous equation"))) NIL NIL -(-237 S -2291 R) +(-237 S -3490 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL ((|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (QUOTE (-844))) (|HasAttribute| |#3| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-368))) (|HasCategory| |#3| (QUOTE (-722))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (QUOTE (-1094)))) -(-238 -2291 R) +(-238 -3490 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) ((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . T)) NIL -(-239 -2291 A B) +(-239 -3490 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 -2291 R) +(-240 -3490 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4400 |has| |#2| (-1045)) (-4401 |has| |#2| (-1045)) (-4403 |has| |#2| (-6 -4403)) ((-4408 "*") |has| |#2| (-172)) (-4406 . T)) -((-2797 (-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 (-722))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|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}"))) ((-4407 . T) (-4406 . 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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 -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-2750 (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (|HasCategory| |#3| (QUOTE (-722))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-2750 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (-2750 (|HasAttribute| |#3| (QUOTE -4403)) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-252 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL @@ -987,7 +987,7 @@ NIL (-264 R S V) ((|constructor| (NIL "\\spadtype{DifferentialSparseMultivariatePolynomial} implements an ordinary differential polynomial ring by combining a domain belonging to the category \\spadtype{DifferentialVariableCategory} with the domain \\spadtype{SparseMultivariatePolynomial}. \\blankline"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#3| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#3| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-265 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -1032,11 +1032,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-276 R -2308) +(-276 R -2313) ((|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 -2308) +(-277 R -2313) ((|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| -2039 -3872 |exactQuo|) +(-289 S R |Mod| -1608 -4317 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL @@ -1106,21 +1106,21 @@ NIL NIL (-294 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-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 -2308 S) +(-297 -2313 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 -2308) +(-298 E -2313) ((|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 -2308) +(-310 -2313) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,{}s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -1183,7 +1183,7 @@ NIL (-313 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent essential singularities of functions. Objects in this domain are quotients of sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) "\\spad{coerce(f)} converts a \\spadtype{UnivariatePuiseuxSeries} to an \\spadtype{ExponentialExpansion}.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> a+,{}f(var))}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2797 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2797 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) +((|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1018))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (-2750 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-816))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-1145))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-233))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -309) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (LIST (QUOTE -286) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1245) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-307))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-545))) (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-846))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))) (-2750 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (-12 (|HasCategory| (-1245 |#1| |#2| |#3| |#4|) (QUOTE (-905))) (|HasCategory| $ (QUOTE (-145)))))) (-314 R S) ((|constructor| (NIL "Lifting of maps to Expressions. Date Created: 16 Jan 1989 Date Last Updated: 22 Jan 1990")) (|map| (((|Expression| |#2|) (|Mapping| |#2| |#1|) (|Expression| |#1|)) "\\spad{map(f,{} e)} applies \\spad{f} to all the constants appearing in \\spad{e}."))) NIL @@ -1194,9 +1194,9 @@ NIL NIL (-316 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) -((-4403 -2797 (-2366 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2797 (-2366 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 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(QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2797 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) -(-317 R -2308) +((-4403 -2750 (-2368 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (-12 (|has| |#1| (-556)) (-2750 (-2368 (|has| |#1| (-1045)) (|has| |#1| (-637 (-564)))) (|has| |#1| (-1045)) (|has| |#1| (-473)))) (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) 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(-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-1045)))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2750 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1106)))) (-2750 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))))) (-2750 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#1| (QUOTE (-1045)))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1106))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| $ (QUOTE (-1045))) (|HasCategory| $ (LIST (QUOTE -1034) (QUOTE (-564))))) +(-317 R -2313) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1207,7 +1207,7 @@ NIL (-319 FE |var| |cen|) ((|constructor| (NIL "ExponentialOfUnivariatePuiseuxSeries is a domain used to represent essential singularities of functions. An object in this domain is a function of the form \\spad{exp(f(x))},{} where \\spad{f(x)} is a Puiseux series with no terms of non-negative degree. Objects are ordered according to order of singularity,{} with functions which tend more rapidly to zero or infinity considered to be larger. Thus,{} if \\spad{order(f(x)) < order(g(x))},{} \\spadignore{i.e.} the first non-zero term of \\spad{f(x)} has lower degree than the first non-zero term of \\spad{g(x)},{} then \\spad{exp(f(x)) > exp(g(x))}. If \\spad{order(f(x)) = order(g(x))},{} then the ordering is essentially random. This domain is used in computing limits involving functions with essential singularities.")) (|exponentialOrder| (((|Fraction| (|Integer|)) $) "\\spad{exponentialOrder(exp(c * x **(-n) + ...))} returns \\spad{-n}. exponentialOrder(0) returns \\spad{0}.")) (|exponent| (((|UnivariatePuiseuxSeries| |#1| |#2| |#3|) $) "\\spad{exponent(exp(f(x)))} returns \\spad{f(x)}")) (|exponential| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{exponential(f(x))} returns \\spad{exp(f(x))}. Note: the function does NOT check that \\spad{f(x)} has no non-negative terms."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|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 -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-320 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1239,12 +1239,12 @@ NIL (-327 S) ((|constructor| (NIL "\\indented{1}{A FlexibleArray is the notion of an array intended to allow for growth} at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) -(-328 S -2308) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +(-328 S -2313) ((|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 -2308) +(-329 -2313) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL @@ -1264,15 +1264,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-334 S -2308 UP UPUP R) +(-334 S -2313 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 -2308 UP UPUP R) +(-335 -2313 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 -2308 UP UPUP R) +(-336 -2313 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 -2308 UP UPUP) +(-341 S -2313 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 -2308 UP UPUP) +(-342 -2313 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-343 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroup(\\spad{p},{}\\spad{n}) implements a finite field extension of degee \\spad{n} over the prime field with \\spad{p} elements. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. The Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-344 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-345 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-346 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1328,31 +1328,31 @@ NIL ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-350 R UP -2308) +(-350 R UP -2313) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-351 |p| |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasis(\\spad{p},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the prime field with \\spad{p} elements. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial created by \\spadfunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}.")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: The time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| (|PrimeField| |#1|))) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| (|PrimeField| |#1|)) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-352 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-353 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-354 |p| |n|) ((|constructor| (NIL "FiniteField(\\spad{p},{}\\spad{n}) implements finite fields with p**n elements. This packages checks that \\spad{p} is prime. For a non-checking version,{} see \\spadtype{InnerFiniteField}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) +((-2750 (|HasCategory| (-906 |#1|) (QUOTE (-145))) (|HasCategory| (-906 |#1|) (QUOTE (-368)))) (|HasCategory| (-906 |#1|) (QUOTE (-147))) (|HasCategory| (-906 |#1|) (QUOTE (-368))) (|HasCategory| (-906 |#1|) (QUOTE (-145)))) (-355 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) -(-356 -2308 GF) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +(-356 -2313 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 -2308 FP FPP) +(-358 -2313 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-359 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) +((-2750 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-368)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-145)))) (-360 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL @@ -1446,7 +1446,7 @@ NIL NIL (-379) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4389 . T) (-4397 . T) (-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-4389 . T) (-4397 . T) (-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-380 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1496,7 +1496,7 @@ NIL ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-392 -2308 UP UPUP R) +(-392 -2313 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 -2446 |returnType| -1586 |symbols|) +(-398 -2445 |returnType| -1370 |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 -2308 UP) +(-399 -2313 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1546,7 +1546,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4389)) (|HasAttribute| |#1| (QUOTE -4397))) (-404) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-405 R S) ((|constructor| (NIL "\\spadtype{FactoredFunctions2} contains functions that involve factored objects whose underlying domains may not be the same. For example,{} \\spadfun{map} might be used to coerce an object of type \\spadtype{Factored(Integer)} to \\spadtype{Factored(Complex(Integer))}.")) (|map| (((|Factored| |#2|) (|Mapping| |#2| |#1|) (|Factored| |#1|)) "\\spad{map(fn,{}u)} is used to apply the function \\userfun{\\spad{fn}} to every factor of \\spadvar{\\spad{u}}. The new factored object will have all its information flags set to \"nil\". This function is used,{} for example,{} to coerce every factor base to another type."))) @@ -1559,7 +1559,7 @@ NIL (-407 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) ((-4393 -12 (|has| |#1| (-6 -4404)) (|has| |#1| (-452)) (|has| |#1| (-6 -4393))) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2797 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4393)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (QUOTE (-816))) (-2750 (|HasCategory| |#1| (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-846)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-824)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-545))) (-12 (|HasAttribute| |#1| (QUOTE -4404)) (|HasAttribute| |#1| (QUOTE -4393)) (|HasCategory| |#1| (QUOTE (-452)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-408 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL @@ -1580,11 +1580,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-413 R -2308 UP A) +(-413 R -2313 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,{}...,{}fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} returns the vector \\spad{[f1,{}...,{}fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,{}...,{}fn])} returns the ideal \\spad{(f1,{}...,{}fn)}."))) ((-4403 . T)) NIL -(-414 R -2308 UP A |ibasis|) +(-414 R -2313 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,{}...,{}fn])} = the module generated by \\spad{(f1,{}...,{}fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1034) (|devaluate| |#2|)))) @@ -1603,7 +1603,7 @@ NIL (-418 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -309) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-1213))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) +((|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))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-1213)))) (|HasCategory| |#1| (QUOTE (-1018))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-452)))) (-419 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1632,7 +1632,7 @@ NIL ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) ((-4406 . T) (-4396 . T) (-4407 . T)) NIL -(-426 R -2308) +(-426 R -2313) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL @@ -1640,7 +1640,7 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) ((-4393 -12 (|has| |#1| (-6 -4393)) (|has| |#2| (-6 -4393))) (-4400 . T) (-4401 . T) (-4403 . T)) ((-12 (|HasAttribute| |#1| (QUOTE -4393)) (|HasAttribute| |#2| (QUOTE -4393)))) -(-428 R -2308) +(-428 R -2313) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL @@ -1650,17 +1650,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-1106))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (-430 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4403 -2797 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) +((-4403 -2750 (|has| |#1| (-1045)) (|has| |#1| (-473))) (-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-556)) (-4398 |has| |#1| (-556))) NIL -(-431 R -2308) +(-431 R -2313) ((|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 -2308) +(-432 R -2313) ((|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 -2308) +(-433 R -2313) ((|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 -2308 UP) +(-435 R -2313 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-48))))) @@ -1700,7 +1700,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-443 R UP -2308) +(-443 R UP -2313) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1747,7 +1747,7 @@ NIL (-454 |vl| R E) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is specified by its third parameter. Suggested types which define term orderings include: \\spadtype{DirectProduct},{} \\spadtype{HomogeneousDirectProduct},{} \\spadtype{SplitHomogeneousDirectProduct} and finally \\spadtype{OrderedDirectProduct} which accepts an arbitrary user function to define a term ordering.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-455 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1812,7 +1812,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-471 |lv| -2308 R) +(-471 |lv| -2313 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1827,11 +1827,11 @@ NIL (-474 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|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 -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (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."))) ((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#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)}"))) ((-4407 . T) (-4406 . T)) @@ -1847,7 +1847,7 @@ NIL (-479 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-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"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . 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(QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-789))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-844))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (QUOTE (-1045)))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2750 (|HasCategory| |#2| (QUOTE (-1045))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-483) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header \\spad{`h'}.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|Identifier|))) "\\spad{headAst(f,{}[x1,{}..,{}xn])} constructs a function definition header."))) NIL @@ -1867,8 +1867,8 @@ NIL (-484 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-485 -2308 UP UPUP R) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +(-485 -2313 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1879,7 +1879,7 @@ NIL (-487) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-488 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1904,7 +1904,7 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-494 -2308 UP |AlExt| |AlPol|) +(-494 -2313 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL @@ -1915,16 +1915,16 @@ NIL (-496 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-497 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-498 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,{}lr,{}n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,{}q,{}n)} returns the list \\spad{[bas,{}bas^Frob,{}bas^(Frob^2),{}...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,{}n,{}m,{}j)} \\undocumented"))) NIL NIL -(-499 R UP -2308) +(-499 R UP -2313) ((|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| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL @@ -1944,7 +1944,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-504 -2308 |Expon| |VarSet| |DPoly|) +(-504 -2313 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-1170))))) @@ -1995,7 +1995,7 @@ NIL (-516 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-517) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL @@ -2003,15 +2003,15 @@ NIL (-518 |p| |n|) ((|constructor| (NIL "InnerFiniteField(\\spad{p},{}\\spad{n}) implements finite fields with \\spad{p**n} elements where \\spad{p} is assumed prime but does not check. For a version which checks that \\spad{p} is prime,{} see \\spadtype{FiniteField}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((-2797 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) +((-2750 (|HasCategory| (-581 |#1|) (QUOTE (-145))) (|HasCategory| (-581 |#1|) (QUOTE (-368)))) (|HasCategory| (-581 |#1|) (QUOTE (-147))) (|HasCategory| (-581 |#1|) (QUOTE (-368))) (|HasCategory| (-581 |#1|) (QUOTE (-145)))) (-519 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-520 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-521 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL @@ -2023,7 +2023,7 @@ NIL (-523 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-524) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL @@ -2056,7 +2056,7 @@ NIL ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL NIL -(-532 K -2308 |Par|) +(-532 K -2313 |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 -2308 |Par|) +(-538 K -2313 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,{}lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,{}lden,{}lvar,{}eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,{}eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,{}eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL @@ -2131,12 +2131,12 @@ NIL (-550 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) -(-551 R -2308) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +(-551 R -2313) ((|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 -2308 UP UPUP R) +(-552 R0 -2313 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."))) -((-3599 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3613 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-555 S) ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) @@ -2156,7 +2156,7 @@ NIL ((|constructor| (NIL "The category of commutative integral domains,{} \\spadignore{i.e.} commutative rings with no zero divisors. \\blankline Conditional attributes: \\indented{2}{canonicalUnitNormal\\tab{20}the canonical field is the same for all associates} \\indented{2}{canonicalsClosed\\tab{20}the product of two canonicals is itself canonical}")) (|unit?| (((|Boolean|) $) "\\spad{unit?(x)} tests whether \\spad{x} is a unit,{} \\spadignore{i.e.} is invertible.")) (|associates?| (((|Boolean|) $ $) "\\spad{associates?(x,{}y)} tests whether \\spad{x} and \\spad{y} are associates,{} \\spadignore{i.e.} differ by a unit factor.")) (|unitCanonical| (($ $) "\\spad{unitCanonical(x)} returns \\spad{unitNormal(x).canonical}.")) (|unitNormal| (((|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) $) "\\spad{unitNormal(x)} tries to choose a canonical element from the associate class of \\spad{x}. The attribute canonicalUnitNormal,{} if asserted,{} means that the \"canonical\" element is the same across all associates of \\spad{x} if \\spad{unitNormal(x) = [u,{}c,{}a]} then \\spad{u*c = x},{} \\spad{a*u = 1}.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} either returns an element \\spad{c} such that \\spad{c*b=a} or \"failed\" if no such element can be found."))) ((-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-557 R -2308) +(-557 R -2313) ((|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 -2308 L) +(-560 R -2313 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 -2308 UP UPUP R) +(-562 -2313 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 -2308 UP) +(-563 -2313 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 -2308 L) +(-566 R -2313 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 -2308) +(-567 R -2313) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1133)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-627))))) -(-568 -2308 UP) +(-568 -2313 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 -2308) +(-570 -2313) ((|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."))) -((-3599 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3613 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-572) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-573 R -2308) +(-573 R -2313) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-627))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-284)))) (|HasCategory| |#1| (QUOTE (-556)))) -(-574 -2308 UP) +(-574 -2313 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 -2308) +(-575 R -2313) ((|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 -2308) +(-583 R -2313) ((|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 -2308) +(-584 E -2313) ((|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 -2308) +(-585 -2313) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) ((-4401 . T) (-4400 . T)) ((|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-1170))))) @@ -2299,7 +2299,7 @@ NIL (-592 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2797 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2750 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-2750 (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-593 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL @@ -2307,7 +2307,7 @@ NIL (-594 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|Fraction| (|Integer|))) "\\spad{cRationalPower(f,{}r)} computes \\spad{f^r}. For use when the coefficient ring is commutative.")) (|cPower| (($ $ |#1|) "\\spad{cPower(f,{}r)} computes \\spad{f^r},{} where \\spad{f} has constant coefficient 1. For use when the coefficient ring is commutative.")) (|integrate| (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. Warning: function does not check for a term of degree \\spad{-1}.")) (|seriesToOutputForm| (((|OutputForm|) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) (|Reference| (|OrderedCompletion| (|Integer|))) (|Symbol|) |#1| (|Fraction| (|Integer|))) "\\spad{seriesToOutputForm(st,{}refer,{}var,{}cen,{}r)} prints the series \\spad{f((var - cen)^r)}.")) (|iCompose| (($ $ $) "\\spad{iCompose(f,{}g)} returns \\spad{f(g(x))}. This is an internal function which should only be called for Taylor series \\spad{f(x)} and \\spad{g(x)} such that the constant coefficient of \\spad{g(x)} is zero.")) (|taylorQuoByVar| (($ $) "\\spad{taylorQuoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...}")) (|iExquo| (((|Union| $ "failed") $ $ (|Boolean|)) "\\spad{iExquo(f,{}g,{}taylor?)} is the quotient of the power series \\spad{f} and \\spad{g}. If \\spad{taylor?} is \\spad{true},{} then we must have \\spad{order(f) >= order(g)}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(fn,{}f)} returns the series \\spad{sum(fn(n) * an * x^n,{}n = n0..)},{} where \\spad{f} is the series \\spad{sum(an * x^n,{}n = n0..)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents.")) (|getStream| (((|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|))) $) "\\spad{getStream(f)} returns the stream of terms representing the series \\spad{f}.")) (|getRef| (((|Reference| (|OrderedCompletion| (|Integer|))) $) "\\spad{getRef(f)} returns a reference containing the order to which the terms of \\spad{f} have been computed.")) (|makeSeries| (($ (|Reference| (|OrderedCompletion| (|Integer|))) (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{makeSeries(refer,{}str)} creates a power series from the reference \\spad{refer} and the stream \\spad{str}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (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))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-564)) (|devaluate| |#1|)))) (|HasCategory| (-564) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-564)))))) (-595 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) ((-4401 |has| |#1| (-556)) (-4400 |has| |#1| (-556)) ((-4408 "*") |has| |#1| (-556)) (-4399 |has| |#1| (-556)) (-4403 . T)) @@ -2320,7 +2320,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-598 R -2308 FG) +(-598 R -2313 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2331,7 +2331,7 @@ NIL (-600 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-601 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL @@ -2350,12 +2350,12 @@ NIL NIL (-605 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A}} \\indented{1}{to define the new multiplications \\spad{a*b := (a *\\$A b + b *\\$A a)/2}} \\indented{1}{(anticommutator).} \\indented{1}{The usual notation \\spad{{a,{}b}_+} cannot be used due to} \\indented{1}{restrictions in the current language.} \\indented{1}{This domain only gives a Jordan algebra if the} \\indented{1}{Jordan-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds} \\indented{1}{for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}.} \\indented{1}{This relation can be checked by} \\indented{1}{\\spadfun{jordanAdmissible?()\\$A}.} \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Jordan algebra. Moreover,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same \\spad{true} for the associated Jordan algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Jordan algebra \\spadtype{AssociatedJordanAlgebra}(\\spad{R},{}A)."))) -((-4403 -2797 (-2366 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2797 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4403 -2750 (-2368 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) +((-2750 (|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|)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-606 |Entry|) ((|constructor| (NIL "This domain allows a random access file to be viewed both as a table and as a file object.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| (-1152) (QUOTE (-846))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-607 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL @@ -2380,7 +2380,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-613 -2308 UP) +(-613 -2313 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2408,7 +2408,7 @@ NIL ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-844)))) -(-620 R -2308) +(-620 R -2313) ((|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 -2308) +(-628 R -2313) ((|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| -2308) +(-629 |lv| -2313) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL (-630) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) ((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1152))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-1152) (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (QUOTE (-1094)))) (-631 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL @@ -2462,8 +2462,8 @@ NIL NIL (-633 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,{}b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-4403 -2797 (-2366 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) -((-2797 (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (LIST (QUOTE -417) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -367) (|devaluate| |#1|)))) +((-4403 -2750 (-2368 (|has| |#2| (-367 |#1|)) (|has| |#1| (-556))) (-12 (|has| |#2| (-417 |#1|)) (|has| |#1| (-556)))) (-4401 . T) (-4400 . T)) +((-2750 (|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|)))) (-2750 (-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 -((-2352 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) +((-2356 (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-363)))) (-637 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4403 . T)) @@ -2495,7 +2495,7 @@ NIL (-641 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-824))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-642 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL @@ -2503,7 +2503,7 @@ NIL (-643 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-644 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2520,7 +2520,7 @@ NIL ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-648 R -2308 L) +(-648 R -2313 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op,{} g,{} x,{} a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{op y = g,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op,{} g,{} x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL @@ -2540,11 +2540,11 @@ NIL ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-653 -2308 UP) +(-653 -2313 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 -1329) +(-654 A -1634) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator} defines a ring of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) @@ -2580,11 +2580,11 @@ NIL ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) ((-4407 . T) (-4406 . T)) NIL -(-663 -2308) +(-663 -2313) ((|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 -2308 |Row| |Col| M) +(-664 -2313 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2595,7 +2595,7 @@ NIL (-666 |n| R) ((|constructor| (NIL "LieSquareMatrix(\\spad{n},{}\\spad{R}) implements the Lie algebra of the \\spad{n} by \\spad{n} matrices over the commutative ring \\spad{R}. The Lie bracket (commutator) of the algebra is given by \\spad{a*b := (a *\\$SQMATRIX(n,{}R) b - b *\\$SQMATRIX(n,{}R) a)},{} where \\spadfun{*\\$SQMATRIX(\\spad{n},{}\\spad{R})} is the usual matrix multiplication."))) ((-4403 . T) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2797 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-556))) (-2750 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-667) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2615,7 +2615,7 @@ NIL (-671 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (QUOTE (-1045))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-672) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition \\spad{`m'}. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL @@ -2671,7 +2671,7 @@ NIL (-685 R) ((|constructor| (NIL "\\spadtype{Matrix} is a matrix domain where 1-based indexing is used for both rows and columns.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|diagonalMatrix| (($ (|Vector| |#1|)) "\\spad{diagonalMatrix(v)} returns a diagonal matrix where the elements of \\spad{v} appear on the diagonal."))) ((-4406 . T) (-4407 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-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))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-307))) (|HasCategory| |#1| (QUOTE (-556))) (|HasAttribute| |#1| (QUOTE (-4408 "*"))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-686 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL @@ -2680,7 +2680,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that \\spad{`x'} really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value \\spad{`x'} into \\%."))) NIL NIL -(-688 S -2308 FLAF FLAS) +(-688 S -2313 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2690,8 +2690,8 @@ NIL NIL (-690) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4399 . T) (-4404 |has| (-695) (-363)) (-4398 |has| (-695) (-363)) (-3609 . T) (-4405 |has| (-695) (-6 -4405)) (-4402 |has| (-695) (-6 -4402)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2797 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2797 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2797 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2797 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4405)) (|HasAttribute| (-695) (QUOTE -4402)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) +((-4399 . T) (-4404 |has| (-695) (-363)) (-4398 |has| (-695) (-363)) (-3624 . T) (-4405 |has| (-695) (-6 -4405)) (-4402 |has| (-695) (-6 -4402)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((|HasCategory| (-695) (QUOTE (-147))) (|HasCategory| (-695) (QUOTE (-145))) (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-368))) (|HasCategory| (-695) (QUOTE (-363))) (-2750 (|HasCategory| (-695) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-233))) (-2750 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (LIST (QUOTE -286) (QUOTE (-695)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -309) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-695)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-695) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-695) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (-2750 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-349)))) (|HasCategory| (-695) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-695) (QUOTE (-1018))) (|HasCategory| (-695) (QUOTE (-1194))) (-12 (|HasCategory| (-695) (QUOTE (-998))) (|HasCategory| (-695) (QUOTE (-1194)))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-363))) (|HasCategory| (-695) (QUOTE (-905)))) (-12 (|HasCategory| (-695) (QUOTE (-349))) (|HasCategory| (-695) (QUOTE (-905))))) (|HasCategory| (-695) (QUOTE (-545))) (-12 (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-1194)))) (|HasCategory| (-695) (QUOTE (-1054))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-363)))) (-2750 (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-556)))) (-12 (|HasCategory| (-695) (QUOTE (-233))) (|HasCategory| (-695) (QUOTE (-363)))) (-12 (|HasCategory| (-695) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-695) (QUOTE (-363)))) (|HasCategory| (-695) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-695) (QUOTE (-846))) (|HasCategory| (-695) (QUOTE (-556))) (|HasAttribute| (-695) (QUOTE -4405)) (|HasAttribute| (-695) (QUOTE -4402)) (-12 (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-145)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-695) (QUOTE (-307))) (|HasCategory| (-695) (QUOTE (-905)))) (|HasCategory| (-695) (QUOTE (-349))))) (-691 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) ((-4407 . T)) @@ -2704,13 +2704,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-694 OV E -2308 PG) +(-694 OV E -2313 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}"))) -((-3599 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) +((-3613 . T) (-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-696 R) ((|constructor| (NIL "\\indented{1}{Modular hermitian row reduction.} Author: Manuel Bronstein Date Created: 22 February 1989 Date Last Updated: 24 November 1993 Keywords: matrix,{} reduction.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelonLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| |#1|) "\\spad{rowEchelonLocal(m,{} d,{} p)} computes the row-echelon form of \\spad{m} concatenated with \\spad{d} times the identity matrix over a local ring where \\spad{p} is the only prime.")) (|rowEchLocal| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchLocal(m,{}p)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus over a local ring where \\spad{p} is the only prime.")) (|rowEchelon| (((|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rowEchelon(m,{} d)} computes a modular row-echelon form mod \\spad{d} of \\indented{3}{[\\spad{d}\\space{5}]} \\indented{3}{[\\space{2}\\spad{d}\\space{3}]} \\indented{3}{[\\space{4}. ]} \\indented{3}{[\\space{5}\\spad{d}]} \\indented{3}{[\\space{3}\\spad{M}\\space{2}]} where \\spad{M = m mod d}.")) (|rowEch| (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{rowEch(m)} computes a modular row-echelon form of \\spad{m},{} finding an appropriate modulus."))) @@ -2736,7 +2736,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-702 S -3933 I) +(-702 S -3950 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#3| |#2|) |#1| (|Symbol|)) "\\spad{compiledFunction(expr,{} x)} returns a function \\spad{f: D -> I} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{D}.")) (|unaryFunction| (((|Mapping| |#3| |#2|) (|Symbol|)) "\\spad{unaryFunction(a)} is a local function"))) NIL NIL @@ -2756,14 +2756,14 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-707 R |Mod| -2039 -3872 |exactQuo|) +(-707 R |Mod| -1608 -4317 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-708 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-709 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2772,7 +2772,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4401 |has| |#1| (-172)) (-4400 |has| |#1| (-172)) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147)))) -(-711 R |Mod| -2039 -3872 |exactQuo|) +(-711 R |Mod| -1608 -4317 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) ((-4403 . T)) NIL @@ -2784,7 +2784,7 @@ NIL ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) ((-4401 . T) (-4400 . T)) NIL -(-714 -2308) +(-714 -2313) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,{}x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,{}b,{}c,{}d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,{}1],{}[1,{}0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,{}h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,{}0],{}[0,{}1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,{}h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,{}k],{}[0,{}1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,{}b,{}c,{}d)} returns \\spad{matrix [[a,{}b],{}[c,{}d]]}."))) ((-4403 . T)) NIL @@ -2820,7 +2820,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) NIL NIL -(-723 -2308 UP) +(-723 -2313 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f,{} D)} returns \\spad{[p,{}n,{}s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f,{} D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p,{} D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m,{} s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p,{} D)} returns \\spad{[n,{}s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL @@ -2839,7 +2839,7 @@ NIL (-727 |vl| R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are from a user specified list of symbols. The ordering is specified by the position of the variable in the list. The coefficient ring may be non commutative,{} but the variables are assumed to commute."))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-860 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-728 E OV R PRF) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are rational functions over some ring \\spad{R} over which we can factor. It is used internally by packages such as primary decomposition which need to work with polynomials with rational function coefficients,{} \\spadignore{i.e.} themselves fractions of polynomials.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(prf)} factors a polynomial with rational function coefficients.")) (|pushuconst| ((|#4| (|Fraction| (|Polynomial| |#3|)) |#2|) "\\spad{pushuconst(r,{}var)} takes a rational function and raises all occurances of the variable \\spad{var} to the polynomial level.")) (|pushucoef| ((|#4| (|SparseUnivariatePolynomial| (|Polynomial| |#3|)) |#2|) "\\spad{pushucoef(upoly,{}var)} converts the anonymous univariate polynomial \\spad{upoly} to a polynomial in \\spad{var} over rational functions.")) (|pushup| ((|#4| |#4| |#2|) "\\spad{pushup(prf,{}var)} raises all occurences of the variable \\spad{var} in the coefficients of the polynomial \\spad{prf} back to the polynomial level.")) (|pushdterm| ((|#4| (|SparseUnivariatePolynomial| |#4|) |#2|) "\\spad{pushdterm(monom,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the monomial \\spad{monom}.")) (|pushdown| ((|#4| |#4| |#2|) "\\spad{pushdown(prf,{}var)} pushes all top level occurences of the variable \\spad{var} into the coefficient domain for the polynomial \\spad{prf}.")) (|totalfract| (((|Record| (|:| |sup| (|Polynomial| |#3|)) (|:| |inf| (|Polynomial| |#3|))) |#4|) "\\spad{totalfract(prf)} takes a polynomial whose coefficients are themselves fractions of polynomials and returns a record containing the numerator and denominator resulting from putting \\spad{prf} over a common denominator.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2972,11 +2972,11 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-761 -2308) +(-761 -2313) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-762 P -2308) +(-762 P -2313) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL @@ -2984,7 +2984,7 @@ NIL NIL NIL NIL -(-764 UP -2308) +(-764 UP -2313) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -3000,7 +3000,7 @@ NIL ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,{}b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,{}b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) (((-4408 "*") . T)) NIL -(-768 R -2308) +(-768 R -2313) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,{}y),{} N(x,{}y),{} y,{} x)} returns \\spad{F(x,{}y)} such that \\spad{F(x,{}y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,{}y) dx + N(x,{}y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL @@ -3020,7 +3020,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-773 -2308 |ExtF| |SUEx| |ExtP| |n|) +(-773 -2313 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL @@ -3035,7 +3035,7 @@ NIL (-776 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) 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|#1| (QUOTE (-545)))) (-2356 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2356 (|HasCategory| |#1| (LIST (QUOTE -38) (QUOTE (-564))))) (-2356 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-1170)))) (-2356 (|HasCategory| |#1| (LIST (QUOTE -988) (QUOTE (-564))))))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-777 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL @@ -3043,7 +3043,7 @@ NIL (-778 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4402 |has| |#1| (-363)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-1145))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-233))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-779 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL @@ -3104,23 +3104,23 @@ NIL ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) NIL -(-794 -2797 R OS S) +(-794 -2750 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-795 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2797 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (-2750 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-995 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (-796) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-797 R -2308 L) +(-797 R -2313 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-798 R -2308) +(-798 R -2313) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -3128,7 +3128,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-800 R -2308) +(-800 R -2313) ((|constructor| (NIL "\\spadtype{ODEIntegration} provides an interface to the integrator. This package is intended for use by the differential equations solver but not at top-level.")) (|diff| (((|Mapping| |#2| |#2|) (|Symbol|)) "\\spad{diff(x)} returns the derivation with respect to \\spad{x}.")) (|expint| ((|#2| |#2| (|Symbol|)) "\\spad{expint(f,{} x)} returns e^{the integral of \\spad{f} with respect to \\spad{x}}.")) (|int| ((|#2| |#2| (|Symbol|)) "\\spad{int(f,{} x)} returns the integral of \\spad{f} with respect to \\spad{x}."))) NIL NIL @@ -3136,11 +3136,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-802 -2308 UP UPUP R) +(-802 -2313 UP UPUP R) ((|constructor| (NIL "In-field solution of an linear ordinary differential equation,{} pure algebraic case.")) (|algDsolve| (((|Record| (|:| |particular| (|Union| |#4| "failed")) (|:| |basis| (|List| |#4|))) (|LinearOrdinaryDifferentialOperator1| |#4|) |#4|) "\\spad{algDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no solution in \\spad{R}. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{y_i's} form a basis for the solutions in \\spad{R} of the homogeneous equation."))) NIL NIL -(-803 -2308 UP L LQ) +(-803 -2313 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -3148,38 +3148,38 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-805 -2308 UP L LQ) +(-805 -2313 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-806 -2308 UP) +(-806 -2313 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-807 -2308 L UP A LO) +(-807 -2313 L UP A LO) ((|constructor| (NIL "Elimination of an algebraic from the coefficentss of a linear ordinary differential equation.")) (|reduceLODE| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) |#5| |#4|) "\\spad{reduceLODE(op,{} g)} returns \\spad{[m,{} v]} such that any solution in \\spad{A} of \\spad{op z = g} is of the form \\spad{z = (z_1,{}...,{}z_m) . (b_1,{}...,{}b_m)} where the \\spad{b_i's} are the basis of \\spad{A} over \\spad{F} returned by \\spadfun{basis}() from \\spad{A},{} and the \\spad{z_i's} satisfy the differential system \\spad{M.z = v}."))) NIL NIL -(-808 -2308 UP) +(-808 -2313 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-809 -2308 LO) +(-809 -2313 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 -(-810 -2308 LODO) +(-810 -2313 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 -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-1094)))) (|HasAttribute| |#2| (QUOTE -4403)) (|HasCategory| |#2| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))))) (-812 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"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-814 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-813 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable."))) (((-4408 "*") |has| |#2| (-363)) (-4399 |has| |#2| (-363)) (-4404 |has| |#2| (-363)) (-4398 |has| |#2| (-363)) (-4403 . T) (-4401 . T) (-4400 . T)) @@ -3247,7 +3247,7 @@ NIL (-829 R) ((|constructor| (NIL "Adjunction of a complex infinity to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one,{} \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is infinite.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|infinity| (($) "\\spad{infinity()} returns infinity."))) ((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-830 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator `op'.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of `op'."))) NIL @@ -3287,12 +3287,12 @@ NIL (-839 R) ((|constructor| (NIL "Adjunction of two real infinites quantities to a set. Date Created: 4 Oct 1989 Date Last Updated: 1 Nov 1989")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a finite rational number if it is one and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a finite rational number. Error: if \\spad{x} cannot be so converted.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a finite rational number.")) (|whatInfinity| (((|SingleInteger|) $) "\\spad{whatInfinity(x)} returns 0 if \\spad{x} is finite,{} 1 if \\spad{x} is +infinity,{} and \\spad{-1} if \\spad{x} is -infinity.")) (|infinite?| (((|Boolean|) $) "\\spad{infinite?(x)} tests if \\spad{x} is +infinity or -infinity,{}")) (|finite?| (((|Boolean|) $) "\\spad{finite?(x)} tests if \\spad{x} is finite.")) (|minusInfinity| (($) "\\spad{minusInfinity()} returns -infinity.")) (|plusInfinity| (($) "\\spad{plusInfinity()} returns +infinity."))) ((-4403 |has| |#1| (-844))) -((|HasCategory| |#1| (QUOTE (-844))) (-2797 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) +((|HasCategory| |#1| (QUOTE (-844))) (-2750 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-844)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#1| (QUOTE (-844))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-545))) (|HasCategory| |#1| (QUOTE (-21)))) (-840) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-841 -2291 S) +(-841 -3490 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,{}v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL @@ -3328,11 +3328,11 @@ NIL ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) -(-850 R |sigma| -2564) +(-850 R |sigma| -2288) ((|constructor| (NIL "This is the domain of sparse univariate skew polynomials over an Ore coefficient field. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,{} x)} returns the output form of \\spad{p} using \\spad{x} for the otherwise anonymous variable."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-363)))) -(-851 |x| R |sigma| -2564) +(-851 |x| R |sigma| -2288) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}."))) ((-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-363)))) @@ -3399,15 +3399,15 @@ NIL (-867 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2797 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) +((|HasCategory| (-866 |#1|) (QUOTE (-905))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-147))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-866 |#1|) (QUOTE (-1018))) (|HasCategory| (-866 |#1|) (QUOTE (-816))) (-2750 (|HasCategory| (-866 |#1|) (QUOTE (-816))) (|HasCategory| (-866 |#1|) (QUOTE (-846)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-1145))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| (-866 |#1|) (QUOTE (-233))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -514) (QUOTE (-1170)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -309) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -866) (|devaluate| |#1|)) (LIST (QUOTE -866) (|devaluate| |#1|)))) (|HasCategory| (-866 |#1|) (QUOTE (-307))) (|HasCategory| (-866 |#1|) (QUOTE (-545))) (|HasCategory| (-866 |#1|) (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-866 |#1|) (QUOTE (-905)))) (|HasCategory| (-866 |#1|) (QUOTE (-145))))) (-868 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2797 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-1018))) (|HasCategory| |#2| (QUOTE (-816))) (-2750 (|HasCategory| |#2| (QUOTE (-816))) (|HasCategory| |#2| (QUOTE (-846)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-545))) (|HasCategory| |#2| (QUOTE (-846))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-869 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))))) (-870) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3463,7 +3463,7 @@ NIL (-883 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr,{} pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,{}...,{}vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,{}...,{}en],{} pat)} matches the pattern pat on the list of expressions \\spad{[e1,{}...,{}en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,{}...,{}en],{} pat)} tests if the list of expressions \\spad{[e1,{}...,{}en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr,{} pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2352 (|HasCategory| |#2| (QUOTE (-1045)))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2352 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) +((-12 (-2356 (|HasCategory| |#2| (QUOTE (-1045)))) (-2356 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (-12 (|HasCategory| |#2| (QUOTE (-1045))) (-2356 (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-1170))))) (-884 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3472,7 +3472,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-886 R -3933) +(-886 R -3950) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3496,7 +3496,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-892 UP -2308) +(-892 UP -2313) ((|constructor| (NIL "This package \\undocumented")) (|rightFactorCandidate| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{rightFactorCandidate(p,{}n)} \\undocumented")) (|leftFactor| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftFactor(p,{}q)} \\undocumented")) (|decompose| (((|Union| (|Record| (|:| |left| |#1|) (|:| |right| |#1|)) "failed") |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{decompose(up,{}m,{}n)} \\undocumented") (((|List| |#1|) |#1|) "\\spad{decompose(up)} \\undocumented"))) NIL NIL @@ -3519,7 +3519,7 @@ NIL (-897 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-898 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL @@ -3535,7 +3535,7 @@ NIL (-901 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) ((-4403 . T)) -((-2797 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) +((-2750 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-846)))) (-902 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3556,7 +3556,7 @@ NIL ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) ((|HasCategory| $ (QUOTE (-147))) (|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-368)))) -(-907 R0 -2308 UP UPUP R) +(-907 R0 -2313 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#5|)) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsionIfCan(f)}\\\\ undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| |#2| |#3| |#4| |#5|)) "\\spad{order(f)} \\undocumented"))) NIL NIL @@ -3584,7 +3584,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-914 -2308) +(-914 -2313) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3600,11 +3600,11 @@ NIL ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4408 "*") . T)) NIL -(-918 -2308 P) +(-918 -2313 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-919 |xx| -2308) +(-919 |xx| -2313) ((|constructor| (NIL "This package exports interpolation algorithms")) (|interpolate| (((|SparseUnivariatePolynomial| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(lf,{}lg)} \\undocumented") (((|UnivariatePolynomial| |#1| |#2|) (|UnivariatePolynomial| |#1| |#2|) (|List| |#2|) (|List| |#2|)) "\\spad{interpolate(u,{}lf,{}lg)} \\undocumented"))) NIL NIL @@ -3628,7 +3628,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-925 R -2308) +(-925 R -2313) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3640,7 +3640,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-928 S R -2308) +(-928 S R -2313) ((|constructor| (NIL "This package provides pattern matching functions on function spaces.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL @@ -3660,11 +3660,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -882) (|devaluate| |#1|)))) -(-933 R -2308 -3933) +(-933 R -2313 -3950) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-934 -3933) +(-934 -3950) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3687,7 +3687,7 @@ NIL (-939 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-940 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL @@ -3712,7 +3712,7 @@ NIL ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) NIL -(-946 E V R P -2308) +(-946 E V R P -2313) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3723,8 +3723,8 @@ NIL (-948 R) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials whose variables are arbitrary symbols. The ordering is alphabetic determined by the Symbol type. The coefficient ring may be non commutative,{} but the variables are assumed to commute.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(p,{}x)} computes the integral of \\spad{p*dx},{} \\spadignore{i.e.} integrates the polynomial \\spad{p} with respect to the variable \\spad{x}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) -(-949 E V R P -2308) +((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1170) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +(-949 E V R P -2313) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-452)))) @@ -3747,12 +3747,12 @@ NIL (-954 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-955) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-956 -2308) +(-956 -2313) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3767,11 +3767,11 @@ NIL (-959 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4404))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-131)))) (|HasAttribute| |#1| (QUOTE -4404))) (-960 A B) ((|constructor| (NIL "This domain implements cartesian product")) (|selectsecond| ((|#2| $) "\\spad{selectsecond(x)} \\undocumented")) (|selectfirst| ((|#1| $) "\\spad{selectfirst(x)} \\undocumented")) (|makeprod| (($ |#1| |#2|) "\\spad{makeprod(a,{}b)} \\undocumented"))) ((-4403 -12 (|has| |#2| (-473)) (|has| |#1| (-473)))) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722))))) (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-368)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-473))) (|HasCategory| |#2| (QUOTE (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-789))) (|HasCategory| |#2| (QUOTE (-789))))) (-12 (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#2| (QUOTE (-722)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-131))) (|HasCategory| |#2| (QUOTE (-131)))) (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-846))))) (-961) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3852,7 +3852,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-981 K R UP -2308) +(-981 K R UP -2313) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3911,11 +3911,11 @@ NIL (-995 R) ((|constructor| (NIL "\\spadtype{Quaternion} implements quaternions over a \\indented{2}{commutative ring. The main constructor function is \\spadfun{quatern}} \\indented{2}{which takes 4 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j}} \\indented{2}{imaginary part and the \\spad{k} imaginary part.}"))) ((-4399 |has| |#1| (-290)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-290))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -514) (QUOTE (-1170)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-1054))) (|HasCategory| |#1| (QUOTE (-545)))) (-996 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|List| |#1|)) "\\spad{queue([x,{}y,{}...,{}z])} creates a queue with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom) element \\spad{z}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-997 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3924,14 +3924,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-999 -2308 UP UPUP |radicnd| |n|) +(-999 -2313 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4399 |has| (-407 |#2|) (-363)) (-4404 |has| (-407 |#2|) (-363)) (-4398 |has| (-407 |#2|) (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2797 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2797 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2797 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) +((|HasCategory| (-407 |#2|) (QUOTE (-145))) (|HasCategory| (-407 |#2|) (QUOTE (-147))) (|HasCategory| (-407 |#2|) (QUOTE (-349))) (-2750 (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (|HasCategory| (-407 |#2|) (QUOTE (-363))) (|HasCategory| (-407 |#2|) (QUOTE (-368))) (-2750 (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (QUOTE (-349)))) (-2750 (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-349))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 |#2|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-12 (|HasCategory| (-407 |#2|) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-407 |#2|) (QUOTE (-363)))) (-12 (|HasCategory| (-407 |#2|) (QUOTE (-233))) (|HasCategory| (-407 |#2|) (QUOTE (-363))))) (-1000 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2797 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) +((|HasCategory| (-564) (QUOTE (-905))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-1170)))) (|HasCategory| (-564) (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-147))) (|HasCategory| (-564) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-1018))) (|HasCategory| (-564) (QUOTE (-816))) (-2750 (|HasCategory| (-564) (QUOTE (-816))) (|HasCategory| (-564) (QUOTE (-846)))) (|HasCategory| (-564) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-1145))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| (-564) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| (-564) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| (-564) (QUOTE (-233))) (|HasCategory| (-564) (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| (-564) (LIST (QUOTE -514) (QUOTE (-1170)) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -309) (QUOTE (-564)))) (|HasCategory| (-564) (LIST (QUOTE -286) (QUOTE (-564)) (QUOTE (-564)))) (|HasCategory| (-564) (QUOTE (-307))) (|HasCategory| (-564) (QUOTE (-545))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-564) (LIST (QUOTE -637) (QUOTE (-564)))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-564) (QUOTE (-905)))) (|HasCategory| (-564) (QUOTE (-145))))) (-1001) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,{}b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL @@ -3964,19 +3964,19 @@ NIL ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) ((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) NIL -(-1009 R -2308) +(-1009 R -2313) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n,{} f,{} g,{} x,{} lim,{} ext)} returns \\spad{[y,{} h,{} b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-1010 R -2308) +(-1010 R -2313) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n,{} f,{} g_1,{} g_2,{} x,{}lim,{}ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,{}dy2/dx) + ((0,{} - n df/dx),{}(n df/dx,{}0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-1011 -2308 UP) +(-1011 -2313 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a,{} B,{} C,{} n,{} D)} returns either: 1. \\spad{[Q,{} b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1,{} C1,{} m,{} \\alpha,{} \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f,{} g)} returns a \\spad{[y,{} b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,{}g,{}D)} returns \\spad{[A,{} B,{} C,{} T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-1012 -2308 UP) +(-1012 -2313 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f,{} g1,{} g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} if \\spad{y_1,{}y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,{}g1,{}g2,{}D)} returns \\spad{[A,{} B,{} H,{} C1,{} C2,{} T]} such that \\spad{(y1',{} y2') + ((0,{} -f),{} (f,{} 0)) (y1,{}y2) = (g1,{}g2)} has a solution if and only if \\spad{y1 = Q1 / T,{} y2 = Q2 / T},{} where \\spad{B,{}C1,{}C2,{}Q1,{}Q2} have no normal poles and satisfy A \\spad{(Q1',{} Q2') + ((H,{} -B),{} (B,{} H)) (Q1,{}Q2) = (C1,{}C2)} \\spad{D} is the derivation to use."))) NIL NIL @@ -4011,8 +4011,8 @@ NIL (-1020 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) ((-4399 . T) (-4404 . T) (-4398 . T) (-4401 . T) (-4400 . T) ((-4408 "*") . T) (-4403 . T)) -((-2797 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) -(-1021 -2308 L) +((-2750 (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-407 (-564)) (LIST (QUOTE -1034) (QUOTE (-564))))) +(-1021 -2313 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -4048,14 +4048,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-1030 -2308 |Expon| |VarSet| |FPol| |LFPol|) +(-1030 -2313 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) (((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL (-1031) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1032) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -4112,7 +4112,7 @@ NIL ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) ((-4403 . T)) NIL -(-1046 |xx| -2308) +(-1046 |xx| -2313) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4127,7 +4127,7 @@ NIL (-1049 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) ((-4406 . T) (-4401 . T) (-4400 . T)) -((-2797 (-12 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) +((-2750 (-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)))) (-2750 (|HasCategory| |#3| (QUOTE (-172))) (|HasCategory| |#3| (QUOTE (-363)))) (|HasCategory| |#3| (QUOTE (-363))) (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (QUOTE (-307))) (|HasCategory| |#3| (QUOTE (-556))) (|HasCategory| |#3| (QUOTE (-172))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858))))) (-1050 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,{}m,{}r)} returns a matrix \\spad{n} where \\spad{n[i,{}j] = f(m[i,{}j],{}r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,{}m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL @@ -4159,7 +4159,7 @@ NIL (-1057) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -2538) (QUOTE (-52))))))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (QUOTE (-1170))) (LIST (QUOTE |:|) (QUOTE -3726) (QUOTE (-52))))))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-52) (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| (-52) (QUOTE (-1094))) (|HasCategory| (-52) (LIST (QUOTE -309) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (QUOTE (-1094))) (|HasCategory| (-1170) (QUOTE (-846))) (|HasCategory| (-52) (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-52) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (LIST (QUOTE -611) (QUOTE (-858))))) (-1058 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL @@ -4208,11 +4208,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1070 |Base| R -2308) +(-1070 |Base| R -2313) ((|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 -2308) +(-1071 |Base| R -2313) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,{}...,{}rn])} creates the rule set \\spad{{r1,{}...,{}rn}}."))) NIL NIL @@ -4227,7 +4227,7 @@ NIL (-1074 R UP M) ((|constructor| (NIL "Domain which represents simple algebraic extensions of arbitrary rings. The first argument to the domain,{} \\spad{R},{} is the underlying ring,{} the second argument is a domain of univariate polynomials over \\spad{K},{} while the last argument specifies the defining minimal polynomial. The elements of the domain are canonically represented as polynomials of degree less than that of the minimal polynomial with coefficients in \\spad{R}. The second argument is both the type of the third argument and the underlying representation used by \\spadtype{SAE} itself."))) ((-4399 |has| |#1| (-363)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) +((|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-349))) (-2750 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-349)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-368))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-349)))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-349))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-12 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170))))) (-12 (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (QUOTE (-363))))) (-1075 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL @@ -4255,7 +4255,7 @@ NIL (-1081 R) ((|constructor| (NIL "\\spadtype{SequentialDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is sequential. \\blankline"))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1082 (-1170)) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-233))) (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1082 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL @@ -4315,7 +4315,7 @@ NIL (-1096 S) ((|constructor| (NIL "A set over a domain \\spad{D} models the usual mathematical notion of a finite set of elements from \\spad{D}. Sets are unordered collections of distinct elements (that is,{} order and duplication does not matter). The notation \\spad{set [a,{}b,{}c]} can be used to create a set and the usual operations such as union and intersection are available to form new sets. In our implementation,{} \\Language{} maintains the entries in sorted order. Specifically,{} the parts function returns the entries as a list in ascending order and the extract operation returns the maximum entry. Given two sets \\spad{s} and \\spad{t} where \\spad{\\#s = m} and \\spad{\\#t = n},{} the complexity of \\indented{2}{\\spad{s = t} is \\spad{O(min(n,{}m))}} \\indented{2}{\\spad{s < t} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{union(s,{}t)},{} \\spad{intersect(s,{}t)},{} \\spad{minus(s,{}t)},{} \\spad{symmetricDifference(s,{}t)} is \\spad{O(max(n,{}m))}} \\indented{2}{\\spad{member(x,{}t)} is \\spad{O(n log n)}} \\indented{2}{\\spad{insert(x,{}t)} and \\spad{remove(x,{}t)} is \\spad{O(n)}}"))) ((-4406 . T) (-4396 . T) (-4407 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#1| (QUOTE (-368))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1097 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4359,7 +4359,7 @@ NIL (-1107 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) 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(QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-789))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-844))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (|HasCategory| (-564) (QUOTE (-846))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (QUOTE (-233))) (|HasCategory| |#3| (QUOTE (-1045)))) (-12 (|HasCategory| |#3| (QUOTE (-1045))) (|HasCategory| |#3| (LIST (QUOTE -896) (QUOTE (-1170))))) (-2750 (|HasCategory| |#3| (QUOTE (-1045))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564)))))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -1034) (QUOTE (-564))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#3| (QUOTE (-1094)))) (|HasAttribute| |#3| (QUOTE -4403)) (|HasCategory| |#3| (QUOTE (-131))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#3| (QUOTE (-1094))) (|HasCategory| |#3| (LIST (QUOTE -309) (|devaluate| |#3|))))) (-1108 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL @@ -4368,7 +4368,7 @@ NIL ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for \\spad{`s'}.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature \\spad{`s'}.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,{}s,{}t)} builds the signature AST \\spad{n:} \\spad{s} \\spad{->} \\spad{t}"))) NIL NIL -(-1110 R -2308) +(-1110 R -2313) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4407,16 +4407,16 @@ NIL (-1119 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-905))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) +((|HasCategory| |#1| (QUOTE (-905))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (|HasCategory| |#1| (QUOTE (-452))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-363))) (|HasAttribute| |#1| (QUOTE -4404)) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-905)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1120 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|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))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1121 R E V P) ((|constructor| (NIL "The category of square-free and normalized triangular sets. Thus,{} up to the primitivity axiom of [1],{} these sets are Lazard triangular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991}"))) ((-4407 . T) (-4406 . T)) NIL -(-1122 UP -2308) +(-1122 UP -2313) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,{}g,{}h,{}i,{}k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,{}g,{}h,{}j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,{}g,{}h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,{}g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,{}g,{}h,{}i,{}j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,{}g,{}h,{}i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,{}g,{}h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,{}g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,{}f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL @@ -4471,11 +4471,11 @@ NIL (-1135 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2797 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))) (-2750 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -309) (LIST (QUOTE -1134) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1134 |#1| |#2|) (QUOTE (-1094))))) (|HasCategory| (-1134 |#1| |#2|) (LIST (QUOTE -611) (QUOTE (-858))))) (-1136 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) ((-4403 . T) (-4395 |has| |#2| (-6 (-4408 "*"))) (-4406 . T) (-4400 . T) (-4401 . T)) -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2797 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (-12 (|HasCategory| |#2| (QUOTE (-233))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (QUOTE (-307))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-363))) (-2750 (|HasAttribute| |#2| (QUOTE (-4408 "*"))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-172)))) (-1137 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL @@ -4495,7 +4495,7 @@ NIL (-1141 S) ((|constructor| (NIL "Linked List implementation of a Stack")) (|stack| (($ (|List| |#1|)) "\\spad{stack([x,{}y,{}...,{}z])} creates a stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1142 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL @@ -4507,7 +4507,7 @@ NIL (-1144 |Key| |Ent| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) ((-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094)))) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-846))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094)))) (-1145) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4531,7 +4531,7 @@ NIL (-1150 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) ((-4407 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1151) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) ((-4407 . T) (-4406 . T)) @@ -4539,11 +4539,11 @@ NIL (-1152) NIL ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) +((-2750 (-12 (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144))))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (|HasCategory| (-144) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| (-144) (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| (-144) (QUOTE (-1094))) (|HasCategory| (-144) (LIST (QUOTE -309) (QUOTE (-144)))))) (-1153 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. 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(|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4574,9 +4574,9 @@ NIL NIL (-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Laurent series."))) -(((-4408 "*") -2797 (-2366 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-172)) (-2366 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4399 -2797 (-2366 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-816))) (|has| |#1| (-556)) (-2366 (|has| |#1| (-363)) (|has| (-1168 |#1| |#2| |#3|) (-905)))) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . 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We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . 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(NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) 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T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2797 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4404))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-2750 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-452))) (-12 (|HasCategory| (-967) (QUOTE (-131))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasAttribute| |#1| (QUOTE -4404))) (-1173) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4659,7 +4659,7 @@ NIL (-1182 |Key| |Entry|) ((|constructor| (NIL "This is the general purpose table type. The keys are hashed to look up the entries. This creates a \\spadtype{HashTable} if equal for the Key domain is consistent with Lisp EQUAL otherwise an \\spadtype{AssociationList}"))) ((-4406 . T) (-4407 . T)) -((-12 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3090) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2538) (|devaluate| |#2|)))))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2797 (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -309) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3058) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3726) (|devaluate| |#2|)))))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#2| (QUOTE (-1094)))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -612) (QUOTE (-536)))) (-12 (|HasCategory| |#2| (QUOTE (-1094))) (|HasCategory| |#2| (LIST (QUOTE -309) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#2| (QUOTE (-1094))) (-2750 (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#2| (LIST (QUOTE -611) (QUOTE (-858)))) (|HasCategory| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (LIST (QUOTE -611) (QUOTE (-858))))) (-1183 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL @@ -4711,7 +4711,7 @@ NIL (-1195 S) ((|constructor| (NIL "\\spadtype{Tree(S)} is a basic domains of tree structures. Each tree is either empty or else is a {\\it node} consisting of a value and a list of (sub)trees.")) (|cyclicParents| (((|List| $) $) "\\spad{cyclicParents(t)} returns a list of cycles that are parents of \\spad{t}.")) (|cyclicEqual?| (((|Boolean|) $ $) "\\spad{cyclicEqual?(t1,{} t2)} tests of two cyclic trees have the same structure.")) (|cyclicEntries| (((|List| $) $) "\\spad{cyclicEntries(t)} returns a list of top-level cycles in tree \\spad{t}.")) (|cyclicCopy| (($ $) "\\spad{cyclicCopy(l)} makes a copy of a (possibly) cyclic tree \\spad{l}.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(t)} tests if \\spad{t} is a cyclic tree.")) (|tree| (($ |#1|) "\\spad{tree(nd)} creates a tree with value \\spad{nd},{} and no children") (($ (|List| |#1|)) "\\spad{tree(ls)} creates a tree from a list of elements of \\spad{s}.") (($ |#1| (|List| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4407 . T) (-4406 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) +((-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1094))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (-1196 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4720,7 +4720,7 @@ NIL ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1198 R -2308) +(-1198 R -2313) ((|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 -2308) +(-1200 R -2313) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -882) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -882) (|devaluate| |#1|))))) @@ -4743,7 +4743,7 @@ NIL (-1203 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|Mapping| $) (|Symbol|) |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ (|Symbol|) |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(s)} regroups terms of \\spad{s} by total degree \\indented{1}{and forms a series.}") (($ (|Symbol|)) "\\spad{coerce(s)} converts a variable to a Taylor series")) (|coefficient| (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-147))) (|HasCategory| |#1| (QUOTE (-145))) (-2797 (|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))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-363)))) (-1204 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL @@ -4756,7 +4756,7 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL ((|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) -(-1207 -2308) +(-1207 -2313) ((|constructor| (NIL "A basic package for the factorization of bivariate polynomials over a finite field. The functions here represent the base step for the multivariate factorizer.")) (|twoFactor| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) (|Integer|)) "\\spad{twoFactor(p,{}n)} returns the factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}. Also,{} \\spad{p} is assumed primitive and square-free and \\spad{n} is the degree of the inner variable of \\spad{p} (maximum of the degrees of the coefficients of \\spad{p}).")) (|generalSqFr| (((|Factored| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|))) "\\spad{generalSqFr(p)} returns the square-free factorisation of polynomial \\spad{p},{} a sparse univariate polynomial (sup) over a sup over \\spad{F}.")) 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(LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-816))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-172)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-905))) (|HasCategory| |#1| (QUOTE (-363)))) (-12 (|HasCategory| (-1251 |#1| |#2| |#3|) (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-363)))) (|HasCategory| |#1| (QUOTE (-145))))) (-1224 ZP) ((|constructor| (NIL "Package for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL @@ -4859,7 +4859,7 @@ NIL (-1232 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) (((-4408 "*") |has| |#2| (-172)) (-4399 |has| |#2| (-556)) (-4402 |has| |#2| (-363)) (-4404 |has| |#2| (-6 -4404)) (-4401 . T) (-4400 . T) (-4403 . T)) -((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2797 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2797 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2797 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) +((|HasCategory| |#2| (QUOTE (-905))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-172))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-556)))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-379)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-379))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -882) (QUOTE (-564)))) (|HasCategory| |#2| (LIST (QUOTE -882) (QUOTE (-564))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-379)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -612) (LIST (QUOTE -888) (QUOTE (-564)))))) (-12 (|HasCategory| (-1076) (LIST (QUOTE -612) (QUOTE (-536)))) (|HasCategory| |#2| (LIST (QUOTE -612) (QUOTE (-536))))) (|HasCategory| |#2| (QUOTE (-846))) (|HasCategory| |#2| (LIST (QUOTE -637) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-147))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (QUOTE (-564)))) (-2750 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| |#2| (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (-2750 (|HasCategory| |#2| (QUOTE (-172))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-556))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-452))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-363))) (|HasCategory| |#2| (QUOTE (-1145))) (|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasCategory| |#2| (QUOTE (-233))) (|HasAttribute| |#2| (QUOTE -4404)) (|HasCategory| |#2| (QUOTE (-452))) (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (-2750 (-12 (|HasCategory| $ (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-905)))) (|HasCategory| |#2| (QUOTE (-145))))) (-1233 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL @@ -4875,7 +4875,7 @@ NIL (-1236 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2345) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) +((|HasCategory| |#2| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1106))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2350) (LIST (|devaluate| |#2|) (QUOTE (-1170)))))) (-1237 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) @@ -4903,15 +4903,15 @@ NIL (-1243 |Coef| ULS) ((|constructor| (NIL "This package enables one to construct a univariate Puiseux series domain from a univariate Laurent series domain. Univariate Puiseux series are represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) +((|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|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 -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-1244 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4404 |has| |#1| (-363)) (-4398 |has| |#1| (-363)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2797 (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (|HasCategory| |#1| (QUOTE (-172))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564))) (|devaluate| |#1|)))) (|HasCategory| (-407 (-564)) (QUOTE (-1106))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-363))) (|HasCategory| |#1| (QUOTE (-556)))) (-2750 (|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 -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -407) (QUOTE (-564)))))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) (-1245 R FE |var| |cen|) ((|constructor| (NIL "UnivariatePuiseuxSeriesWithExponentialSingularity is a domain used to represent functions with essential singularities. Objects in this domain are sums,{} where each term in the sum is a univariate Puiseux series times the exponential of a univariate Puiseux series. Thus,{} the elements of this domain are sums of expressions of the form \\spad{g(x) * exp(f(x))},{} where \\spad{g}(\\spad{x}) is a univariate Puiseux series and \\spad{f}(\\spad{x}) is a univariate Puiseux series with no terms of non-negative degree.")) (|dominantTerm| (((|Union| (|Record| (|:| |%term| (|Record| (|:| |%coef| (|UnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expon| (|ExponentialOfUnivariatePuiseuxSeries| |#2| |#3| |#4|)) (|:| |%expTerms| (|List| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#2|)))))) (|:| |%type| (|String|))) "failed") $) "\\spad{dominantTerm(f(var))} returns the term that dominates the limiting behavior of \\spad{f(var)} as \\spad{var -> cen+} together with a \\spadtype{String} which briefly describes that behavior. The value of the \\spadtype{String} will be \\spad{\"zero\"} (resp. \\spad{\"infinity\"}) if the term tends to zero (resp. infinity) exponentially and will \\spad{\"series\"} if the term is a Puiseux series.")) (|limitPlus| (((|Union| (|OrderedCompletion| |#2|) "failed") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4408 "*") |has| (-1244 |#2| |#3| |#4|) (-172)) (-4399 |has| (-1244 |#2| |#3| |#4|) (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-147))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-172))) (-2797 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) +((|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))) (-2750 (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564)))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| (-1244 |#2| |#3| |#4|) (LIST (QUOTE -1034) (QUOTE (-564)))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-363))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-452))) (|HasCategory| (-1244 |#2| |#3| |#4|) (QUOTE (-556)))) (-1246 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL @@ -4927,7 +4927,7 @@ NIL (-1249 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2700) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#2| (QUOTE (-955))) (|HasCategory| |#2| (QUOTE (-1194))) (|HasSignature| |#2| (LIST (QUOTE -3743) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1871) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1170))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#2| (QUOTE (-363)))) (-1250 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#1|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#1|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) @@ -4935,12 +4935,12 @@ NIL (-1251 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) (((-4408 "*") |has| |#1| (-172)) (-4399 |has| |#1| (-556)) (-4400 . T) (-4401 . T) (-4403 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2797 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2345) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2797 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -2700) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -2560) (LIST (LIST (QUOTE -641) (QUOTE (-1170))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasCategory| |#1| (QUOTE (-556))) (-2750 (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-556)))) (|HasCategory| |#1| (QUOTE (-172))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-147))) (-12 (|HasCategory| |#1| (LIST (QUOTE -896) (QUOTE (-1170)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-767)) (|devaluate| |#1|)))) (|HasCategory| (-767) (QUOTE (-1106))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasSignature| |#1| (LIST (QUOTE -2350) (LIST (|devaluate| |#1|) (QUOTE (-1170)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-363))) (-2750 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-564)))) (|HasCategory| |#1| (QUOTE (-955))) (|HasCategory| |#1| (QUOTE (-1194))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -407) (QUOTE (-564))))) (|HasSignature| |#1| (LIST (QUOTE -1871) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1170))))) (|HasSignature| |#1| (LIST (QUOTE -3743) (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 -2308 UP L UTS) +(-1253 -2313 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s,{} n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL ((|HasCategory| |#1| (QUOTE (-556)))) @@ -4967,7 +4967,7 @@ NIL (-1259 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4407 . T) (-4406 . T)) -((-2797 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2797 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2797 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) +((-2750 (-12 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-2750 (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858))))) (|HasCategory| |#1| (LIST (QUOTE -612) (QUOTE (-536)))) (-2750 (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094)))) (|HasCategory| |#1| (QUOTE (-846))) (|HasCategory| (-564) (QUOTE (-846))) (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-722))) (|HasCategory| |#1| (QUOTE (-1045))) (-12 (|HasCategory| |#1| (QUOTE (-998))) (|HasCategory| |#1| (QUOTE (-1045)))) (|HasCategory| |#1| (LIST (QUOTE -611) (QUOTE (-858)))) (-12 (|HasCategory| |#1| (QUOTE (-1094))) (|HasCategory| |#1| (LIST (QUOTE -309) (|devaluate| |#1|))))) (-1260) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL @@ -5000,7 +5000,7 @@ NIL ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1268 K R UP -2308) +(-1268 K R UP -2313) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -5036,11 +5036,11 @@ NIL ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) ((-4399 |has| |#2| (-6 -4399)) (-4401 . T) (-4400 . T) (-4403 . T)) NIL -(-1277 S -2308) +(-1277 S -2313) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-368))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-147)))) -(-1278 -2308) +(-1278 -2313) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,{}s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) ((-4398 . T) (-4404 . T) (-4399 . T) ((-4408 "*") . T) (-4400 . T) (-4401 . T) (-4403 . T)) NIL diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 162685cd..94d2b1ed 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,15 +1,15 @@ -(162119 . 3451461731) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) -((((-564)) . T) (($) -2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) +(162119 . 3451578541) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +((((-564)) . T) (($) -2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T)) (((|#2| |#2|) . T)) ((((-564)) . T)) -((($ $) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) +((($ $) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T)) -((($) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) +((($) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564))))) (|has| |#1| (-905)) ((((-858)) . T)) ((((-858)) . T)) @@ -24,19 +24,19 @@ ((((-225)) . T) (((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-844))) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -(-2797 (|has| |#1| (-816)) (|has| |#1| (-846))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-844))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +(-2750 (|has| |#1| (-816)) (|has| |#1| (-846))) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2| |#3|) . T)) ((((-1175)) . T)) ((((-564)) . T) (((-866 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) -((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-858)) . T)) ((((-1175)) . T)) (((|#4|) . T)) @@ -46,14 +46,14 @@ (((|#1|) . T) ((|#2|) . T)) ((((-1175)) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(((|#2| (-482 (-2078 |#1|) (-767))) . T)) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2| (-482 (-2062 |#1|) (-767))) . T)) (((|#1| (-531 (-1170))) . T)) (((#0=(-866 |#1|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-1152)) . T) (((-954 (-129))) . T) (((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (|has| |#4| (-368)) (|has| |#3| (-368)) (((|#1|) . T)) @@ -67,13 +67,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-556)) -((((-564)) . T) (((-407 (-564))) -2797 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -((((-2 (|:| -2016 |#1|) (|:| -3756 |#2|))) . T)) +((((-564)) . T) (((-407 (-564))) -2750 (|has| |#2| (-38 (-407 (-564)))) (|has| |#2| (-1034 (-407 (-564))))) ((|#2|) . T) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((-860 |#1|)) . T)) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +((((-2 (|:| -2005 |#1|) (|:| -1377 |#2|))) . T)) ((($) . T)) -((((-564)) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-564)) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) ((|#1|) . T) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1170)) . T)) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) ((((-1170)) . T)) ((((-564)) . T) (($) . T)) @@ -84,66 +84,66 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (($) . T)) -((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) ((((-858)) . T)) (((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -(((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +(((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) (((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . 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T)) -(-2797 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2797 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2750 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2750 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1094)) @@ -157,33 +157,33 @@ ((((-564)) . T)) ((((-564)) . T)) (((|#1|) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| (-767)) . T)) (|has| |#2| (-789)) -(-2797 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) (|has| |#2| (-844)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-564) (-129)) . T)) (((|#1|) . 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T)) (|has| |#1| (-556)) (|has| |#1| (-556)) @@ -256,21 +256,21 @@ (((|#2|) . T) (($) . T) (((-407 (-564))) . T)) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) -((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (((-1168 |#1| |#2| |#3|)) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) (($) . 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T)) (((|#1| (-967)) . T)) (((#0=(-866 |#1|) $) |has| #0# (-286 #0# #0#))) @@ -314,7 +314,7 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1145)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-145)) (|has| (-1245 |#1| |#2| |#3| |#4|) (-147)) (|has| |#1| (-145)) @@ -326,27 +326,27 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) -((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-814 (-1170))) . T) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . 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T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) @@ -475,10 +475,10 @@ ((((-564) |#4|) . T)) ((((-564) |#3|) . T)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-407 (-564))) . T) (((-564)) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -489,7 +489,7 @@ ((((-564)) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . 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T)) ((((-858)) . T)) ((((-858)) . T)) @@ -732,22 +732,22 @@ (|has| |#1| (-1094)) (((|#2|) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564))))) -(((|#4|) -2797 (|has| |#4| (-172)) (|has| |#4| (-363)))) -(((|#3|) -2797 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(((|#4|) -2750 (|has| |#4| (-172)) (|has| |#4| (-363)))) +(((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)))) ((((-858)) . T)) (((|#1|) . T)) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((($ $) . T) ((#0=(-1170) $) |has| |#1| (-233)) ((#0# |#1|) |has| |#1| (-233)) ((#1=(-814 (-1170)) |#1|) . T) ((#1# $) . 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T)) (|has| (-407 |#2|) (-147)) (|has| (-407 |#2|) (-145)) @@ -760,15 +760,15 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-858)) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-388) (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-388) (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#2| (-1145)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) @@ -786,7 +786,7 @@ ((((-388) (-1152)) . T)) (|has| |#1| (-556)) ((((-564) |#1|) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) . T)) @@ -802,7 +802,7 @@ ((((-641 |#1|)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#2|) |has| |#2| (-309 |#2|))) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -812,7 +812,7 @@ (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T)) (|has| |#2| (-368)) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) @@ -826,8 +826,8 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($ $) . T)) ((((-858)) . T)) ((($ $) . T)) @@ -837,12 +837,12 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-407 (-564))) . T) (((-564)) . T)) ((((-564) (-144)) . T)) ((((-144)) . T)) (((|#1|) . T)) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-112)) . T)) @@ -851,26 +851,26 @@ ((((-858)) . T)) ((((-1175)) . T)) (|has| |#1| (-816)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-846)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-556)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (((-564)) . T)) (|has| |#1| (-905)) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-858)) . 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T)) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (|has| $ (-147)) (|has| $ (-147)) ((((-1175)) . T)) @@ -942,14 +942,14 @@ ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) ((($ $) |has| |#1| (-286 $ $)) ((|#1| $) |has| |#1| (-286 |#1| |#1|))) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) ((((-1170)) . T)) (|has| |#1| (-556)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) @@ -960,7 +960,7 @@ (|has| |#1| (-147)) (|has| |#1| (-145)) (|has| |#4| (-844)) -(((|#2| (-240 (-2078 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-240 (-2062 |#1|) (-767)) (-860 |#1|)) . T)) (|has| |#3| (-844)) (((|#1| (-531 |#3|) |#3|) . T)) (|has| |#1| (-147)) @@ -975,20 +975,20 @@ (|has| |#1| (-145)) ((((-407 (-564))) |has| |#2| (-363)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-349)) (|has| |#1| (-368))) ((((-1136 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-172)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-233)) (|has| |#2| (-1045))) -(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) -(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) +(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) ((((-695)) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-556)) (((|#1|) . T)) (((|#1|) . T)) @@ -1012,11 +1012,11 @@ (((|#1| (-407 (-564))) . T)) (((|#3|) . T) (((-610 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1|) . 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T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))))) ((((-858)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -1036,10 +1036,10 @@ ((($ $) . T) ((#0=(-860 |#1|) $) . T) ((#0# |#2|) . 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T)) (((|#1|) |has| |#1| (-309 |#1|))) @@ -1127,11 +1127,11 @@ (|has| |#1| (-368)) ((((-1170) $) |has| |#1| (-514 (-1170) $)) (($ $) |has| |#1| (-309 $)) ((|#1| |#1|) |has| |#1| (-309 |#1|)) (((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|))) ((((-1170)) |has| |#1| (-896 (-1170)))) -(-2797 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) +(-2750 (-12 (|has| |#1| (-233)) (|has| |#1| (-363))) (|has| |#1| (-349))) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-388) |#1|) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-1094)) (((|#2|) . T) (((-858)) . T)) ((((-858)) . T)) @@ -1139,8 +1139,8 @@ ((((-906 |#1|)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) (((|#1| |#2|) . T)) ((($) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1149,16 +1149,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (((|#1| |#1|) . T)) (((#0=(-866 |#1|)) |has| #0# (-309 #0#))) -((((-564)) . 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T)) (|has| |#1| (-1194)) (((#0=(-564) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) ((((-407 (-564))) . T) (($) . T)) @@ -1169,8 +1169,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (|has| |#1| (-363)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) . T) ((#0=(-407 (-564)) #0#) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((($ $) . T) ((#0=(-407 (-564)) #0#) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1| |#1|) . T)) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -1185,14 +1185,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) -((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) +((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) ((($) . T)) -(((#0=(-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) +(((#0=(-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) (|has| |#2| (-846)) ((($) . T)) (((|#2|) |has| |#2| (-1094))) -((((-858)) -2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +((((-858)) -2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) ((((-1152) (-52)) . T)) @@ -1201,10 +1201,10 @@ ((((-564)) |has| #0=(-407 |#2|) (-637 (-564))) ((#0#) . T)) ((($) . T) (((-564)) . T)) ((((-564) (-144)) . T)) -((((-564) (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#1| |#2|) . T)) ((((-407 (-564))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-858)) . T)) ((((-906 |#1|)) . T)) (|has| |#1| (-363)) @@ -1231,21 +1231,21 @@ ((((-858)) . T)) ((($) . T)) (((|#2|) . T) (($) . T)) -((((-564) (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#1| |#2|) . T)) +((((-564) (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-172))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) |has| |#1| (-172)) (($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905)))) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-564)) . 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T)) @@ -1253,39 +1253,39 @@ (|has| |#1| (-556)) ((((-1152) |#1|) . T)) (|has| |#1| (-1145)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-954 |#1|)) . T)) -(((#0=(-407 (-564)) #0#) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) +(((#0=(-407 (-564)) #0#) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) ((|#1| |#1|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-564))) (((-564)) |has| |#1| (-1034 (-564))) (((-1170)) |has| |#1| (-1034 (-1170))) ((|#1|) . T)) ((((-564) |#2|) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . 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T)) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-858)) -2797 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) +((((-858)) -2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-611 (-858))) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) (((-1259 |#3|)) . T)) ((((-564) |#2|) . T)) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(((|#2| |#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(((|#2| |#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($ $) |has| |#2| (-172))) (((|#2|) . T) (((-564)) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T) ((|#2|) . T)) ((((-858)) . T)) ((((-858)) . T)) ((((-1152) (-1170) (-564) (-225) (-858)) . T)) @@ -1320,8 +1320,8 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-1045))) (($) |has| |#2| (-172))) (|has| $ (-147)) ((((-407 |#2|)) . T)) ((((-889 |#1|)) . T) ((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) @@ -1333,11 +1333,11 @@ (((|#3|) |has| |#3| (-172))) (|has| |#1| (-147)) (|has| |#1| (-145)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) (((|#1|) . T)) (|has| |#2| (-233)) @@ -1374,7 +1374,7 @@ ((((-995 |#1|)) . T) ((|#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-407 (-564))) . T) (((-407 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1166 |#1|)) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) @@ -1382,9 +1382,9 @@ (|has| |#1| (-846)) (((|#2|) . T)) ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) ((((-564) |#2|) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#2|) . T)) ((((-564) |#3|) . T)) (((|#2|) . T)) @@ -1397,7 +1397,7 @@ (|has| |#1| (-1094)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) (((|#2| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#2|) . T)) @@ -1432,19 +1432,19 @@ (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1| |#2|) . T)) ((((-564) (-144)) . T)) -(((#0=(-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) #0#) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) -((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +(((#0=(-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) #0#) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#1| (-846)) (((|#2| (-767) (-1076)) . T)) (((|#1| |#2|) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) (|has| |#1| (-787)) (((|#1|) |has| |#1| (-172))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-2797 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) -(-2797 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) +(-2750 (|has| |#1| (-147)) (-12 (|has| |#1| (-363)) (|has| |#2| (-147)))) +(-2750 (|has| |#1| (-145)) (-12 (|has| |#1| (-363)) (|has| |#2| (-145)))) (((|#4|) . T)) (|has| |#1| (-145)) ((((-1152) |#1|) . T)) @@ -1458,10 +1458,10 @@ (((|#3|) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) (((|#1|) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094))) (((-954 |#1|)) . T)) (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1475,8 +1475,8 @@ ((($) . T)) ((((-388) (-1152)) . T)) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3090 (-1152)) (|:| -2538 #0#))) . T)) +((((-858)) -2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-611 (-858))) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((-1259 |#2|)) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3058 (-1152)) (|:| -3726 #0#))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) @@ -1484,7 +1484,7 @@ (|has| |#2| (-145)) (|has| |#2| (-147)) (|has| |#1| (-473)) -(-2797 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2750 (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) (|has| |#1| (-363)) ((((-858)) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -1495,8 +1495,8 @@ (|has| |#1| (-844)) ((((-858)) . T)) (((|#2|) . T)) -((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) -(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556)))) +((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-1251 |#1| |#2| |#3|)) |has| |#1| (-363)) ((|#1|) |has| |#1| (-172))) +(((|#1|) |has| |#1| (-172)) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556)))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#2|) . T) (((-564)) . T) (((-815 |#1|)) . T)) (((|#1| |#2|) . T)) @@ -1505,7 +1505,7 @@ ((((-858)) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) -(((|#2| (-482 (-2078 |#1|) (-767)) (-860 |#1|)) . T)) +(((|#2| (-482 (-2062 |#1|) (-767)) (-860 |#1|)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1| (-531 (-1170)) (-1170)) . T)) (((|#1|) . T)) @@ -1525,16 +1525,16 @@ (|has| |#1| (-147)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) +(((|#1|) . T) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-1170) (-52)) . T)) ((($ $) . T)) (((|#1| (-564)) . T)) ((((-906 |#1|)) . T)) -(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045))) (($) -2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) (|has| |#1| (-846)) (|has| |#1| (-846)) @@ -1553,11 +1553,11 @@ (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) (|has| |#2| (-846)) (|has| |#1| (-846)) -(((|#3|) -2797 (|has| |#3| (-172)) (|has| |#3| (-363)))) -(-2797 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) +(((|#3|) -2750 (|has| |#3| (-172)) (|has| |#3| (-363)))) +(-2750 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-905))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-564) |#2|) . T)) -(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)))) (|has| |#1| (-349)) (((|#3| |#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) (((|#2|) . T) (((-564)) . T)) @@ -1566,7 +1566,7 @@ (|has| |#1| (-816)) (|has| |#1| (-816)) (((|#1|) . T)) -(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-844)) (|has| |#1| (-844)) (|has| |#1| (-844)) @@ -1575,13 +1575,13 @@ ((((-564)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-1170)) |has| |#1| (-896 (-1170))) (((-1076)) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((#0=(-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))))) +(((#0=(-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-1094)) ((((-858)) . T) (((-1175)) . T)) @@ -1600,11 +1600,11 @@ (((|#1| (-767) (-1076)) . T)) (((|#3|) . T)) ((((-144)) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2797 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2750 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) (((|#1|) . T)) ((((-144)) . T)) (((|#2|) |has| |#2| (-172))) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((|#1|) . T)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -1627,32 +1627,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) ((((-668 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1661,7 +1661,7 @@ ((((-858)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) ((((-1175)) . T)) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T) (((-564)) . T)) (((|#3|) . T) (((-564)) . T) (((-610 $)) . T)) @@ -1669,12 +1669,12 @@ ((((-858)) . T)) ((((-858)) . T)) (((|#2|) . T)) -(-2797 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#3| (-25)) (|has| |#3| (-131)) (|has| |#3| (-172)) (|has| |#3| (-363)) (|has| |#3| (-368)) (|has| |#3| (-722)) (|has| |#3| (-789)) (|has| |#3| (-844)) (|has| |#3| (-1045)) (|has| |#3| (-1094))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) (|has| |#1| (-1194)) (|has| |#1| (-1194)) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (|has| |#1| (-1194)) (|has| |#1| (-1194)) (((|#3| |#3|) . T)) @@ -1687,16 +1687,16 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((((-1152) (-52)) . T)) (|has| |#1| (-1094)) -(-2797 (|has| |#2| (-816)) (|has| |#2| (-846))) +(-2750 (|has| |#2| (-816)) (|has| |#2| (-846))) (((|#1|) . T)) (((|#1|) |has| |#1| (-172)) (($) . T)) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((($) . T)) ((((-1168 |#1| |#2| |#3|)) -12 (|has| (-1168 |#1| |#2| |#3|) (-309 (-1168 |#1| |#2| |#3|))) (|has| |#1| (-363)))) ((((-858)) . T)) ((((-564)) . T) (($) . T)) ((((-767)) . T)) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((($) . T) (((-564)) . T)) @@ -1704,30 +1704,30 @@ (|has| |#2| (-905)) (|has| |#1| (-363)) (((|#2|) |has| |#2| (-1094))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-536)) . T) (((-407 (-1166 (-564)))) . T) (((-225)) . T) (((-379)) . T)) ((((-379)) . T) (((-225)) . T) (((-858)) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) (|has| |#1| (-905)) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) ((($) . T) ((|#2|) . T)) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) ((((-858)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((($ $) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((($ $) . T)) ((((-564) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-564)) . T)) ((((-112)) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-38 (-407 (-564)))) (((|#1| (-564)) . T)) ((($) . T)) @@ -1749,7 +1749,7 @@ (((|#1| (-1223 |#1| |#2| |#3|)) . T)) (((|#1| (-767)) . T)) (((|#1|) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-858)) . T)) (|has| |#1| (-1094)) ((((-1152) |#1|) . T)) @@ -1769,18 +1769,18 @@ (((|#1|) . T)) ((((-564)) . T)) ((((-858)) . T)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) (((|#3|) . T)) -(-2797 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2750 (|has| |#3| (-172)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2797 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-610 $)) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) -2750 (-12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-767)) . T)) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (((|#1|) |has| |#1| (-309 |#1|))) ((((-1245 |#1| |#2| |#3| |#4|)) . T)) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -1788,7 +1788,7 @@ (|has| |#1| (-556)) (((|#1|) . T)) ((((-858)) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) (((|#1|) |has| |#1| (-172))) ((($) |has| |#1| (-556)) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) @@ -1796,7 +1796,7 @@ (((|#1|) . T)) (((|#3|) |has| |#3| (-1094))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(((|#2|) -2797 (|has| |#2| (-172)) (|has| |#2| (-363)))) +(((|#2|) -2750 (|has| |#2| (-172)) (|has| |#2| (-363)))) ((((-1244 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-816)) @@ -1806,8 +1806,8 @@ (|has| |#1| (-844)) (|has| |#1| (-844)) (((|#1| (-564) (-1076)) . T)) -(-2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +(-2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (|has| |#1| (-846)) @@ -1820,33 +1820,33 @@ (|has| |#1| (-1094)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (|has| |#1| (-1094)) -((((-564)) -2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) +((((-564)) -2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)))) (((|#1|) . T)) (|has| |#1| (-1094)) ((((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-637 (-564)))) ((|#2|) |has| |#1| (-363))) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) -((((-685 (-339 (-2357) (-2357 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +((((-685 (-339 (-2363) (-2363 (QUOTE X) (QUOTE HESS)) (-695)))) . T)) (((|#2|) |has| |#2| (-172))) (((|#1|) |has| |#1| (-172))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) ((((-858)) . T)) (|has| |#3| (-844)) ((((-858)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-858)) . T)) -(((|#1| |#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1| |#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#1|) . T)) ((((-564)) . T)) ((((-564)) . T)) -(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) +(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-1045)))) (((|#2|) |has| |#2| (-363))) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) (|has| |#1| (-846)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-905))) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) ((((-858)) . T)) ((((-858)) . T)) @@ -1877,25 +1877,25 @@ (|has| |#1| (-145)) ((((-564)) . T) ((|#1|) . T) (($) . T) (((-407 (-564))) . T) (((-1170)) |has| |#1| (-1034 (-1170)))) (((|#1| |#2|) . T)) -((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2797 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) +((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) -2750 (|has| |#1| (-844)) (|has| |#1| (-1034 (-564)))) ((|#1|) . T)) ((((-144)) . T)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (((|#1|) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) (((|#2|) . T) ((|#1|) . T) (((-564)) . T)) ((((-858)) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| (-407 |#2|) (-233)) ((((-641 |#1|)) . T)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-1045))) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) (|has| |#1| (-363)) (((|#1|) |has| |#1| (-172))) (((|#1| |#1|) . T)) @@ -1922,7 +1922,7 @@ (((|#1| (-407 (-564)) (-1076)) . T)) (((|#1| (-767) (-1076)) . T)) (((#0=(-407 |#2|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-564)) -2797 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) +(((|#1|) . T) (((-564)) -2750 (|has| (-407 (-564)) (-1034 (-564))) (|has| |#1| (-1034 (-564)))) (((-407 (-564))) . T)) (((|#1| (-600 |#1| |#3|) (-600 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -1943,25 +1943,25 @@ (((|#2|) |has| |#2| (-172))) (|has| |#2| (-844)) ((((-564)) . T) ((|#2|) . T) (((-407 (-564))) |has| |#2| (-1034 (-407 (-564))))) -((((-112)) |has| |#1| (-1094)) (((-858)) -2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) +((((-112)) |has| |#1| (-1094)) (((-858)) -2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) ((((-858)) . T)) ((((-564) |#1|) . T)) ((((-858)) . T)) ((((-695)) . T) (((-407 (-564))) . T) (((-564)) . T)) (((|#1| |#1|) |has| |#1| (-172))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|))))) +(((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|))))) ((((-379)) . T)) ((((-695)) . T)) ((((-407 (-564))) . #0=(|has| |#2| (-363))) (($) . #0#)) (((|#1|) |has| |#1| (-172))) ((((-407 (-948 |#1|))) . T)) (((|#2| |#2|) . T)) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-846)) @@ -1972,14 +1972,14 @@ (((|#3|) |has| |#3| (-1045))) ((((-1170)) |has| |#2| (-896 (-1170)))) ((((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-473)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-368)) (|has| |#1| (-363)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-473)) (|has| |#1| (-556)) (|has| |#1| (-1045)) (|has| |#1| (-1106))) (|has| |#1| (-38 (-407 (-564)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -2000,11 +2000,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-846)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) |has| (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)) (-309 (-2 (|:| -3090 |#1|) (|:| -2538 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) |has| (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)) (-309 (-2 (|:| -3058 |#1|) (|:| -3726 |#2|)))) ((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -2022,11 +2022,11 @@ ((((-536)) |has| |#1| (-612 (-536))) (((-888 (-564))) |has| |#1| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#1| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#1| (-1018))) (((-225)) . #0#)) (((|#1|) |has| |#1| (-363))) ((((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((($ $) . T) (((-610 $) $) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) ((($) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (((-407 (-564))) . T)) -((($) -2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) +((($) -2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (|has| |#1| (-363)) @@ -2037,11 +2037,11 @@ ((((-379)) . T)) (((|#3|) -12 (|has| |#3| (-309 |#3|)) (|has| |#3| (-1094)))) ((((-858)) . T)) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-905))) (((|#1|) . T)) (|has| |#1| (-846)) (|has| |#1| (-846)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-536)) |has| |#1| (-612 (-536)))) (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) ((((-767)) . T)) @@ -2052,13 +2052,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((((-564)) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|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)) -(-2797 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2797 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2750 (-12 (|has| (-1251 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2750 (-12 (|has| (-1251 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-363)) (|has| |#1| (-145)) (|has| |#1| (-147)) @@ -2073,23 +2073,23 @@ (((|#2|) . T)) (|has| |#1| (-1094)) (((|#1| |#2|) . T)) -((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) +((((-564)) . T) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-1034 (-407 (-564)))))) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) (((|#3|) |has| |#3| (-172))) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) ((((-858)) . T)) ((((-564)) . T)) (((|#1| $) |has| |#1| (-286 |#1| |#1|))) ((((-407 (-564))) . T) (($) . T) (((-407 |#1|)) . T) ((|#1|) . T)) ((((-948 |#1|)) . T) (((-858)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -2797 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -2750 (|has| |#1| (-290)) (|has| |#1| (-363))) ((#0=(-407 (-564)) #0#) |has| |#1| (-363))) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) ((((-948 |#1|)) . T)) ((($) . T)) ((((-564) |#1|) . T)) ((((-1170)) |has| (-407 |#2|) (-896 (-1170)))) -(((|#1|) . T) (($) -2797 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) +(((|#1|) . T) (($) -2750 (|has| |#1| (-290)) (|has| |#1| (-363))) (((-407 (-564))) |has| |#1| (-363))) ((((-536)) |has| |#2| (-612 (-536)))) ((((-685 |#2|)) . T) (((-858)) . T)) (((|#1|) . T)) @@ -2097,8 +2097,8 @@ (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) ((((-866 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2797 (|has| |#4| (-789)) (|has| |#4| (-844))) -(-2797 (|has| |#3| (-789)) (|has| |#3| (-844))) +(-2750 (|has| |#4| (-789)) (|has| |#4| (-844))) +(-2750 (|has| |#3| (-789)) (|has| |#3| (-844))) ((((-858)) . T)) ((((-858)) . T)) (((|#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) @@ -2114,17 +2114,17 @@ ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) ((((-407 (-564))) . T) (($) . T)) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-1213))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-1213))) ((($) . T)) ((((-407 (-564))) |has| #0=(-407 |#2|) (-1034 (-407 (-564)))) (((-564)) |has| #0# (-1034 (-564))) ((#0#) . T)) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| (-767)) . T)) (|has| |#1| (-846)) (((|#1|) . T) (((-564)) |has| |#1| (-637 (-564)))) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2797 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((-407 (-564))) -2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((|#1|) . T)) ((((-564)) . T)) (|has| |#1| (-38 (-407 (-564)))) -((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))))) +((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))))) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (|has| |#1| (-844)) (|has| |#1| (-38 (-407 (-564)))) @@ -2148,29 +2148,29 @@ (|has| |#1| (-38 (-407 (-564)))) ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) ((((-858)) . T)) -(((|#2|) . T) (((-564)) . T) (($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(((|#2|) . 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T)) -((($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) +((($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) ((($) . T)) ((((-407 (-948 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -((($) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-536)) |has| |#4| (-612 (-536)))) ((((-858)) . T) (((-641 |#4|)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-844)) -(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) |has| (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|)) (-309 (-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))))) +(((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))) (((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) |has| (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|)) (-309 (-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))))) (|has| |#1| (-1094)) (|has| |#1| (-363)) (|has| |#1| (-846)) @@ -2179,16 +2179,16 @@ (((|#1|) . T)) ((((-668 |#1|)) . T)) ((($) . T) (((-407 (-564))) . T)) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) |has| |#1| (-172))) (|has| |#1| (-145)) (|has| |#1| (-147)) -(-2797 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) -(-2797 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) +(-2750 (-12 (|has| (-1168 |#1| |#2| |#3|) (-147)) (|has| |#1| (-363))) (|has| |#1| (-147))) +(-2750 (-12 (|has| (-1168 |#1| |#2| |#3|) (-145)) (|has| |#1| (-363))) (|has| |#1| (-145))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-147)) (|has| |#1| (-145)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) (|has| |#1| (-844)) (((|#1| |#2|) . T)) @@ -2212,9 +2212,9 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -(((|#1|) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)))) +(((|#1|) -2750 (|has| |#1| (-172)) (|has| |#1| (-363)))) ((((-316 |#1|)) . T)) (((|#2|) |has| |#2| (-363))) (((|#2|) . T)) @@ -2236,13 +2236,13 @@ (|has| |#1| (-145)) (|has| |#1| (-147)) ((($ $) . T)) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-473)) (|has| |#1| (-722)) (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045)) (|has| |#1| (-1106)) (|has| |#1| (-1094))) (|has| |#1| (-556)) (((|#2|) . T)) ((((-564)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1|) . T)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) (((|#1| (-59 |#1|) (-59 |#1|)) . T)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2258,7 +2258,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1244 |#2| |#3| |#4|)) . T) (((-564)) . T) (((-1245 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-407 (-564))) . T)) -((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2797 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2797 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) +((((-48)) -12 (|has| |#1| (-556)) (|has| |#1| (-1034 (-564)))) (((-564)) -2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1034 (-564))) (|has| |#1| (-1045))) ((|#1|) . T) (((-610 $)) . T) (($) |has| |#1| (-556)) (((-407 (-564))) -2750 (|has| |#1| (-556)) (|has| |#1| (-1034 (-407 (-564))))) (((-407 (-948 |#1|))) |has| |#1| (-556)) (((-948 |#1|)) |has| |#1| (-1045)) (((-1170)) . T)) ((((-407 (-564))) |has| |#2| (-1034 (-407 (-564)))) (((-564)) |has| |#2| (-1034 (-564))) ((|#2|) . T) (((-860 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-407 (-564))) . T)) ((((-1119 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) @@ -2271,12 +2271,12 @@ (((|#1| |#2|) . T)) ((((-1170) |#1|) . T)) (((|#4|) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1170) (-52)) . T)) ((((-1244 |#2| |#3| |#4|) (-319 |#2| |#3| |#4|)) . T)) ((((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) (((-564)) |has| |#1| (-1034 (-564))) ((|#1|) . T)) ((((-858)) . T)) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-368)) (|has| |#2| (-722)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045)) (|has| |#2| (-1094))) (((#0=(-1245 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-172)) ((#0=(-407 (-564)) #0#) |has| |#1| (-556)) (($ $) |has| |#1| (-556))) (((|#1|) . T) (($) . T) (((-407 (-564))) . T)) @@ -2296,14 +2296,14 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((|#2| |#3|) . T)) -(-2797 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#2| (-363)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1| (-531 |#2|)) . T)) (((|#1| (-767)) . T)) (((|#1| (-531 (-1082 (-1170)))) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (|has| |#2| (-905)) -(-2797 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-858)) . T)) ((($ $) . T) ((#0=(-1244 |#2| |#3| |#4|) #0#) . T) ((#1=(-407 (-564)) #1#) |has| #0# (-38 (-407 (-564))))) ((((-906 |#1|)) . T)) @@ -2312,14 +2312,14 @@ ((((-858)) . T)) ((($) . T)) ((($) . T)) -(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-363)) (((|#1| |#2|) . T)) ((($) . T) ((#0=(-1244 |#2| |#3| |#4|)) . T) (((-407 (-564))) |has| #0# (-38 (-407 (-564))))) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(-2797 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2797 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) +(-2750 (-12 (|has| |#1| (-307)) (|has| |#1| (-905))) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-896 (-1170))) (|has| |#1| (-1045))) ((((-564)) |has| |#1| (-637 (-564))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-858)) . T)) @@ -2352,27 +2352,27 @@ (((|#1|) |has| |#1| (-172))) ((((-858)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-309 |#4|)) (|has| |#4| (-1094)))) -(((|#2|) -2797 (|has| |#2| (-6 (-4408 "*"))) (|has| |#2| (-172)))) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(((|#2|) -2750 (|has| |#2| (-6 (-4408 "*"))) (|has| |#2| (-172)))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#2| (-846)) (|has| |#2| (-905)) (|has| |#1| (-905)) (((|#2|) |has| |#2| (-172))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) ((((-858)) . T)) ((((-858)) . T)) ((((-536)) . T) (((-564)) . T) (((-888 (-564))) . T) (((-379)) . T) (((-225)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) (((|#1|) . T)) ((((-858)) . T)) (((|#1| |#2|) . T)) (((|#1| (-407 (-564))) . T)) (((|#1|) . T)) -(-2797 (|has| |#1| (-290)) (|has| |#1| (-363))) +(-2750 (|has| |#1| (-290)) (|has| |#1| (-363))) ((((-144)) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T)) (|has| |#1| (-844)) @@ -2388,7 +2388,7 @@ ((((-858)) . T)) ((((-858)) . T)) ((((-187)) . T) (((-858)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2401,7 +2401,7 @@ ((((-858)) . T)) ((((-1152)) . T)) ((((-1170) |#1|) |has| |#1| (-514 (-1170) |#1|)) ((|#1| |#1|) |has| |#1| (-309 |#1|))) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (|has| |#1| (-846)) ((((-858)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) @@ -2413,16 +2413,16 @@ (((|#2|) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) ((($) . T) (((-564)) . T) (((-407 (-564))) . T) (((-610 $)) . T)) -(-2797 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2797 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2750 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2750 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-1170) (-52)) . T)) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (|has| |#1| (-905)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) (|has| |#1| (-905)) @@ -2439,12 +2439,12 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (|has| |#1| (-816)) (((#0=(-906 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((((-407 |#2|)) . T)) (|has| |#1| (-844)) -((((-1195 |#1|)) . T) (((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-1195 |#1|)) . T) (((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) . T) ((#1=(-564) #1#) . T) (($ $) . T)) ((((-906 |#1|)) . T) (($) . T) (((-407 (-564))) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) @@ -2455,11 +2455,11 @@ (((|#2|) . T)) ((((-858)) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T) (((-564)) . T)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3090 (-1170)) (|:| -2538 #0#))) . T)) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3058 (-1170)) (|:| -3726 #0#))) . T)) (|has| |#1| (-349)) ((((-564)) . T)) ((((-858)) . T)) @@ -2467,15 +2467,15 @@ (((#0=(-1245 |#1| |#2| |#3| |#4|) $) |has| #0# (-286 #0# #0#))) (|has| |#1| (-363)) (((#0=(-1076) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) (((#0=(-407 (-564)) #0#) . T) ((#1=(-695) #1#) . T) (($ $) . T)) ((((-316 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) |has| |#1| (-363))) ((((-858)) . T)) (|has| |#1| (-1094)) (((|#1|) . T)) -(((|#1|) -2797 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) -(((|#1|) -2797 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2750 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) +(((|#1|) -2750 (|has| |#2| (-367 |#1|)) (|has| |#2| (-417 |#1|)))) (((|#2|) . T)) ((((-407 (-564))) . T) (((-695)) . T) (($) . T)) ((((-579)) . T)) @@ -2498,7 +2498,7 @@ (((|#1|) . T)) ((((-564)) . T)) (((|#2|) . T) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((|#1|) . T) (($) . T) (((-564)) . T)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((|#2|) . T) (((-564)) |has| |#2| (-637 (-564)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2536,7 +2536,7 @@ (|has| |#2| (-1018)) ((($) . T)) (|has| |#1| (-905)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2544,9 +2544,9 @@ ((($) . T)) (|has| |#1| (-363)) ((((-906 |#1|)) . T)) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) -(-2797 (|has| |#1| (-368)) (|has| |#1| (-846))) +(-2750 (|has| |#1| (-368)) (|has| |#1| (-846))) (((|#1|) . T)) ((((-767)) . T)) ((((-858)) . T)) @@ -2557,16 +2557,16 @@ ((((-564)) . T) (($) . T)) ((((-564)) . T) (($) . T)) ((((-767) |#1|) . T)) -(((|#2| (-240 (-2078 |#1|) (-767))) . T)) +(((|#2| (-240 (-2062 |#1|) (-767))) . T)) (((|#1| (-531 |#3|)) . T)) ((((-407 (-564))) . T)) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((((-1152)) . T) (((-858)) . T)) -(((#0=(-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) #0#) |has| (-2 (|:| -3090 (-1170)) (|:| -2538 (-52))) (-309 (-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))))) +(((#0=(-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) #0#) |has| (-2 (|:| -3058 (-1170)) (|:| -3726 (-52))) (-309 (-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))))) ((((-1152)) . T)) (|has| |#1| (-905)) (|has| |#2| (-363)) -(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) (((|#1|) . T)) @@ -2583,11 +2583,11 @@ (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-307)) (|has| |#1| (-363)) (|has| |#1| (-349))) (|has| |#1| (-38 (-407 (-564)))) (-12 (|has| |#1| (-545)) (|has| |#1| (-824))) ((((-858)) . T)) -((((-1170)) -2797 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) +((((-1170)) -2750 (-12 (|has| |#1| (-15 * (|#1| (-564) |#1|))) (|has| |#1| (-896 (-1170)))) (-12 (|has| |#1| (-363)) (|has| |#2| (-896 (-1170)))))) (|has| |#1| (-363)) ((((-1170)) -12 (|has| |#1| (-15 * (|#1| (-407 (-564)) |#1|))) (|has| |#1| (-896 (-1170))))) (|has| |#1| (-363)) @@ -2598,7 +2598,7 @@ (((|#2|) |has| |#1| (-363))) (((|#2|) |has| |#1| (-363))) ((((-564)) . T) (($) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) @@ -2623,9 +2623,9 @@ ((((-379)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-379)))) (((-564)) -12 (|has| |#1| (-363)) (|has| |#2| (-882 (-564))))) (|has| |#1| (-363)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) (|has| |#1| (-363)) (|has| |#1| (-556)) (((|#1|) . T)) @@ -2634,22 +2634,22 @@ ((((-1152)) . T) (((-506)) . T) (((-225)) . T) (((-564)) . T)) (((|#1|) . T)) ((((-407 |#2|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) -(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#2|) . T)) (((|#2|) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (|has| |#1| (-38 (-407 (-564)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-1152) |#1|) . T)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-368))) (|has| |#1| (-147)) ((((-581 |#1|)) . T)) ((($) . T)) @@ -2657,7 +2657,7 @@ (|has| |#1| (-556)) (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564)))) -(-2797 (|has| |#1| (-145)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-349))) (|has| |#1| (-147)) ((((-858)) . T)) ((($) . T)) @@ -2685,7 +2685,7 @@ ((((-858)) . T)) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2707,7 +2707,7 @@ ((((-564)) . T)) ((((-858)) . T)) ((((-564)) . T)) -(-2797 (|has| |#2| (-789)) (|has| |#2| (-844))) +(-2750 (|has| |#2| (-789)) (|has| |#2| (-844))) ((((-169 (-379))) . T) (((-225)) . T) (((-379)) . T)) ((((-858)) . T)) ((((-858)) . T)) @@ -2719,9 +2719,9 @@ (((|#1|) . T) (($) . T) (((-407 (-564))) . 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T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) ((((-379)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2751,7 +2751,7 @@ (|has| |#1| (-556)) (|has| |#1| (-1094)) ((((-776 |#1| (-860 |#2|))) |has| (-776 |#1| (-860 |#2|)) (-309 (-776 |#1| (-860 |#2|))))) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2763,13 +2763,13 @@ (|has| |#2| (-363)) ((((-581 |#1|)) . T) (((-407 (-564))) . T) (($) . T) (((-564)) . T)) ((((-564)) . T) (((-407 (-564))) . T) (($) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 (-52)))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 (-52)))) . T)) (((|#1|) . T)) (((|#1|) . T) (((-564)) . T)) (((|#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) ((((-858)) . T)) ((((-858)) . 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T)) +((((-1166 |#1|)) . T) (((-564)) . T) (($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) (((-1076)) . T) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564)))))) +(-2750 (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-172)) (|has| |#1| (-556)) (|has| |#1| (-1045))) +((((-1119 |#1| (-1170))) . T) (((-564)) . T) (((-1082 (-1170))) . T) (($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-1034 (-407 (-564))))) (((-1170)) . T)) (((#0=(-581 |#1|) #0#) . T) (($ $) . T) ((#1=(-407 (-564)) #1#) . T)) ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) (((|#1|) |has| |#1| (-172))) @@ -2799,7 +2799,7 @@ (((|#1|) . T)) ((((-858)) . T)) ((((-294 |#3|)) . T)) -(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2797 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +(((#0=(-407 (-564)) #0#) |has| |#2| (-38 (-407 (-564)))) ((|#2| |#2|) . T) (($ $) -2750 (|has| |#2| (-172)) (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) @@ -2807,21 +2807,21 @@ (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) (((|#1|) . T) (((-407 (-564))) . T) (($) . T)) -((($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . T) ((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564))))) -((($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1| |#1|) . 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T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) (|has| |#2| (-905)) (|has| |#1| (-905)) -((($) -2797 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-172)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-858)) . T)) (((|#1|) . T)) -((((-2 (|:| -3090 (-1152)) (|:| -2538 |#1|))) . T)) +((((-2 (|:| -3058 (-1152)) (|:| -3726 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2836,10 +2836,10 @@ (((|#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094)))) (((#0=(-407 (-564)) #0#) . T)) ((((-407 (-564))) . T)) -(-2797 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-25)) (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) (((|#1|) . T)) (((|#1|) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-407 (-564))) . T) (((-564)) . T) (($) . T)) ((((-536)) . T)) ((((-858)) . T)) @@ -2856,12 +2856,12 @@ ((($ $) . T) ((#0=(-407 (-564)) #0#) . T)) ((((-1170)) |has| |#1| (-896 (-1170)))) ((((-906 |#1|)) . T) (((-407 (-564))) . T) (($) . T)) -((($) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) -(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2797 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((($) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#1|) . T)) +(((#0=(-407 (-564)) #0#) |has| |#1| (-38 (-407 (-564)))) ((|#1| |#1|) . T) (($ $) -2750 (|has| |#1| (-172)) (|has| |#1| (-556)))) ((($) . T) (((-407 (-564))) . T)) (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((|#2|) |has| |#2| (-1045)) (((-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045)))) -((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2797 (|has| |#1| (-172)) (|has| |#1| (-556)))) +((((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T) (($) -2750 (|has| |#1| (-172)) (|has| |#1| (-556)))) (|has| |#1| (-556)) (((|#1|) |has| |#1| (-363))) ((((-564)) . T)) @@ -2880,8 +2880,8 @@ ((((-858)) . T)) (|has| |#2| (-816)) (|has| |#2| (-816)) -((((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-407 (-564))) -2797 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) +((((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) ((|#2|) |has| |#1| (-363)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-407 (-564))) -2750 (|has| |#1| (-38 (-407 (-564)))) (|has| |#1| (-363))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (((|#1|) . T) (((-564)) |has| |#1| (-1034 (-564))) (((-407 (-564))) |has| |#1| (-1034 (-407 (-564))))) ((((-564)) |has| |#1| (-882 (-564))) (((-379)) |has| |#1| (-882 (-379)))) @@ -2907,12 +2907,12 @@ (((|#2| (-767)) . T)) ((((-1170)) . T)) ((((-866 |#1|)) . 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T)) (((|#2| |#2|) . T) ((#0=(-407 (-564)) #0#) . T) (($ $) . T)) ((((-564)) . T)) @@ -3256,17 +3256,17 @@ ((((-129)) . T)) ((((-858)) . T)) ((((-1251 |#1| |#2| |#3|)) |has| |#1| (-363))) -((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) +((((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) |has| |#2| (-172)) (($) -2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905)))) (((|#2|) . T) ((|#6|) . T)) ((($) . T) (((-407 (-564))) |has| |#2| (-38 (-407 (-564)))) ((|#2|) . T)) (|has| |#1| (-363)) -((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1098)) . T)) ((((-858)) . T)) -((($) -2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((($) . T) (((-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((|#1|) . T)) ((($) . T)) -((($) -2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) +((($) -2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((|#1|) |has| |#1| (-172)) (((-407 (-564))) |has| |#1| (-38 (-407 (-564))))) ((((-1251 |#1| |#2| |#3|)) . T) (((-1223 |#1| |#2| |#3|)) . T)) ((((-1170)) . T) (((-858)) . T)) (|has| |#2| (-905)) @@ -3276,7 +3276,7 @@ (((|#1|) . T)) (((|#1| |#1|) |has| |#1| (-172))) ((((-695)) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-1175)) . T)) (((|#1|) |has| |#1| (-172))) ((((-1175)) . T)) @@ -3288,13 +3288,13 @@ ((((-1175)) . T)) ((((-1175)) . T)) ((((-1175)) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-349))) ((((-1175)) . T)) ((((-1175)) . T)) (|has| |#1| (-363)) (|has| |#1| (-363)) -(-2797 (|has| |#1| (-172)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-172)) (|has| |#1| (-556))) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) (((|#1| (-767)) . T)) @@ -3309,16 +3309,16 @@ ((((-888 (-379))) . T) (((-888 (-564))) . T) (((-1170)) . T) (((-536)) . T)) (((|#1|) . T)) ((((-858)) . T)) -(-2797 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) -(-2797 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) +(-2750 (|has| |#2| (-131)) (|has| |#2| (-172)) (|has| |#2| (-363)) (|has| |#2| (-789)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-131)) (|has| |#2| (-131))) (-12 (|has| |#1| (-789)) (|has| |#2| (-789)))) ((((-564)) . T)) ((((-564)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-2797 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) +(-2750 (|has| |#2| (-172)) (|has| |#2| (-722)) (|has| |#2| (-844)) (|has| |#2| (-1045))) ((((-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045)))) -(-2797 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) +(-2750 (-12 (|has| |#1| (-473)) (|has| |#2| (-473))) (-12 (|has| |#1| (-722)) (|has| |#2| (-722)))) (|has| |#1| (-145)) (|has| |#1| (-147)) (|has| |#1| (-363)) @@ -3344,7 +3344,7 @@ (((|#1| |#2|) . T)) ((((-564)) . T) ((|#2|) |has| |#2| (-172))) ((((-114)) . T) ((|#1|) . T) (((-564)) . T)) -(-2797 (|has| |#1| (-349)) (|has| |#1| (-368))) +(-2750 (|has| |#1| (-349)) (|has| |#1| (-368))) (((|#1| |#2|) . T)) ((((-225)) . T)) ((((-407 (-564))) . T) (($) . T) (((-564)) . T)) @@ -3356,7 +3356,7 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-536)) |has| |#1| (-612 (-536)))) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-846)) (|has| |#1| (-1094)))) ((($) . T) (((-407 (-564))) . T)) (|has| |#1| (-905)) (|has| |#1| (-905)) @@ -3367,14 +3367,14 @@ (((|#1| |#1|) |has| |#1| (-172))) (((|#1|) . T) (((-564)) . T)) ((((-1175)) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-556))) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-556))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#2|) . T)) -(-2797 (|has| |#1| (-21)) (|has| |#1| (-844))) +(-2750 (|has| |#1| (-21)) (|has| |#1| (-844))) (((|#1|) |has| |#1| (-172))) (((|#1|) . T)) (((|#1|) . T)) -((((-858)) -2797 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) +((((-858)) -2750 (-12 (|has| |#1| (-611 (-858))) (|has| |#2| (-611 (-858)))) (-12 (|has| |#1| (-1094)) (|has| |#2| (-1094))))) ((((-407 |#2|) |#3|) . T)) ((((-407 (-564))) . T) (($) . T)) (|has| |#1| (-38 (-407 (-564)))) @@ -3386,19 +3386,19 @@ (((|#1|) . T) (((-407 (-564))) . T) (((-564)) . T) (($) . T)) (((#0=(-564) #0#) . T)) ((($) . T) (((-407 (-564))) . T)) -(-2797 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) -(-2797 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) +(-2750 (|has| |#4| (-172)) (|has| |#4| (-722)) (|has| |#4| (-844)) (|has| |#4| (-1045))) +(-2750 (|has| |#3| (-172)) (|has| |#3| (-722)) (|has| |#3| (-844)) (|has| |#3| (-1045))) ((((-858)) . T) (((-1175)) . 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T)) ((((-1168 |#1| |#2| |#3|)) |has| |#1| (-363))) -(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) +(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) ((($) . T)) (|has| |#1| (-1018)) -(((|#2|) . T) (((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) ((((-858)) . T)) ((((-536)) |has| |#2| (-612 (-536))) (((-888 (-564))) |has| |#2| (-612 (-888 (-564)))) (((-888 (-379))) |has| |#2| (-612 (-888 (-379)))) (((-379)) . #0=(|has| |#2| (-1018))) (((-225)) . #0#)) ((((-294 |#3|)) . T)) @@ -3433,15 +3433,15 @@ ((((-1168 |#1| |#2| |#3|)) . T)) ((((-1168 |#1| |#2| |#3|)) . T) (((-1161 |#1| |#2| |#3|)) . T)) ((((-858)) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-564) |#1|) . 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T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) ((((-129)) . T) (((-858)) . T)) ((((-564) |#1|) . T)) ((((-129)) . T)) @@ -3465,13 +3465,13 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-363)) (|has| |#2| (-286 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-2797 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) -(-2797 (|has| |#1| (-846)) (|has| |#1| (-1094))) +(-2750 (|has| |#1| (-363)) (|has| |#1| (-452)) (|has| |#1| (-905))) +(-2750 (|has| |#1| (-846)) (|has| |#1| (-1094))) ((((-858)) . T)) ((((-858)) . T)) ((((-858)) . T)) (((|#1| (-531 |#2|)) . T)) -((((-2 (|:| -3090 (-1170)) (|:| -2538 (-52)))) . T)) +((((-2 (|:| -3058 (-1170)) (|:| -3726 (-52)))) . T)) ((((-564) (-129)) . T)) (((|#1| (-564)) . T)) (((|#1| (-407 (-564))) . T)) @@ -3485,8 +3485,8 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) -(-2797 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) -(-2797 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) +(-2750 (|has| |#2| (-452)) (|has| |#2| (-556)) (|has| |#2| (-905))) +(-2750 (|has| |#1| (-452)) (|has| |#1| (-556)) (|has| |#1| (-905))) ((($) . T)) (((|#2| (-531 (-860 |#1|))) . T)) ((((-1175)) . T)) @@ -3501,13 +3501,13 @@ ((((-1175)) . T)) ((((-858)) . T) (((-1175)) . T)) ((((-1175)) . T)) -((((-858)) -2797 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) +((((-858)) -2750 (|has| |#1| (-611 (-858))) (|has| |#1| (-1094)))) (((|#1|) . T)) (((|#2| (-767)) . T)) (((|#1| |#2|) . T)) ((((-1152) |#1|) . T)) ((((-407 |#2|)) . T)) -((((-2 (|:| -3090 |#1|) (|:| -2538 |#2|))) . T)) +((((-2 (|:| -3058 |#1|) (|:| -3726 |#2|))) . T)) (|has| |#1| (-556)) (|has| |#1| (-556)) ((($) . T) ((|#2|) . T)) @@ -3516,14 +3516,14 @@ ((((-564)) . T) (($) . 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-131) T) ((-394 . -1094) T) ((-690 . -370) 143997) ((-866 . -1052) T) ((-223 . -618) 143974) ((-327 . -286) 143951) ((-474 . -111) 143772) ((-1243 . -1045) T) ((-1222 . -1045) T) ((-812 . -377) 143756) ((-169 . -722) T) ((-650 . -102) T) ((-1243 . -243) 143735) ((-1243 . -233) 143687) ((-1222 . -233) 143592) ((-1222 . -243) 143571) ((-999 . -402) NIL) ((-666 . -637) 143519) ((-316 . -38) 143429) ((-313 . -38) 143358) ((-69 . -611) 143340) ((-319 . -493) 143306) ((-1182 . -288) 143285) ((-1217 . -846) T) ((-1107 . -1106) 143195) ((-83 . -1209) T) ((-61 . -611) 143177) ((-479 . -288) 143156) ((-1274 . -1034) 143133) ((-1158 . -1094) T) ((-1107 . -23) 143003) ((-812 . -896) 142939) ((-1232 . -722) T) ((-1096 . -1209) T) ((-474 . -614) 142765) ((-1081 . -290) 142696) ((-962 . -1094) T) ((-889 . -102) T) ((-778 . -290) 142607) ((-327 . -19) 142591) ((-59 . -288) 142568) ((-776 . -290) 142499) ((-851 . -722) T) ((-117 . -844) NIL) ((-516 . -288) 142476) ((-327 . -602) 142453) ((-496 . -288) 142430) ((-454 . -290) 142361) ((-1031 . -309) 142212) ((-677 . -490) 142193) ((-571 . -722) T) ((-672 . -490) 142174) ((-677 . -611) 142124) ((-672 . -611) 142090) ((-658 . -611) 142072) ((-478 . -490) 142053) ((-478 . -611) 142019) ((-245 . -612) 141980) ((-245 . -490) 141957) ((-138 . -490) 141938) ((-137 . -490) 141919) ((-133 . -490) 141900) ((-245 . -611) 141792) ((-213 . -102) T) ((-138 . -611) 141758) ((-137 . -611) 141724) ((-133 . -611) 141690) ((-1141 . -34) T) ((-939 . -1209) T) ((-343 . -713) 141635) ((-666 . -25) T) ((-666 . -21) T) ((-1170 . -614) 141616) ((-474 . -1045) T) ((-633 . -417) 141581) ((-605 . -417) 141546) ((-1114 . -1145) T) ((-581 . -290) T) ((-518 . -290) T) ((-1244 . -307) 141525) ((-474 . -233) 141477) ((-474 . -243) 141456) ((-1223 . -307) 141435) ((-1223 . -1018) NIL) ((-1074 . -131) T) ((-868 . -791) 141414) ((-144 . -102) T) ((-40 . -1094) T) ((-868 . -788) 141393) ((-641 . -1006) 141377) ((-580 . -1052) T) ((-564 . -1052) T) ((-495 . -1052) T) 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137495) ((-954 . -34) T) ((-355 . -233) 137474) ((-355 . -243) T) ((-352 . -233) 137453) ((-352 . -243) T) ((-344 . -233) 137432) ((-344 . -243) T) ((-247 . -326) 137389) ((-264 . -326) 137361) ((-264 . -233) 137340) ((-1150 . -151) 137324) ((-251 . -896) 137256) ((-250 . -896) 137188) ((-1076 . -846) T) ((-414 . -1106) T) ((-1049 . -23) T) ((-906 . -1045) T) ((-322 . -644) 137170) ((-1020 . -844) T) ((-1203 . -998) 137136) ((-1167 . -916) 137115) ((-1161 . -916) 137094) ((-1161 . -816) NIL) ((-906 . -243) T) ((-813 . -363) 137073) ((-385 . -23) T) ((-127 . -1094) 137051) ((-121 . -1094) 137029) ((-906 . -233) T) ((-128 . -34) T) ((-379 . -644) 136994) ((-866 . -713) 136981) ((-1042 . -151) 136946) ((-40 . -172) T) ((-690 . -411) 136928) ((-708 . -309) 136915) ((-832 . -644) 136875) ((-823 . -644) 136849) ((-319 . -25) T) ((-319 . -21) T) ((-654 . -286) 136828) ((-580 . -1094) T) ((-564 . -1094) T) ((-495 . -1094) T) ((-245 . -288) 136805) ((-313 . -231) 136766) ((-1166 . -882) NIL) ((-55 . -1094) T) ((-1119 . -882) 136625) ((-129 . -846) T) ((-1166 . -1034) 136505) ((-1119 . -1034) 136388) ((-183 . -611) 136370) ((-850 . -1034) 136266) ((-778 . -286) 136193) ((-813 . -1106) T) ((-1030 . -722) T) ((-600 . -647) 136177) ((-1042 . -972) 136106) ((-995 . -102) T) ((-813 . -23) T) ((-708 . -1145) 136084) ((-690 . -1052) T) ((-600 . -373) 136068) ((-351 . -452) T) ((-343 . -290) T) ((-1260 . -1094) T) ((-248 . -1094) T) ((-399 . -102) T) ((-289 . -21) T) ((-289 . -25) T) ((-361 . -722) T) ((-706 . -1094) T) ((-695 . -1094) T) ((-361 . -473) T) ((-1203 . -611) 136050) ((-1166 . -377) 136034) ((-1119 . -377) 136018) ((-1020 . -411) 135980) ((-141 . -229) 135962) ((-379 . -790) T) ((-379 . -787) T) ((-866 . -172) T) ((-379 . -722) T) ((-707 . -611) 135944) ((-708 . -38) 135773) ((-1259 . -1257) 135757) ((-351 . -402) T) ((-1259 . -1094) 135707) ((-580 . -713) 135694) ((-564 . -713) 135681) ((-495 . -713) 135646) ((-316 . -627) 135625) ((-832 . -722) T) ((-823 . -722) T) 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-614) 134844) ((-487 . -556) T) ((-478 . -614) 134825) ((-359 . -25) T) ((-359 . -21) T) ((-353 . -25) T) ((-217 . -556) T) ((-353 . -21) T) ((-345 . -25) T) ((-345 . -21) T) ((-245 . -614) 134802) ((-138 . -614) 134783) ((-137 . -614) 134764) ((-133 . -614) 134745) ((-108 . -25) T) ((-108 . -21) T) ((-48 . -1052) T) ((-580 . -172) T) ((-564 . -172) T) ((-495 . -172) T) ((-654 . -611) 134727) ((-733 . -732) 134711) ((-336 . -611) 134693) ((-68 . -383) T) ((-68 . -395) T) ((-1096 . -107) 134677) ((-1056 . -882) 134659) ((-948 . -882) 134584) ((-649 . -1106) T) ((-621 . -713) 134571) ((-481 . -882) NIL) ((-1140 . -102) T) ((-1088 . -616) 134555) ((-1056 . -1034) 134537) ((-97 . -611) 134519) ((-477 . -147) T) ((-948 . -1034) 134399) ((-117 . -713) 134344) ((-649 . -23) T) ((-481 . -1034) 134220) ((-1081 . -612) NIL) ((-1081 . -611) 134202) ((-778 . -612) NIL) ((-778 . -611) 134163) ((-776 . -612) 133797) ((-776 . -611) 133711) ((-1107 . -637) 133617) ((-461 . -611) 133599) ((-454 . -611) 133581) ((-454 . -612) 133442) ((-1031 . -229) 133388) ((-868 . -905) 133367) ((-126 . -34) T) ((-813 . -131) T) ((-645 . -611) 133349) ((-578 . -102) T) ((-355 . -1278) 133333) ((-352 . -1278) 133317) ((-344 . -1278) 133301) ((-127 . -514) 133234) ((-121 . -514) 133167) ((-511 . -788) T) ((-511 . -791) T) ((-510 . -790) T) ((-103 . -309) 133105) ((-222 . -102) 133083) ((-690 . -1094) T) ((-695 . -172) T) ((-868 . -644) 133035) ((-65 . -384) T) ((-275 . -611) 133017) ((-65 . -395) T) ((-948 . -377) 133001) ((-866 . -290) T) ((-50 . -611) 132983) ((-995 . -38) 132931) ((-581 . -611) 132913) ((-481 . -377) 132897) ((-581 . -612) 132879) ((-518 . -611) 132861) ((-906 . -1278) 132848) ((-867 . -1209) T) ((-697 . -452) T) ((-495 . -514) 132814) ((-487 . -363) T) ((-355 . -368) 132793) ((-352 . -368) 132772) ((-344 . -368) 132751) ((-710 . -722) T) ((-217 . -363) T) ((-116 . -452) T) ((-1282 . -1273) 132735) ((-867 . -880) 132712) ((-867 . -882) NIL) ((-960 . -846) 132611) ((-811 . -846) 132562) ((-1216 . -102) T) ((-650 . -652) 132546) ((-1195 . -34) T) ((-171 . -611) 132528) ((-1107 . -21) 132438) ((-1107 . -25) 132289) ((-867 . -1034) 132266) ((-948 . -896) 132247) ((-1232 . -47) 132224) ((-906 . -368) T) ((-59 . -647) 132208) ((-516 . -647) 132192) ((-481 . -896) 132169) ((-71 . -441) T) ((-71 . -395) T) ((-496 . -647) 132153) ((-59 . -373) 132137) ((-621 . -172) T) ((-516 . -373) 132121) ((-496 . -373) 132105) ((-823 . -704) 132089) ((-1166 . -307) 132068) ((-1172 . -131) T) ((-117 . -172) T) ((-1140 . -309) 132006) ((-169 . -1209) T) ((-633 . -740) 131990) ((-605 . -740) 131974) ((-1271 . -131) T) ((-1244 . -916) 131953) ((-1223 . -916) 131932) ((-1223 . -816) NIL) ((-690 . -713) 131882) ((-1222 . -905) 131835) ((-1020 . -1094) T) ((-867 . -377) 131812) ((-867 . -338) 131789) ((-901 . -1106) T) ((-169 . -880) 131773) ((-169 . -882) 131698) ((-487 . -1106) T) ((-354 . -1094) T) ((-217 . -1106) T) ((-76 . -441) T) ((-76 . -395) T) ((-169 . -1034) 131594) ((-319 . -846) T) ((-1259 . -514) 131527) ((-1243 . -644) 131424) ((-1222 . -644) 131294) ((-868 . -790) 131273) ((-868 . -787) 131252) ((-868 . -722) T) ((-487 . -23) T) ((-223 . -611) 131234) ((-174 . -452) T) ((-222 . -309) 131172) ((-86 . -441) T) ((-86 . -395) T) ((-217 . -23) T) ((-1283 . -1276) 131151) ((-580 . -290) T) ((-564 . -290) T) ((-673 . -1034) 131135) ((-495 . -290) T) ((-136 . -470) 131090) ((-48 . -1094) T) ((-708 . -231) 131074) ((-867 . -896) NIL) ((-1232 . -882) NIL) ((-885 . -102) T) ((-881 . -102) T) ((-388 . -1094) T) ((-169 . -377) 131058) ((-169 . -338) 131042) ((-1232 . -1034) 130922) ((-851 . -1034) 130818) ((-1136 . -102) T) ((-649 . -131) T) ((-117 . -514) 130726) ((-658 . -788) 130705) ((-658 . -791) 130684) ((-571 . -1034) 130666) ((-294 . -1266) 130636) ((-862 . -102) T) ((-959 . -556) 130615) ((-1203 . -1051) 130498) ((-482 . -637) 130404) ((-900 . -1094) T) ((-1020 . -713) 130341) ((-707 . -1051) 130306) ((-615 . -102) T) ((-600 . -34) T) ((-1141 . -1209) T) 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. -1045) T) ((-385 . -21) T) ((-385 . -25) T) ((-690 . -514) NIL) ((-1020 . -172) T) ((-707 . -243) T) ((-1056 . -545) T) ((-506 . -102) T) ((-502 . -102) T) ((-354 . -172) T) ((-343 . -611) 129021) ((-394 . -611) 129003) ((-474 . -722) T) ((-1114 . -844) T) ((-888 . -1034) 128971) ((-108 . -846) T) ((-654 . -1051) 128955) ((-487 . -131) T) ((-1245 . -1052) T) ((-217 . -131) T) ((-1150 . -102) 128933) ((-99 . -1094) T) ((-245 . -662) 128917) ((-245 . -647) 128901) ((-654 . -111) 128880) ((-585 . -614) 128864) ((-316 . -411) 128848) ((-245 . -373) 128832) ((-1153 . -235) 128779) ((-995 . -231) 128763) ((-74 . -1209) T) ((-48 . -172) T) ((-697 . -387) T) ((-697 . -143) T) ((-1282 . -102) T) ((-1189 . -614) 128745) ((-1081 . -1051) 128588) ((-264 . -905) 128567) ((-247 . -905) 128546) ((-778 . -1051) 128369) ((-776 . -1051) 128212) ((-606 . -1209) T) ((-1158 . -611) 128194) ((-1081 . -111) 128023) ((-1042 . -102) T) ((-475 . -1209) T) ((-461 . -1051) 127994) ((-454 . -1051) 127837) ((-660 . -644) 127821) ((-867 . -307) T) ((-778 . -111) 127630) ((-776 . -111) 127459) ((-355 . -644) 127411) ((-352 . -644) 127363) ((-344 . -644) 127315) ((-264 . -644) 127240) ((-247 . -644) 127165) ((-1152 . -846) T) ((-1082 . -1034) 127149) ((-461 . -111) 127110) ((-454 . -111) 126939) ((-1070 . -1034) 126916) ((-996 . -34) T) ((-962 . -611) 126898) ((-954 . -1209) T) ((-126 . -1006) 126882) ((-959 . -1106) T) ((-867 . -1018) NIL) ((-731 . -1106) T) ((-711 . -1106) T) ((-654 . -614) 126800) ((-1259 . -489) 126784) ((-1136 . -38) 126744) ((-959 . -23) T) ((-861 . -1094) T) ((-839 . -102) T) ((-813 . -21) T) ((-813 . -25) T) ((-731 . -23) T) ((-711 . -23) T) ((-110 . -657) T) ((-906 . -644) 126709) ((-581 . -1051) 126674) ((-518 . -1051) 126619) ((-227 . -57) 126577) ((-453 . -23) T) ((-407 . -102) T) ((-263 . -102) T) ((-690 . -290) T) ((-862 . -38) 126547) ((-581 . -111) 126503) ((-518 . -111) 126432) ((-1081 . -614) 126168) ((-418 . -1106) T) ((-316 . -1052) 126058) ((-313 . -1052) T) ((-128 . -1209) T) ((-778 . -614) 125806) ((-776 . -614) 125572) ((-654 . -1045) T) ((-1287 . -1094) T) ((-454 . -614) 125357) ((-169 . -307) 125288) ((-418 . -23) T) ((-40 . -611) 125270) ((-40 . -612) 125254) ((-108 . -988) 125236) ((-116 . -865) 125220) ((-645 . -614) 125204) ((-48 . -514) 125170) ((-1195 . -1006) 125154) ((-1175 . -611) 125121) ((-1182 . -34) T) ((-950 . -611) 125087) ((-917 . -611) 125069) ((-1107 . -846) 125020) ((-767 . -611) 125002) ((-668 . -611) 124984) ((-1150 . -309) 124922) ((-479 . -34) T) ((-1086 . -1209) T) ((-477 . -452) T) ((-1135 . -34) T) ((-1081 . -1045) T) ((-50 . -614) 124891) ((-778 . -1045) T) ((-776 . -1045) T) ((-643 . -235) 124875) ((-630 . -235) 124821) ((-581 . -614) 124771) ((-518 . -614) 124701) ((-1232 . -307) 124680) ((-1081 . -326) 124641) ((-454 . -1045) T) ((-1172 . -21) T) ((-1081 . -233) 124620) ((-778 . -326) 124597) ((-778 . -233) T) ((-776 . -326) 124569) ((-727 . -1213) 124548) ((-327 . -647) 124532) ((-1172 . -25) T) ((-59 . -34) T) ((-519 . -34) T) ((-516 . -34) T) ((-454 . -326) 124511) ((-327 . -373) 124495) ((-497 . -34) T) ((-496 . -34) T) ((-999 . -1145) NIL) ((-727 . -556) 124426) ((-633 . -102) T) ((-605 . -102) T) ((-355 . -722) T) ((-352 . -722) T) ((-344 . -722) T) ((-264 . -722) T) ((-247 . -722) T) ((-1042 . -309) 124334) ((-897 . -1094) 124312) ((-50 . -1045) T) ((-1271 . -21) T) ((-1271 . -25) T) ((-1168 . -556) 124291) ((-1167 . -1213) 124270) ((-581 . -1045) T) ((-518 . -1045) T) ((-1161 . -1213) 124249) ((-361 . -1034) 124233) ((-322 . -1034) 124217) ((-1020 . -290) T) ((-379 . -882) 124199) ((-1167 . -556) 124150) ((-1161 . -556) 124101) ((-999 . -38) 124046) ((-795 . -1106) T) ((-906 . -722) T) ((-581 . -243) T) ((-581 . -233) T) ((-518 . -233) T) ((-518 . -243) T) ((-1120 . -556) 124025) ((-354 . -290) T) ((-643 . -691) 124009) ((-379 . -1034) 123969) ((-1114 . -1052) T) ((-103 . -125) 123953) ((-795 . -23) T) ((-1281 . -1276) 123929) ((-1259 . -286) 123906) ((-407 . -309) 123871) 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-611) 123303) ((-121 . -611) 123235) ((-1287 . -172) T) ((-1167 . -363) 123214) ((-1161 . -363) 123193) ((-316 . -1094) T) ((-418 . -131) T) ((-313 . -1094) T) ((-407 . -38) 123145) ((-1127 . -102) T) ((-1245 . -713) 123037) ((-650 . -1052) T) ((-1129 . -1254) T) ((-319 . -145) 123016) ((-319 . -147) 122995) ((-139 . -1094) T) ((-136 . -1094) T) ((-114 . -1094) T) ((-854 . -102) T) ((-580 . -611) 122977) ((-564 . -612) 122876) ((-564 . -611) 122858) ((-495 . -611) 122840) ((-495 . -612) 122785) ((-485 . -23) T) ((-482 . -846) 122736) ((-487 . -637) 122718) ((-961 . -611) 122700) ((-217 . -637) 122682) ((-225 . -404) T) ((-658 . -644) 122666) ((-55 . -611) 122648) ((-1166 . -916) 122627) ((-727 . -1106) T) ((-351 . -102) T) ((-1208 . -1077) T) ((-1114 . -840) T) ((-814 . -846) T) ((-727 . -23) T) ((-343 . -1051) 122572) ((-1152 . -1151) T) ((-1141 . -107) 122556) ((-1168 . -1106) T) ((-1167 . -1106) T) ((-515 . -1034) 122540) ((-1161 . -1106) T) ((-1120 . -1106) T) ((-343 . -111) 122469) ((-1000 . -1213) T) ((-126 . -1209) T) ((-910 . -1213) T) ((-690 . -286) NIL) ((-1260 . -611) 122451) ((-1168 . -23) T) ((-1167 . -23) T) ((-1161 . -23) T) ((-1000 . -556) T) ((-1136 . -231) 122435) ((-910 . -556) T) ((-1120 . -23) T) ((-248 . -611) 122417) ((-1069 . -1094) T) ((-795 . -131) T) ((-706 . -611) 122399) ((-316 . -713) 122309) ((-313 . -713) 122238) ((-695 . -611) 122220) ((-695 . -612) 122165) ((-407 . -400) 122149) ((-438 . -1094) T) ((-487 . -25) T) ((-487 . -21) T) ((-1114 . -1094) T) ((-217 . -25) T) ((-217 . -21) T) ((-708 . -411) 122133) ((-710 . -1034) 122102) ((-1259 . -611) 122014) ((-1259 . -612) 121975) ((-1245 . -172) T) ((-245 . -34) T) ((-343 . -614) 121905) ((-394 . -614) 121887) ((-922 . -970) T) ((-1195 . -1209) T) ((-658 . -787) 121866) ((-658 . -790) 121845) ((-398 . -395) T) ((-523 . -102) 121823) ((-1031 . -1094) T) ((-222 . -991) 121807) ((-504 . -102) T) ((-621 . -611) 121789) ((-45 . -846) NIL) ((-621 . -612) 121766) ((-1031 . -608) 121741) 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117307) ((-388 . -490) 117288) ((-1031 . -514) 117132) ((-388 . -611) 117098) ((-812 . -556) 117029) ((-585 . -644) 117004) ((-264 . -47) 116976) ((-247 . -47) 116933) ((-531 . -509) 116910) ((-580 . -614) 116882) ((-564 . -614) 116854) ((-495 . -614) 116787) ((-1068 . -1209) T) ((-996 . -1209) T) ((-695 . -1051) 116752) ((-1251 . -23) T) ((-1251 . -1106) T) ((-1244 . -1106) T) ((-1223 . -1106) T) ((-999 . -370) 116724) ((-112 . -368) T) ((-474 . -896) 116630) ((-1244 . -23) T) ((-900 . -611) 116612) ((-55 . -614) 116594) ((-91 . -107) 116578) ((-1203 . -722) T) ((-901 . -846) 116529) ((-697 . -1145) T) ((-695 . -111) 116485) ((-1223 . -23) T) ((-595 . -1106) T) ((-594 . -1106) T) ((-708 . -713) 116314) ((-707 . -722) T) ((-1114 . -290) T) ((-1000 . -131) T) ((-487 . -846) T) ((-967 . -131) T) ((-910 . -131) T) ((-795 . -25) T) ((-217 . -846) T) ((-795 . -21) T) ((-580 . -1045) T) ((-564 . -1045) T) ((-495 . -1045) T) ((-595 . -23) T) ((-343 . -1278) 116291) ((-319 . -452) 116270) 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115278) ((-264 . -1034) 115122) ((-247 . -1034) 114998) ((-117 . -111) 114927) ((-59 . -1209) T) ((-519 . -1209) T) ((-516 . -1209) T) ((-497 . -1209) T) ((-496 . -1209) T) ((-437 . -611) 114909) ((-434 . -611) 114891) ((-3 . -102) T) ((-1023 . -1202) 114860) ((-829 . -102) T) ((-685 . -57) 114818) ((-695 . -1045) T) ((-50 . -644) 114792) ((-289 . -452) T) ((-476 . -1202) 114761) ((0 . -102) T) ((-581 . -644) 114726) ((-518 . -644) 114671) ((-49 . -102) T) ((-906 . -1034) 114658) ((-695 . -243) T) ((-1074 . -409) 114637) ((-727 . -637) 114585) ((-995 . -1094) T) ((-708 . -172) 114476) ((-621 . -614) 114371) ((-487 . -988) 114353) ((-264 . -377) 114337) ((-247 . -377) 114321) ((-399 . -1094) T) ((-1022 . -102) 114299) ((-339 . -38) 114283) ((-217 . -988) 114265) ((-117 . -614) 114195) ((-174 . -38) 114127) ((-1243 . -307) 114106) ((-1222 . -307) 114085) ((-654 . -722) T) ((-99 . -611) 114067) ((-1161 . -637) 114019) ((-485 . -25) T) ((-485 . -21) T) ((-1222 . -1018) 113971) ((-621 . -1045) T) ((-379 . -404) T) ((-390 . -102) T) ((-1099 . -616) 113886) ((-264 . -896) 113832) ((-247 . -896) 113809) ((-117 . -1045) T) ((-812 . -1106) T) ((-1081 . -722) T) ((-621 . -233) 113788) ((-619 . -102) T) ((-778 . -722) T) ((-776 . -722) T) ((-413 . -1106) T) ((-117 . -243) T) ((-40 . -368) NIL) ((-117 . -233) NIL) ((-1214 . -846) T) ((-454 . -722) T) ((-812 . -23) T) ((-727 . -25) T) ((-727 . -21) T) ((-1071 . -286) 113767) ((-78 . -396) T) ((-78 . -395) T) ((-533 . -763) 113749) ((-690 . -1051) 113699) ((-1251 . -131) T) ((-1244 . -131) T) ((-1223 . -131) T) ((-1168 . -25) T) ((-1136 . -411) 113683) ((-633 . -367) 113615) ((-605 . -367) 113547) ((-1150 . -1143) 113531) ((-103 . -1094) 113509) ((-1168 . -21) T) ((-1167 . -21) T) ((-861 . -611) 113491) ((-995 . -713) 113439) ((-223 . -644) 113406) ((-690 . -111) 113340) ((-50 . -722) T) ((-1167 . -25) T) ((-351 . -349) T) ((-1161 . -21) T) ((-1074 . -452) 113291) ((-1161 . -25) T) ((-708 . -514) 113238) ((-581 . -722) T) 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((-812 . -131) T) ((-117 . -791) NIL) ((-117 . -788) NIL) ((-355 . -307) T) ((-352 . -307) T) ((-344 . -307) T) ((-251 . -1106) 110962) ((-250 . -1106) 110872) ((-1020 . -1045) T) ((-999 . -1052) T) ((-48 . -614) 110805) ((-343 . -644) 110750) ((-619 . -38) 110734) ((-1272 . -611) 110696) ((-1272 . -612) 110657) ((-1071 . -611) 110639) ((-1020 . -243) T) ((-354 . -1045) T) ((-811 . -1266) 110609) ((-251 . -23) T) ((-250 . -23) T) ((-983 . -611) 110591) ((-733 . -612) 110552) ((-733 . -611) 110534) ((-795 . -846) 110513) ((-1153 . -151) 110460) ((-995 . -514) 110372) ((-354 . -233) T) ((-354 . -243) T) ((-388 . -614) 110353) ((-1000 . -25) T) ((-141 . -611) 110335) ((-141 . -612) 110294) ((-906 . -307) T) ((-1000 . -21) T) ((-967 . -25) T) ((-910 . -21) T) ((-910 . -25) T) ((-427 . -21) T) ((-427 . -25) T) ((-839 . -411) 110278) ((-48 . -1045) T) ((-1281 . -1273) 110262) ((-1279 . -1273) 110246) ((-1031 . -602) 110221) ((-316 . -612) 110082) ((-316 . -611) 110064) ((-313 . -612) NIL) 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-145) NIL) ((-1114 . -612) 109167) ((-438 . -611) 109149) ((-217 . -147) T) ((-217 . -145) NIL) ((-1114 . -611) 109131) ((-129 . -102) T) ((-52 . -102) T) ((-1223 . -637) 109083) ((-479 . -107) 109033) ((-989 . -23) T) ((-1283 . -38) 109003) ((-1166 . -1106) T) ((-1119 . -1106) T) ((-1056 . -1213) T) ((-311 . -102) T) ((-850 . -1106) T) ((-948 . -1213) 108982) ((-481 . -1213) 108961) ((-727 . -846) 108940) ((-1056 . -556) T) ((-948 . -556) 108871) ((-1166 . -23) T) ((-1119 . -23) T) ((-850 . -23) T) ((-481 . -556) 108802) ((-1136 . -713) 108734) ((-1140 . -514) 108667) ((-1031 . -612) NIL) ((-1031 . -611) 108649) ((-96 . -1077) T) ((-862 . -713) 108619) ((-1203 . -47) 108588) ((-251 . -131) T) ((-250 . -131) T) ((-1098 . -1094) T) ((-999 . -1094) T) ((-62 . -611) 108570) ((-1161 . -846) NIL) ((-1020 . -788) T) ((-1020 . -791) T) ((-1287 . -1051) 108557) ((-1287 . -111) 108542) ((-866 . -644) 108529) ((-1251 . -25) T) ((-1251 . -21) T) ((-1244 . -21) T) ((-1244 . -25) T) ((-1223 . -21) T) ((-1223 . -25) T) ((-1023 . -151) 108513) ((-868 . -816) 108492) ((-868 . -916) T) ((-708 . -286) 108419) ((-595 . -21) T) ((-595 . -25) T) ((-594 . -21) T) ((-40 . -722) T) ((-222 . -514) 108352) ((-594 . -25) T) ((-476 . -151) 108336) ((-463 . -151) 108320) ((-917 . -790) T) ((-917 . -722) T) ((-767 . -789) T) ((-767 . -790) T) ((-506 . -1094) T) ((-502 . -1094) T) ((-767 . -722) T) ((-225 . -363) T) ((-1150 . -1094) 108298) ((-867 . -1213) T) ((-650 . -611) 108280) ((-867 . -556) T) ((-690 . -368) NIL) ((-1287 . -614) 108262) ((-1282 . -1094) T) ((-359 . -1266) 108246) ((-666 . -102) T) ((-353 . -1266) 108230) ((-345 . -1266) 108214) ((-548 . -102) T) ((-520 . -846) 108193) ((-813 . -452) 108172) ((-1042 . -1094) T) ((-1042 . -1065) 108101) ((-1023 . -972) 108070) ((-815 . -1106) T) ((-999 . -713) 108015) ((-386 . -1106) T) ((-476 . -972) 107984) ((-463 . -972) 107953) ((-110 . -151) 107935) ((-73 . -611) 107917) ((-889 . -611) 107899) ((-1074 . -720) 107878) ((-1287 . -1045) T) 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105407) ((-1081 . -882) NIL) ((-867 . -1106) T) ((-117 . -905) NIL) ((-1281 . -1280) 105383) ((-1279 . -1280) 105362) ((-778 . -882) NIL) ((-776 . -882) 105221) ((-1274 . -25) T) ((-1274 . -21) T) ((-1206 . -102) 105199) ((-1100 . -395) T) ((-621 . -644) 105186) ((-454 . -882) NIL) ((-671 . -102) 105164) ((-1081 . -1034) 104991) ((-867 . -23) T) ((-778 . -1034) 104850) ((-776 . -1034) 104707) ((-117 . -644) 104652) ((-454 . -1034) 104528) ((-316 . -614) 104092) ((-313 . -614) 103975) ((-645 . -1034) 103959) ((-625 . -102) T) ((-222 . -489) 103943) ((-1259 . -34) T) ((-136 . -614) 103927) ((-633 . -713) 103911) ((-605 . -713) 103895) ((-666 . -38) 103855) ((-319 . -102) T) ((-85 . -611) 103837) ((-50 . -1034) 103821) ((-1114 . -1051) 103808) ((-1081 . -377) 103792) ((-778 . -377) 103776) ((-695 . -722) T) ((-695 . -790) T) ((-695 . -787) T) ((-581 . -1034) 103763) ((-518 . -1034) 103740) ((-60 . -57) 103702) ((-324 . -131) T) ((-316 . -1045) 103592) ((-313 . -1045) T) ((-169 . -1106) T) 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-231) 99766) ((-581 . -307) T) ((-518 . -307) T) ((-294 . -514) 99715) ((-108 . -309) NIL) ((-72 . -395) T) ((-1107 . -102) 99505) ((-829 . -411) 99489) ((-1114 . -791) T) ((-1114 . -788) T) ((-697 . -1094) T) ((-578 . -611) 99471) ((-379 . -363) T) ((-169 . -493) 99449) ((-222 . -611) 99381) ((-134 . -1094) T) ((-116 . -1094) T) ((-48 . -722) T) ((-1042 . -489) 99346) ((-141 . -425) 99328) ((-141 . -368) T) ((-1023 . -102) T) ((-512 . -509) 99307) ((-708 . -614) 99063) ((-476 . -102) T) ((-463 . -102) T) ((-1030 . -1106) T) ((-1216 . -611) 99045) ((-1175 . -1034) 98981) ((-1168 . -35) 98947) ((-1168 . -95) 98913) ((-1168 . -1197) 98879) ((-1168 . -1194) 98845) ((-1152 . -309) NIL) ((-89 . -396) T) ((-89 . -395) T) ((-1074 . -1145) 98824) ((-1167 . -1194) 98790) ((-1167 . -1197) 98756) ((-1030 . -23) T) ((-1167 . -95) 98722) ((-571 . -493) T) ((-1167 . -35) 98688) ((-1161 . -1194) 98654) ((-1161 . -1197) 98620) ((-1161 . -95) 98586) ((-361 . -1106) T) ((-359 . -1145) 98565) ((-353 . -1145) 98544) ((-345 . -1145) 98523) ((-1161 . -35) 98489) ((-1120 . -35) 98455) ((-1120 . -95) 98421) ((-108 . -1145) T) ((-1120 . -1197) 98387) ((-829 . -1052) 98366) ((-643 . -309) 98304) ((-630 . -309) 98155) ((-1120 . -1194) 98121) ((-708 . -1045) T) ((-1056 . -637) 98103) ((-1074 . -38) 97971) ((-948 . -637) 97919) ((-1000 . -147) T) ((-1000 . -145) NIL) ((-379 . -1106) T) ((-324 . -25) T) ((-322 . -23) T) ((-939 . -846) 97898) ((-708 . -326) 97875) ((-481 . -637) 97823) ((-40 . -1034) 97711) ((-708 . -233) T) ((-697 . -713) 97698) ((-339 . -1094) T) ((-174 . -1094) T) ((-331 . -846) T) ((-418 . -452) 97648) ((-379 . -23) T) ((-359 . -38) 97613) ((-353 . -38) 97578) ((-345 . -38) 97543) ((-80 . -441) T) ((-80 . -395) T) ((-225 . -25) T) ((-225 . -21) T) ((-832 . -1106) T) ((-108 . -38) 97493) ((-823 . -1106) T) ((-770 . -1094) T) ((-116 . -713) 97480) ((-668 . -1034) 97464) ((-610 . -102) T) ((-832 . -23) T) ((-823 . -23) T) ((-1150 . -286) 97441) ((-1107 . -309) 97379) ((-1096 . -235) 97363) ((-64 . -396) T) ((-64 . -395) T) ((-110 . -102) T) ((-40 . -377) 97340) ((-96 . -102) T) ((-649 . -848) 97324) ((-1129 . -1077) T) ((-1056 . -21) T) ((-1056 . -25) T) ((-811 . -231) 97293) ((-948 . -25) T) ((-948 . -21) T) ((-619 . -1052) T) ((-1114 . -368) T) ((-481 . -25) T) ((-481 . -21) T) ((-1023 . -309) 97231) ((-885 . -611) 97213) ((-881 . -611) 97195) ((-251 . -846) 97146) ((-250 . -846) 97097) ((-523 . -514) 97030) ((-867 . -637) 97007) ((-476 . -309) 96945) ((-463 . -309) 96883) ((-351 . -290) T) ((-1150 . -1247) 96867) ((-1136 . -611) 96829) ((-1136 . -612) 96790) ((-1134 . -102) T) ((-995 . -1051) 96686) ((-40 . -896) 96638) ((-1150 . -602) 96615) ((-1287 . -644) 96602) ((-862 . -490) 96579) ((-1057 . -151) 96525) ((-868 . -1213) T) ((-995 . -111) 96407) ((-339 . -713) 96391) ((-862 . -611) 96353) ((-174 . -713) 96285) ((-407 . -286) 96243) ((-868 . -556) T) ((-108 . -400) 96225) ((-84 . -384) T) ((-84 . -395) T) ((-697 . -172) T) ((-615 . -611) 96207) ((-99 . -722) T) ((-482 . -102) 95997) ((-99 . -473) T) ((-116 . -172) T) ((-1107 . -38) 95967) ((-169 . -637) 95915) ((-1049 . -102) T) ((-995 . -614) 95805) ((-867 . -25) T) ((-811 . -238) 95784) ((-867 . -21) T) ((-814 . -102) T) ((-414 . -102) T) ((-385 . -102) T) ((-110 . -309) NIL) ((-227 . -102) 95762) ((-127 . -1209) T) ((-121 . -1209) T) ((-1030 . -131) T) ((-666 . -367) 95746) ((-995 . -1045) T) ((-1232 . -637) 95694) ((-1098 . -611) 95676) ((-999 . -611) 95658) ((-515 . -23) T) ((-510 . -23) T) ((-343 . -307) T) ((-508 . -23) T) ((-322 . -131) T) ((-3 . -1094) T) ((-999 . -612) 95642) ((-995 . -243) 95621) ((-995 . -233) 95600) ((-1287 . -722) T) ((-1251 . -145) 95579) ((-829 . -1094) T) ((-1251 . -147) 95558) ((-1244 . -147) 95537) ((-1244 . -145) 95516) ((-1243 . -1213) 95495) ((-1223 . -145) 95402) ((-1223 . -147) 95309) ((-1222 . -1213) 95288) ((-379 . -131) T) ((-564 . -882) 95270) ((0 . -1094) T) ((-174 . -172) T) ((-169 . -21) T) ((-169 . -25) T) ((-49 . -1094) T) ((-1245 . -644) 95175) ((-1243 . -556) 95126) ((-710 . -1106) T) ((-1222 . -556) 95077) ((-564 . -1034) 95059) ((-594 . -147) 95038) ((-594 . -145) 95017) ((-495 . -1034) 94960) ((-1129 . -1131) T) ((-87 . -384) T) ((-87 . -395) T) ((-868 . -363) T) ((-832 . -131) T) ((-823 . -131) T) ((-710 . -23) T) ((-506 . -611) 94926) ((-502 . -611) 94908) ((-1283 . -1052) T) ((-379 . -1054) T) ((-1022 . -1094) 94886) ((-55 . -1034) 94868) ((-897 . -34) T) ((-482 . -309) 94806) ((-591 . -102) T) ((-1150 . -612) 94767) ((-1150 . -611) 94699) ((-1166 . -846) 94678) ((-45 . -102) T) ((-1119 . -846) 94657) ((-813 . -102) T) ((-1232 . -25) T) ((-1232 . -21) T) ((-851 . -25) T) ((-44 . -367) 94641) ((-851 . -21) T) ((-727 . -452) 94592) ((-1282 . -611) 94574) ((-1049 . -309) 94512) ((-667 . -1077) T) ((-604 . -1077) T) ((-390 . -1094) T) ((-571 . -25) T) ((-571 . -21) T) ((-180 . -1077) T) ((-161 . -1077) T) ((-156 . -1077) T) ((-154 . -1077) T) ((-619 . -1094) T) ((-695 . -882) 94494) ((-1259 . -1209) T) ((-227 . -309) 94432) ((-144 . -368) T) ((-1042 . -612) 94374) ((-1042 . -611) 94317) ((-313 . -905) NIL) ((-1217 . -840) T) ((-695 . -1034) 94262) ((-707 . -916) T) ((-474 . -1213) 94241) ((-1167 . -452) 94220) ((-1161 . -452) 94199) ((-330 . -102) T) ((-868 . -1106) T) ((-316 . -644) 94020) ((-313 . -644) 93949) ((-474 . -556) 93900) ((-339 . -514) 93866) ((-550 . -151) 93816) ((-40 . -307) T) ((-839 . -611) 93798) ((-697 . -290) T) ((-868 . -23) T) ((-379 . -493) T) ((-1074 . -231) 93768) ((-512 . -102) T) ((-407 . -612) 93575) ((-407 . -611) 93557) ((-263 . -611) 93539) ((-116 . -290) T) ((-1245 . -722) T) ((-1243 . -363) 93518) ((-1222 . -363) 93497) ((-1272 . -34) T) ((-1217 . -1094) T) ((-117 . -1209) T) ((-108 . -231) 93479) ((-1172 . -102) T) ((-477 . -1094) T) ((-523 . -489) 93463) ((-733 . -34) T) ((-482 . -38) 93433) ((-141 . -34) T) ((-117 . -880) 93410) ((-117 . -882) NIL) ((-621 . -1034) 93293) ((-641 . -846) 93272) ((-1271 . -102) T) ((-295 . -102) T) ((-708 . -368) 93251) 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-23) T) ((-714 . -1106) T) ((-710 . -131) T) ((-649 . -102) T) ((-477 . -713) 92004) ((-45 . -282) 91954) ((-105 . -1094) T) ((-68 . -611) 91936) ((-966 . -102) T) ((-860 . -102) T) ((-621 . -896) 91895) ((-1283 . -1094) T) ((-381 . -1094) T) ((-1208 . -1094) T) ((-1107 . -231) 91864) ((-82 . -1209) T) ((-1056 . -846) T) ((-948 . -846) 91843) ((-117 . -896) NIL) ((-778 . -916) 91822) ((-709 . -846) T) ((-531 . -1094) T) ((-500 . -1094) T) ((-355 . -1213) T) ((-352 . -1213) T) ((-344 . -1213) T) ((-264 . -1213) 91801) ((-247 . -1213) 91780) ((-533 . -856) T) ((-481 . -846) 91759) ((-1152 . -824) T) ((-1136 . -1051) 91743) ((-390 . -757) T) ((-690 . -1209) T) ((-687 . -1034) 91727) ((-355 . -556) T) ((-352 . -556) T) ((-344 . -556) T) ((-264 . -556) 91658) ((-247 . -556) 91589) ((-525 . -1077) T) ((-1136 . -111) 91568) ((-453 . -740) 91538) ((-862 . -1051) 91508) ((-813 . -38) 91450) ((-690 . -880) 91432) ((-690 . -882) 91414) ((-295 . -309) 91218) ((-906 . -1213) T) ((-666 . -411) 91202) ((-862 . -111) 91167) ((-690 . -1034) 91112) ((-1000 . -452) T) ((-906 . -556) T) ((-533 . -611) 91094) ((-581 . -916) T) ((-474 . -1106) T) ((-518 . -916) T) ((-1150 . -288) 91071) ((-910 . -452) T) ((-65 . -611) 91053) ((-630 . -229) 90999) ((-474 . -23) T) ((-1114 . -790) T) ((-868 . -131) T) ((-1114 . -787) T) ((-1274 . -1276) 90978) ((-1114 . -722) T) ((-650 . -644) 90952) ((-294 . -611) 90693) ((-1136 . -614) 90611) ((-1031 . -34) T) ((-811 . -844) 90590) ((-580 . -307) T) ((-564 . -307) T) ((-495 . -307) T) ((-1283 . -713) 90560) ((-690 . -377) 90542) ((-690 . -338) 90524) ((-477 . -172) T) ((-381 . -713) 90494) ((-862 . -614) 90429) ((-867 . -846) NIL) ((-564 . -1018) T) ((-495 . -1018) T) ((-1127 . -611) 90411) ((-1107 . -238) 90390) ((-214 . -102) T) ((-1144 . -102) T) ((-71 . -611) 90372) ((-1136 . -1045) T) ((-1172 . -38) 90269) ((-854 . -611) 90251) ((-564 . -545) T) ((-666 . -1052) T) ((-727 . -945) 90204) ((-1136 . -233) 90183) ((-1076 . -1094) T) ((-1030 . -25) T) ((-1030 . -21) T) ((-999 . -1051) 90128) ((-901 . -102) T) ((-862 . -1045) T) ((-690 . -896) NIL) ((-355 . -329) 90112) ((-355 . -363) T) ((-352 . -329) 90096) ((-352 . -363) T) ((-344 . -329) 90080) ((-344 . -363) T) ((-487 . -102) T) ((-1271 . -38) 90050) ((-546 . -846) T) ((-523 . -683) 90000) ((-217 . -102) T) ((-1020 . -1034) 89880) ((-999 . -111) 89809) ((-1168 . -969) 89778) ((-1167 . -969) 89740) ((-520 . -151) 89724) ((-1074 . -370) 89703) ((-351 . -611) 89685) ((-322 . -21) T) ((-354 . -1034) 89662) ((-322 . -25) T) ((-1161 . -969) 89631) ((-1120 . -969) 89598) ((-76 . -611) 89580) ((-695 . -307) T) ((-169 . -846) 89559) ((-129 . -840) T) ((-906 . -363) T) ((-379 . -25) T) ((-379 . -21) T) ((-906 . -329) 89546) ((-86 . -611) 89528) ((-695 . -1018) T) ((-673 . -846) T) ((-1243 . -131) T) ((-1222 . -131) T) ((-897 . -1006) 89512) ((-832 . -21) T) ((-48 . -1034) 89455) ((-832 . -25) T) ((-823 . -25) T) ((-823 . -21) T) ((-1281 . -1052) T) ((-549 . -102) T) ((-1279 . -1052) T) 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. -131) T) ((-217 . -309) NIL) ((-407 . -111) 88435) ((-811 . -1052) 88365) ((-733 . -1092) 88349) ((-1243 . -493) 88315) ((-1222 . -493) 88281) ((-548 . -840) T) ((-141 . -1092) 88263) ((-477 . -290) T) ((-1282 . -1045) T) ((-1214 . -102) T) ((-1057 . -102) T) ((-839 . -614) 88131) ((-500 . -514) NIL) ((-482 . -238) 88110) ((-407 . -614) 88008) ((-1166 . -145) 87987) ((-1166 . -147) 87966) ((-1119 . -147) 87945) ((-1119 . -145) 87924) ((-633 . -1051) 87908) ((-605 . -1051) 87892) ((-1168 . -1250) 87876) ((-666 . -1094) T) ((-666 . -1048) 87816) ((-1168 . -1237) 87793) ((-548 . -1094) T) ((-487 . -1145) T) ((-1167 . -1242) 87754) ((-1167 . -1237) 87724) ((-1167 . -1240) 87708) ((-217 . -1145) T) ((-343 . -916) T) ((-814 . -266) 87692) ((-633 . -111) 87671) ((-605 . -111) 87650) ((-1161 . -1221) 87611) ((-839 . -1045) 87590) ((-1161 . -1237) 87567) ((-515 . -25) T) ((-495 . -302) T) ((-511 . -23) T) ((-510 . -25) T) ((-508 . -25) T) ((-507 . -23) T) ((-1161 . -1219) 87551) ((-407 . -1045) T) ((-319 . -1052) T) ((-690 . -307) T) ((-108 . -844) T) ((-708 . -722) T) ((-407 . -243) T) ((-407 . -233) 87530) ((-487 . -38) 87480) ((-217 . -38) 87430) ((-474 . -493) 87396) ((-1216 . -368) T) ((-1152 . -1138) T) ((-1095 . -102) T) ((-697 . -611) 87378) ((-697 . -612) 87293) ((-710 . -21) T) ((-710 . -25) T) ((-1129 . -102) T) ((-134 . -611) 87275) ((-116 . -611) 87257) ((-157 . -25) T) ((-1281 . -1094) T) ((-868 . -637) 87205) ((-1279 . -1094) T) ((-959 . -102) T) ((-731 . -102) T) ((-711 . -102) T) ((-453 . -102) T) ((-812 . -452) 87156) ((-44 . -1094) T) ((-1082 . -846) T) ((-660 . -131) T) ((-1057 . -309) 87007) ((-666 . -713) 86991) ((-289 . -1052) T) ((-355 . -131) T) ((-352 . -131) T) ((-344 . -131) T) ((-264 . -131) T) ((-247 . -131) T) ((-418 . -102) T) ((-152 . -1094) T) ((-45 . -229) 86941) ((-954 . -846) 86920) ((-995 . -644) 86858) ((-240 . -1266) 86828) ((-1020 . -307) T) ((-294 . -1051) 86749) ((-906 . -131) T) ((-40 . -916) T) ((-487 . -400) 86731) ((-354 . -307) T) ((-217 . -400) 86713) ((-1074 . -411) 86697) ((-294 . -111) 86613) ((-1177 . -846) T) ((-1176 . -846) T) ((-868 . -25) T) ((-868 . -21) T) ((-339 . -611) 86595) ((-1245 . -47) 86539) ((-225 . -147) T) ((-174 . -611) 86521) ((-1107 . -844) 86500) ((-770 . -611) 86482) ((-128 . -846) T) ((-606 . -235) 86429) ((-475 . -235) 86379) ((-1281 . -713) 86349) ((-48 . -307) T) ((-1279 . -713) 86319) ((-65 . -614) 86248) ((-960 . -1094) T) ((-811 . -1094) 86038) ((-312 . -102) T) ((-897 . -1209) T) ((-48 . -1018) T) ((-1222 . -637) 85946) ((-685 . -102) 85924) ((-44 . -713) 85908) ((-550 . -102) T) ((-294 . -614) 85839) ((-67 . -383) T) ((-67 . -395) T) ((-658 . -23) T) ((-666 . -757) T) ((-1206 . -1094) 85817) ((-351 . -1051) 85762) ((-671 . -1094) 85740) ((-1056 . -147) T) ((-948 . -147) 85719) ((-948 . -145) 85698) ((-795 . -102) T) ((-152 . -713) 85682) ((-481 . -147) 85661) ((-481 . -145) 85640) ((-351 . -111) 85569) ((-1074 . -1052) T) ((-322 . -846) 85548) ((-1251 . -969) 85517) 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83434) ((-225 . -35) T) ((-49 . -611) 83416) ((-477 . -1052) T) ((-487 . -231) 83398) ((-484 . -964) 83382) ((-482 . -844) 83361) ((-217 . -231) 83343) ((-81 . -441) T) ((-81 . -395) T) ((-1140 . -34) T) ((-811 . -172) 83322) ((-727 . -102) T) ((-1022 . -611) 83289) ((-500 . -286) 83264) ((-316 . -377) 83233) ((-313 . -377) 83194) ((-313 . -338) 83155) ((-1079 . -611) 83137) ((-812 . -945) 83084) ((-658 . -131) T) ((-1232 . -145) 83063) ((-1232 . -147) 83042) ((-1168 . -102) T) ((-1167 . -102) T) ((-1161 . -102) T) ((-1153 . -1094) T) ((-1120 . -102) T) ((-222 . -34) T) ((-289 . -713) 83029) ((-1153 . -608) 83005) ((-592 . -309) NIL) ((-484 . -1094) 82983) ((-390 . -611) 82965) ((-510 . -846) T) ((-1144 . -229) 82915) ((-1251 . -1250) 82899) ((-1251 . -1237) 82876) ((-1244 . -1242) 82837) ((-1244 . -1237) 82807) ((-1244 . -1240) 82791) ((-1223 . -1221) 82752) ((-1223 . -1237) 82729) ((-619 . -611) 82711) ((-1223 . -1219) 82695) ((-695 . -916) T) ((-1168 . -284) 82661) ((-1167 . -284) 82627) ((-1161 . -284) 82593) ((-1074 . -1094) T) ((-1055 . -1094) T) ((-48 . -302) T) ((-316 . -896) 82559) ((-313 . -896) NIL) ((-1055 . -1062) 82538) ((-1114 . -882) 82520) ((-795 . -38) 82504) ((-264 . -637) 82452) ((-247 . -637) 82400) ((-697 . -1051) 82387) ((-594 . -1237) 82364) ((-1120 . -284) 82330) ((-319 . -172) 82261) ((-359 . -1094) T) ((-353 . -1094) T) ((-345 . -1094) T) ((-500 . -19) 82243) ((-1114 . -1034) 82225) ((-1096 . -151) 82209) ((-108 . -1094) T) ((-116 . -1051) 82196) ((-707 . -363) T) ((-500 . -602) 82171) ((-697 . -111) 82156) ((-436 . -102) T) ((-45 . -1143) 82106) ((-116 . -111) 82091) ((-633 . -716) T) ((-605 . -716) T) ((-811 . -514) 82024) ((-1031 . -1209) T) ((-939 . -151) 82008) ((-1217 . -611) 81990) ((-1166 . -452) 81921) ((-1160 . -1094) T) ((-1152 . -1094) T) ((-525 . -102) T) ((-520 . -102) 81871) ((-1136 . -644) 81845) ((-1119 . -452) 81796) ((-1081 . -1213) 81775) ((-778 . -1213) 81754) ((-776 . -1213) 81733) ((-62 . -1209) T) ((-477 . -611) 81685) ((-477 . -612) 81607) ((-1081 . -556) 81538) ((-990 . -1094) T) ((-778 . -556) 81449) ((-776 . -556) 81380) ((-482 . -411) 81349) ((-621 . -916) 81328) ((-454 . -1213) 81307) ((-727 . -309) 81294) ((-697 . -614) 81266) ((-398 . -611) 81248) ((-671 . -514) 81181) ((-660 . -25) T) ((-660 . -21) T) ((-454 . -556) 81112) ((-355 . -25) T) ((-355 . -21) T) ((-117 . -916) T) ((-117 . -816) NIL) ((-352 . -25) T) ((-352 . -21) T) ((-344 . -25) T) ((-344 . -21) T) ((-264 . -25) T) ((-264 . -21) T) ((-247 . -25) T) ((-247 . -21) T) ((-83 . -384) T) ((-83 . -395) T) ((-134 . -614) 81094) ((-116 . -614) 81066) ((-1261 . -611) 81048) ((-1215 . -846) T) ((-1203 . -1106) T) ((-1203 . -23) T) ((-1161 . -309) 80933) ((-1120 . -309) 80920) ((-1074 . -713) 80788) ((-862 . -644) 80748) ((-939 . -976) 80732) ((-906 . -21) T) ((-289 . -172) T) ((-906 . -25) T) ((-311 . -93) T) ((-868 . -846) 80683) ((-707 . -1106) T) ((-707 . -23) T) ((-697 . -1045) T) ((-643 . -1094) 80661) ((-630 . -1094) T) ((-581 . -1213) T) ((-518 . -1213) T) ((-697 . -233) T) ((-630 . -608) 80636) ((-581 . -556) T) ((-518 . -556) T) ((-359 . -713) 80588) ((-339 . -1051) 80572) ((-353 . -713) 80524) ((-345 . -713) 80476) ((-174 . -1051) 80408) ((-174 . -111) 80319) ((-108 . -713) 80269) ((-339 . -111) 80248) ((-274 . -1094) T) ((-273 . -1094) T) ((-272 . -1094) T) ((-271 . -1094) T) ((-270 . -1094) T) ((-269 . -1094) T) ((-268 . -1094) T) ((-212 . -1094) T) ((-211 . -1094) T) ((-169 . -1197) 80226) ((-169 . -1194) 80204) ((-209 . -1094) T) ((-208 . -1094) T) ((-116 . -1045) T) ((-207 . -1094) T) ((-206 . -1094) T) ((-203 . -1094) T) ((-202 . -1094) T) ((-201 . -1094) T) ((-200 . -1094) T) ((-199 . -1094) T) ((-198 . -1094) T) ((-197 . -1094) T) ((-196 . -1094) T) ((-195 . -1094) T) ((-194 . -1094) T) ((-193 . -1094) T) ((-240 . -102) 79994) ((-169 . -35) 79972) ((-169 . -95) 79950) ((-650 . -1034) 79846) ((-482 . -1052) 79776) ((-1107 . -1094) 79566) ((-1136 . -34) T) ((-666 . -489) 79550) ((-73 . -1209) T) 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-290) 78142) ((-345 . -172) T) ((-174 . -243) T) ((-1222 . -846) 78041) ((-108 . -172) T) ((-868 . -988) 78025) ((-654 . -1106) T) ((-581 . -363) T) ((-581 . -329) 78012) ((-518 . -329) 77989) ((-518 . -363) T) ((-316 . -307) 77968) ((-313 . -307) T) ((-600 . -846) 77947) ((-1107 . -713) 77889) ((-520 . -282) 77873) ((-654 . -23) T) ((-418 . -231) 77857) ((-313 . -1018) NIL) ((-336 . -23) T) ((-103 . -1006) 77841) ((-45 . -36) 77820) ((-610 . -1094) T) ((-351 . -368) T) ((-524 . -102) T) ((-495 . -27) T) ((-240 . -309) 77758) ((-1081 . -1106) T) ((-1282 . -644) 77732) ((-778 . -1106) T) ((-776 . -1106) T) ((-454 . -1106) T) ((-1056 . -452) T) ((-948 . -452) 77683) ((-1109 . -1077) T) ((-110 . -1094) T) ((-1081 . -23) T) ((-813 . -1052) T) ((-778 . -23) T) ((-776 . -23) T) ((-481 . -452) 77634) ((-1153 . -514) 77417) ((-381 . -382) 77396) ((-1172 . -411) 77380) ((-461 . -23) T) ((-454 . -23) T) ((-96 . -1094) T) ((-484 . -514) 77313) ((-289 . -290) T) ((-1076 . -611) 77295) ((-1076 . -612) 77276) ((-407 . -905) 77255) ((-50 . -1106) T) ((-1020 . -916) T) ((-999 . -722) T) ((-708 . -882) NIL) ((-581 . -1106) T) ((-518 . -1106) T) ((-839 . -644) 77228) ((-1203 . -131) T) ((-1161 . -400) 77180) ((-1000 . -309) NIL) ((-811 . -489) 77164) ((-354 . -916) T) ((-1150 . -34) T) ((-407 . -644) 77116) ((-50 . -23) T) ((-707 . -131) T) ((-708 . -1034) 76996) ((-581 . -23) T) ((-108 . -514) NIL) ((-518 . -23) T) ((-169 . -409) 76967) ((-1134 . -1094) T) ((-1274 . -1273) 76951) ((-697 . -791) T) ((-697 . -788) T) ((-1114 . -307) T) ((-379 . -147) T) ((-280 . -611) 76933) ((-1222 . -988) 76903) ((-48 . -916) T) ((-671 . -489) 76887) ((-251 . -1266) 76857) ((-250 . -1266) 76827) ((-1170 . -846) T) ((-1107 . -172) 76806) ((-1114 . -1018) T) ((-1042 . -34) T) ((-832 . -147) 76785) ((-832 . -145) 76764) ((-733 . -107) 76748) ((-610 . -132) T) ((-482 . -1094) 76538) ((-1172 . -1052) T) ((-867 . -452) T) ((-85 . -1209) T) ((-240 . -38) 76508) ((-141 . -107) 76490) ((-708 . -377) 76474) 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. -151) 67858) ((-418 . -1052) T) ((-487 . -713) 67808) ((-482 . -489) 67792) ((-327 . -846) 67771) ((-339 . -644) 67745) ((-50 . -21) T) ((-50 . -25) T) ((-217 . -713) 67695) ((-169 . -720) 67666) ((-174 . -644) 67598) ((-581 . -21) T) ((-581 . -25) T) ((-518 . -25) T) ((-518 . -21) T) ((-475 . -151) 67548) ((-1074 . -611) 67530) ((-1055 . -611) 67512) ((-989 . -102) T) ((-858 . -102) T) ((-795 . -411) 67476) ((-40 . -131) T) ((-695 . -363) T) ((-697 . -722) T) ((-697 . -790) T) ((-697 . -787) T) ((-212 . -891) T) ((-580 . -1106) T) ((-564 . -1106) T) ((-495 . -1106) T) ((-359 . -611) 67458) ((-353 . -611) 67440) ((-345 . -611) 67422) ((-66 . -396) T) ((-66 . -395) T) ((-108 . -612) 67352) ((-108 . -611) 67294) ((-211 . -891) T) ((-954 . -151) 67278) ((-767 . -131) T) ((-666 . -614) 67196) ((-134 . -722) T) ((-116 . -722) T) ((-1243 . -35) 67162) ((-1049 . -489) 67146) ((-580 . -23) T) ((-564 . -23) T) ((-495 . -23) T) ((-1222 . -95) 67112) ((-1222 . -35) 67078) ((-1166 . -102) T) 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65262) ((-201 . -611) 65244) ((-200 . -611) 65226) ((-199 . -611) 65208) ((-198 . -611) 65190) ((-197 . -611) 65172) ((-536 . -1097) 65124) ((-196 . -611) 65106) ((-195 . -611) 65088) ((-45 . -489) 65025) ((-194 . -611) 65007) ((-193 . -611) 64989) ((-152 . -614) 64958) ((-1109 . -102) T) ((-811 . -111) 64848) ((-641 . -102) 64798) ((-482 . -286) 64775) ((-1107 . -611) 64506) ((-1095 . -1094) T) ((-1042 . -1209) T) ((-1282 . -1034) 64490) ((-621 . -1106) T) ((-1166 . -309) 64477) ((-1129 . -1094) T) ((-1119 . -309) 64464) ((-1090 . -1077) T) ((-1084 . -1077) T) ((-1067 . -1077) T) ((-1060 . -1077) T) ((-1032 . -1077) T) ((-1015 . -1077) T) ((-117 . -1106) T) ((-815 . -102) T) ((-624 . -1077) T) ((-621 . -23) T) ((-1144 . -514) 64256) ((-483 . -1077) T) ((-386 . -102) T) ((-324 . -102) T) ((-218 . -1077) T) ((-959 . -1094) T) ((-152 . -1045) T) ((-727 . -411) 64240) ((-117 . -23) T) ((-999 . -896) 64192) ((-731 . -1094) T) ((-711 . -1094) T) ((-453 . -1094) T) ((-407 . -1209) T) ((-316 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. -612) 23648) ((-939 . -611) 23560) ((-641 . -489) 23544) ((-45 . -1006) 23494) ((-615 . -963) T) ((-491 . -102) T) ((-331 . -611) 23476) ((-1107 . -1034) 23303) ((-592 . -647) 23285) ((-130 . -1094) T) ((-128 . -1094) T) ((-592 . -373) 23267) ((-343 . -1266) 23244) ((-439 . -611) 23226) ((-1023 . -1209) T) ((-867 . -290) T) ((-1232 . -514) 23173) ((-476 . -1209) T) ((-463 . -1209) T) ((-585 . -102) T) ((-1166 . -286) 23100) ((-621 . -452) 23079) ((-996 . -991) 23063) ((-1274 . -382) 23035) ((-517 . -1094) T) ((-117 . -452) T) ((-1189 . -102) T) ((-1086 . -1094) 23013) ((-1030 . -1094) T) ((-1109 . -93) T) ((-889 . -846) T) ((-351 . -1213) T) ((-1251 . -1051) 22896) ((-1107 . -377) 22865) ((-1244 . -1051) 22700) ((-1223 . -1051) 22490) ((-1251 . -111) 22359) ((-1244 . -111) 22180) ((-1223 . -111) 21949) ((-1203 . -309) 21936) ((-351 . -556) T) ((-365 . -611) 21918) ((-289 . -307) T) ((-595 . -1051) 21891) ((-594 . -1051) 21774) ((-361 . -1094) T) ((-322 . -1094) T) ((-251 . -611) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 7fe6e29c..8e4bbd99 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3451461725) +(30 . 3451578535) (4409 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -477,662 +477,662 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |nilFactor| |leastAffineMultiple| |diagonalMatrix| - |setMaxPoints3D| |nonQsign| |permutation| |crushedSet| |eq?| - |optional?| |splitDenominator| |problemPoints| |e04fdf| - |exprHasLogarithmicWeights| |cycleLength| |cCos| |gradient| - |figureUnits| |gcdPolynomial| |rotatey| |chineseRemainder| |s21bbf| - 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|imagk| |rightUnits| |LiePolyIfCan| |leftZero| |f04faf| |box| - |patternMatch| |hdmpToP| |minordet| |nthExponent| |mkPrim| - |inverseColeman| |cap| |youngGroup| |overset?| |mapCoef| |typeList| - |OMgetAttr| |cAcoth| |cothIfCan| |curve| |e02akf| |qelt| |identity| - |commutativeEquality| |linear| |nlde| |getOrder| |spherical| |depth| - |constructor| |e04jaf| |open?| ** |qsetelt| |OMlistSymbols| - |mathieu22| |leftTrace| |internalSubQuasiComponent?| |prologue| - |binaryTournament| |e02dff| |minPoints| |xRange| |subset?| |option| - |key?| |polynomial| |lazyPremWithDefault| |quoByVar| |smith| - |completeEval| |point| |minimumExponent| |laguerre| |yRange| - |tanIfCan| |precision| |overlap| |member?| |ratPoly| |next| |randomLC| - |zRange| |enqueue!| |cyclicSubmodule| |besselK| |curryRight| - |fractRadix| |subQuasiComponent?| |OMopenFile| |map!| |lyndon?| |Is| - |pol| |hspace| |removeSuperfluousCases| |insertBottom!| - |OMencodingSGML| |parametersOf| |qsetelt!| |series| |normalize| - |enterInCache| |useEisensteinCriterion?| |palgRDE| |complex?| - |oblateSpheroidal| |bivariateSLPEBR| |s17dlf| |rightTrim| - |definingEquations| |weighted| |f04mbf| |s18def| |setOfMinN| - |rewriteIdealWithRemainder| |sumOfKthPowerDivisors| |OMputVariable| - |getRef| |fglmIfCan| |leftTrim| |meatAxe| |solve1| |integral| - |viewPhiDefault| |iiacos| |selectPDERoutines| |doubleRank| |shuffle| - |makeEq| |resetAttributeButtons| |moduloP| |getProperties| |min| - |leaves| |reverseLex| |viewSizeDefault| |partialDenominators| - |OMgetEndBind| |primextintfrac| |mix| |moebiusMu| |subNodeOf?| - |e01bef| |acsch| |weierstrass| |kind| |swap| |quotedOperators| - |UpTriBddDenomInv| |bombieriNorm| |weight| |ScanArabic| - |constantRight| |e02bef| |op| |countRealRootsMultiple| |f01rcf| - |argumentList!| |univariateSolve| |c06frf| |ref| |hconcat| |refine| - |leadingTerm| |module| |bernoulli| |fortranLiteralLine| - |invertibleSet| |constantCoefficientRicDE| |front| |inRadical?| - |laplace| |showRegion| |solveLinear| |iflist2Result| |fibonacci| - |screenResolution| |yCoord| |prefix?| |constantOperator| |incr| - 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|clearDenominator| |semiIndiceSubResultantEuclidean| - |axesColorDefault| |saturate| |sinhcosh| |useSingleFactorBound| - |topPredicate| |input| |cscIfCan| |isExpt| |removeSinhSq| |palgint| - |s19abf| |c06gbf| |closedCurve| |physicalLength| |mindegTerm| |cCot| - |coshIfCan| |library| |pdct| |f07adf| |scalarMatrix| |knownInfBasis| - |outputGeneral| |computeCycleEntry| |OMputAttr| |iidsum| - |exteriorDifferential| |oddlambert| |returnType!| |blue| |rightUnit| - |conditionsForIdempotents| |internalIntegrate0| |approxSqrt| |chvar| - |factorByRecursion| |source| |prefixRagits| |setTex!| |makeUnit| - |setValue!| |genericRightTrace| |newLine| |addMatchRestricted| - |lazyResidueClass| |subPolSet?| |rootOfIrreduciblePoly| |laurentRep| - |iiasinh| |s15adf| |c06gqf| |denomRicDE| |rdregime| |tab1| |d01gbf| - |presuper| |coerceL| |permutationRepresentation| |symmetricProduct| - |poisson| |mesh?| |rotatex| |leadingSupport| |set| |length| - |headRemainder| |principal?| |back| |mapSolve| |viewZoomDefault| - 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|zeroDimPrimary?| |leftGcd| |square?| |makeYoungTableau| |OMclose| - |firstDenom| |factorPolynomial| |distance| - |dimensionOfIrreducibleRepresentation| |makingStats?| |central?| - |factorOfDegree| |tex| |f01maf| |realEigenvectors| |redmat| - |expandLog| |common| |integralDerivationMatrix| |e04dgf| |removeCosSq| - |operator| |first| |delete| |lfinfieldint| |integerIfCan| - |pointSizeDefault| |index| |makeprod| |areEquivalent?| RF2UTS - |sayLength| |sorted?| |polygamma| |semiDiscriminantEuclidean| |rest| - |setColumn!| |subtractIfCan| |compactFraction| |squareFreeFactors| - |generalizedContinuumHypothesisAssumed?| |maxint| |false| |acosh| - |splitConstant| |cAcot| |f04jgf| |substitute| |vectorise| - |createPrimitivePoly| |reduction| |primlimitedint| |permutationGroup| - |besselY| |henselFact| |atanh| |reindex| |f02agf| - |standardBasisOfCyclicSubmodule| |removeDuplicates| |removeSinSq| - |hasSolution?| |monicRightDivide| |asinIfCan| |atanhIfCan| |pair| - |solveRetract| |mainVariable| |acoth| |quickSort| |s19aaf| - 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|OMputEndObject| |fortranCharacter| |expintfldpoly| |latex| |level| - |palglimint| |d03eef| |autoReduced?| |rename!| |pointColorDefault| - |setProperties!| |semiResultantEuclidean1| |mapmult| |scale| - |stripCommentsAndBlanks| |composites| |reverse!| |OMputBVar| - |irreducibleFactors| |indiceSubResultant| |unmakeSUP| |karatsuba| - |rightDivide| |totalGroebner| |iicsc| |setPrologue!| ~ |s14aaf| - |goodnessOfFit| |incrementKthElement| |string| |SFunction| |legendreP| - |powerAssociative?| |pointPlot| |simplifyExp| |lyndonIfCan| - |dimensions| |nullary?| |perfectSqrt| |matrix| |cAcsc| |numer| - |setnext!| |xn| |create| |cSec| |mvar| |stiffnessAndStabilityFactor| - |infinite?| |open| |beauzamyBound| |quadratic| |ReduceOrder| |denom| - |monomRDEsys| |abs| |f2st| |triangulate| |cot2tan| |ratDenom| - |numericIfCan| |order| |constDsolve| |continuedFraction| - |loadNativeModule| |matrixDimensions| |f02xef| |Beta| - |computeCycleLength| |fintegrate| |infieldint| |extensionDegree| - |computeBasis| |screenResolution3D| |pseudoRemainder| |pi| - |simpleBounds?| |karatsubaDivide| |s18aef| |coercePreimagesImages| - |tValues| |reduceBasisAtInfinity| |genericRightDiscriminant| - |multiset| |f04asf| |primes| |radicalEigenvectors| |e02bdf| |left| - |selectIntegrationRoutines| |reducedForm| |prepareSubResAlgo| - |setPosition| |jacobi| |operations| |extract!| |OMsupportsCD?| |log2| - |makeMulti| |variationOfParameters| |right| |categories| |f04maf| - |makeResult| |randomR| |normalizeIfCan| |diophantineSystem| - |constantLeft| |associative?| |fractionFreeGauss!| |romberg| - |partition| |showTypeInOutput| |returns| |fillPascalTriangle| - |listOfLists| |addPointLast| |subNode?| |OMsupportsSymbol?| - |cycleEntry| |credPol| |inR?| |lSpaceBasis| |modularGcdPrimitive| - |semiSubResultantGcdEuclidean2| |simplify| |generalLambert| - |leftAlternative?| |euler| |acschIfCan| |univariatePolynomialsGcds| - |lambert| |bumptab1| |ip4Address| |aQuartic| |frst| |fixedPoint| - |makeFloatFunction| |iitanh| |completeEchelonBasis| |lowerPolynomial| - |showArrayValues| |setErrorBound| |external?| |e02zaf| |fortranTypeOf| - |overbar| |outputAsFortran| |e01baf| |ignore?| |content| |nthCoef| - |children| |addMatch| |cAcos| |setAdaptive3D| |getZechTable| - |rubiksGroup| |brillhartTrials| |palgint0| |LazardQuotient2| |lintgcd| - |tab| |roughBasicSet| |charClass| |wholeRadix| |csc2sin| |plotPolar| - |irreducibleFactor| |gensym| |simpson| |directSum| |zeroMatrix| - |SturmHabichtCoefficients| |denominators| |nextsubResultant2| - |setFormula!| |internalInfRittWu?| |e02daf| |elliptic| - |discriminantEuclidean| |leftNorm| |iExquo| |expint| |localUnquote| - |float?| |biRank| |complexRoots| |pop!| |makeop| - |rewriteIdealWithQuasiMonicGenerators| |bracket| - |numberOfFractionalTerms| |semiLastSubResultantEuclidean| - |cycleRagits| |lighting| |extendedIntegrate| |primitivePart| - |radicalEigenvalues| |elt| |mainSquareFreePart| |userOrdered?| - |symbol| |internalSubPolSet?| |superHeight| |ldf2vmf| |lifting| - |superscript| |connectTo| |expression| |coHeight| |more?| - |cyclicParents| |viewWriteAvailable| |binding| - |getMultiplicationTable| |floor| |rootSimp| |hcrf| |OMputSymbol| - |OMencodingUnknown| |tanh2coth| |integer| |nativeModuleExtension| - |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| |makeFR| |acsch| |acsc| |axesColorDefault| + |OMgetInteger| |evaluateInverse| |setPrologue!| + |indicialEquationAtInfinity| |besselJ| |sinh| |saturate| + |outputAsFortran| |symmetricGroup| |cos2sec| |s14aaf| + |realEigenvectors| |ode| |showTheFTable| |rroot| |cosh| |sinhcosh| + |hexDigit| |infiniteProduct| |goodnessOfFit| |parabolic| |redmat| + |symbolTable| |integral?| |empty?| |tanh| |useSingleFactorBound| + |read!| |fill!| |incrementKthElement| |leftUnits| |expandLog| + |monomialIntPoly| |monicRightFactorIfCan| |coth| |topPredicate| + |SFunction| |integralDerivationMatrix| |in?| |showTheSymbolTable| + |maxrow| |sech| |cscIfCan| |critMonD1| |lllip| |legendreP| |e04dgf| + |OMUnknownCD?| |clipBoolean| |e04fdf| |pquo| |csch| |label| |isExpt| + |basisOfNucleus| |numberOfChildren| |powerAssociative?| |tail| + |optpair| |removeCosSq| |exprHasLogarithmicWeights| |getConstant| + |bat| |asinh| |removeSinhSq| |associatedEquations| |listOfMonoms| + |pointPlot| |operator| |check| |outputList| |cycleLength| |acosh| + |rules| |arguments| |palgint| |iilog| |rightRemainder| |simplifyExp| + |idealiserMatrix| |lfinfieldint| |exponent| |polyRicDE| |cCos| |atanh| + |s19abf| |safeCeiling| |power!| |unknown| |lyndonIfCan| |rootsOf| + |integerIfCan| |finiteBound| |controlPanel| |gradient| |acoth| + |leader| |c06gbf| |duplicates?| |baseRDEsys| |dimensions| + |pointSizeDefault| |trunc| |LyndonBasis| |retractable?| |figureUnits| + |asech| |closedCurve| |bezoutDiscriminant| |characteristicSet| + |makeprod| |coordinates| |transform| |OMgetString| |gcdPolynomial| + |keys| |physicalLength| |weights| |overlabel| |cycleElt| |algebraic?| + |constructor| ** |areEquivalent?| |infRittWu?| |printCode| + |doubleFloatFormat| |rotatey| |multiple| |mindegTerm| |nor| + |printTypes| |gbasis| |nthExpon| |nsqfree| RF2UTS |hypergeometric0F1| + |addPoint2| |chineseRemainder| |option| |applyQuote| |cCot| + |fortranLogical| |d02ejf| |setLabelValue| |row| |sayLength| + |increasePrecision| |setAttributeButtonStep| |rightGcd| |s21bbf| + |coshIfCan| |hMonic| |rotate!| |parabolicCylindrical| |s15aef| + |fortran| |sorted?| |rationalFunction| |OMread| + |removeRoughlyRedundantFactorsInPols| |palglimint0| |OMputSymbol| + |pdct| |OMlistCDs| |chebyshevU| |unparse| |rdHack1| |norm| |polygamma| + |leftDivide| |purelyTranscendental?| |symmetricSquare| + |OMencodingUnknown| |f07adf| |characteristic| |traverse| |rightTrace| + |definingPolynomial| |factorList| |semiDiscriminantEuclidean| + |setleft!| |iiacoth| |tanh2coth| |part?| |scalarMatrix| |minPoly| + |modularFactor| |createIrreduciblePoly| |OMreceive| |setColumn!| + |indiceSubResultantEuclidean| |rightTrim| |powers| |KrullNumber| + |nativeModuleExtension| |ode2| |knownInfBasis| |setprevious!| + |symmetric?| |legendre| |possiblyInfinite?| |subtractIfCan| + |acoshIfCan| |leftTrim| |genericPosition| |s17acf| |mkIntegral| + |outputGeneral| |rewriteIdealWithHeadRemainder| |argscript| + |rightRecip| |curve?| |trapezoidalo| |compactFraction| |nullSpace| + |concat!| |specialTrigs| |computeCycleEntry| |max| |d01akf| + |numberOfComposites| |ellipticCylindrical| |setStatus!| |addBadValue| + |squareFreeFactors| |createLowComplexityTable| |dequeue!| |isPlus| + |OMputAttr| |conjug| |basicSet| |doublyTransitive?| |printHeader| + |generalizedContinuumHypothesisAssumed?| |kind| |checkPrecision| + |real?| |separate| |viewPosDefault| |binomThmExpt| |iidsum| |toScale| + |factorset| |compdegd| |roughEqualIdeals?| |discreteLog| |isMult| + |maxint| |op| |colorDef| |test| |explicitlyFinite?| + |exteriorDifferential| |perfectNthPower?| |halfExtendedResultant1| + |multiEuclideanTree| |rootOf| |splitConstant| |lazyEvaluate| + |rootPoly| |palgLODE| |lprop| |oddlambert| |interactiveEnv| + |createNormalPrimitivePoly| |supersub| |deepCopy| |cAcot| |showAll?| + |ef2edf| |drawToScale| |llprop| |returnType!| |UnVectorise| + |divideIfCan| |rombergo| |components| |optAttributes| |f04jgf| + |bipolar| |repeating| |primextendedint| |pattern| |pmintegrate| |blue| + |cLog| |eq| |readable?| |uniform01| |vectorise| UP2UTS |maxIndex| + |OMgetError| |numericalIntegration| |rootRadius| |rightUnit| + |explogs2trigs| |iter| |freeOf?| |rootDirectory| |prefix| + |createPrimitivePoly| |mapMatrixIfCan| |antiCommutator| |splitNodeOf!| + |conical| |conditionsForIdempotents| |eof?| |partialFraction| + |nonSingularModel| |orthonormalBasis| |reduction| |cCosh| |getMeasure| + |union| |expandPower| |clearTheIFTable| |internalIntegrate0| + |lieAdmissible?| |exponential| |leftOne| |airyAi| |primlimitedint| + |removeRoughlyRedundantFactorsInContents| |tubePoints| |s17dhf| + |scopes| |message| |approxSqrt| |outputFixed| |chainSubResultants| + |ipow| |plus!| |iiatanh| |permutationGroup| |zeroOf| |entry?| |diff| + |chvar| |fortranInteger| |selectPolynomials| |f07fef| |viewport2D| + |minGbasis| |besselY| |outputArgs| |readIfCan!| |psolve| |close| + |factorByRecursion| |packageCall| |multiplyCoefficients| + |doubleComplex?| |nullary| |decomposeFunc| |henselFact| |numerator| + |recip| |f02bjf| |prefixRagits| |exprToGenUPS| |f01qcf| |lazyPrem| + |typeLists| |reindex| |seriesSolve| |distribute| |empty| |node| + |cAtan| |display| |asimpson| |setTex!| |bumprow| |exp| |deepExpand| + |remainder| |twist| |f02agf| |adaptive| |algintegrate| |isOp| + |makeUnit| |adaptive3D?| |unrankImproperPartitions1| |powmod| + |OMunhandledSymbol| |cons| |rangePascalTriangle| + |standardBasisOfCyclicSubmodule| |cCoth| |f04atf| + |nextLatticePermutation| |setValue!| |f01ref| |triangular?| + |exportedOperators| |algebraicVariables| |completeSmith| |removeSinSq| + |integralRepresents| |polyRDE| |sn| |genericRightTrace| |outerProduct| + |divisorCascade| |surface| |pleskenSplit| |getProperty| + |removeConstantTerm| |hasSolution?| |branchIfCan| |getVariableOrder| + |mainCoefficients| |newLine| |polyred| |parent| |exists?| |OMputError| + |monicRightDivide| |quasiMonicPolynomials| |shiftRoots| |harmonic| + |input| |addMatchRestricted| |fortranComplex| |modifyPointData| + |sequences| UTS2UP |f02wef| |asinIfCan| |trailingCoefficient| |f04axf| + |library| |lazyResidueClass| |complete| |quadraticForm| + |roughUnitIdeal?| |red| |mapUnivariateIfCan| |atanhIfCan| + |drawComplexVectorField| |permutations| |iisqrt2| |subPolSet?| + |rightTraceMatrix| |trivialIdeal?| |character?| |updateStatus!| + |source| |fixedPoints| |solveRetract| |symmetricPower| |mapdiv| + |rootOfIrreduciblePoly| |swapColumns!| |maxPoints| |hasoln| |implies| + |airyBi| |ddFact| |mainVariable| |complexEigenvalues| |power| + |rootSplit| |highCommonTerms| |laurentRep| |imagE| |diagonalMatrix| + |second| |stoseInvertible?sqfreg| |quickSort| |pushFortranOutputStack| + |algebraicDecompose| |jacobiIdentity?| |simpsono| |iiasinh| |set| + |representationType| |swapRows!| |viewThetaDefault| |setMaxPoints3D| + |third| |stFuncN| |sPol| |s19aaf| |OMgetEndAttr| |baseRDE| |signature| + |parseString| |s15adf| |nextPrime| |nonQsign| |resetNew| |qualifier| + |flagFactor| |horizConcat| |alphanumeric| |multisect| |sum| + |permutation| |c06gqf| |redpps| |direction| |f01rdf| |rarrow| + |alternative?| |target| |popFortranOutputStack| |OMputEndAttr| + |relerror| |cAsinh| |clipWithRanges| |denomRicDE| + |useSingleFactorBound?| |crushedSet| |reduceLODE| + |removeSuperfluousQuasiComponents| |bezoutMatrix| |shade| + |changeMeasure| |printStats!| |stop| |rdregime| |leadingBasisTerm| + |expextendedint| |s01eaf| |initTable!| |mkcomm| |octon| + |factorGroebnerBasis| |inverseLaplace| |void| |tab1| |iiacsc| + |hasTopPredicate?| |changeVar| |wronskianMatrix| + |functionIsOscillatory| |groebnerIdeal| |removeCoshSq| + |var2StepsDefault| |systemCommand| |useEisensteinCriterion| |d01gbf| + |e01bff| |Gamma| |s17def| |xCoord| |lp| |identification| |isImplies| + |trueEqual| |unitNormal| |balancedFactorisation| |presuper| |round| + |sub| |enumerate| |makeViewport3D| |integerBound| |ravel| |compBound| + |copies| |chiSquare| |coerceL| |iCompose| |unitVector| |reopen!| + |setMinPoints3D| |imaginary| |reshape| |degreeSubResultant| + |cycleTail| |integrate| |normal| |rootPower| |partitions| |newReduc| + |RemainderList| |recoverAfterFail| |insertMatch| |coth2trigh| + |constantIfCan| |solveInField| |optimize| |rightAlternative?| + |filename| |zeroDimensional?| |leastMonomial| |branchPointAtInfinity?| + |showScalarValues| |diag| |rationalIfCan| |setfirst!| + |fortranLinkerArgs| |OMputAtp| |logical?| |eq?| |numFunEvals| + |setlast!| |colorFunction| |exQuo| |symbolIfCan| |exactQuotient| + |setright!| |integer?| |pole?| |parse| |kovacic| |difference| + |optional?| |members| |cycles| |goodPoint| |cond| |quotientByP| + |root?| |decimal| |internalLastSubResultant| |primintfldpoly| + |mightHaveRoots| |safetyMargin| |SturmHabichtMultiple| + |startPolynomial| |e02ddf| |leftMinimalPolynomial| |jordanAlgebra?| + |unitNormalize| |OMputString| |linearDependenceOverZ| |kroneckerDelta| + |dn| |iisinh| |true| |associator| |OMputInteger| |exprToXXP| + |scaleRoots| |complexSolve| |resize| |edf2ef| |startTable!| + |stirling1| |polCase| |clip| |bfEntry| |inputBinaryFile| + |rightRegularRepresentation| |approxNthRoot| |summation| + |removeRedundantFactorsInPols| |modularGcd| |yellow| + |reducedDiscriminant| |anfactor| |genericLeftNorm| |pointData| + |primeFactor| |lazyPseudoQuotient| |linearPart| |expt| + |reducedContinuedFraction| |musserTrials| |groebgen| |safeFloor| + |cSech| |hermite| |reorder| |element?| |basisOfMiddleNucleus| + |eigenvector| |linSolve| |isPower| |string?| |f02akf| |graphCurves| + |factors| |ListOfTerms| |augment| |leftRecip| |hostPlatform| + |writeUInt8!| |maxColIndex| |drawComplex| |setRealSteps| + |nextNormalPoly| |c06fpf| |OMReadError?| |separant| |contains?| + |d02cjf| |resultantEuclideannaif| |bitLength| |Lazard2| + |doubleResultant| |nextItem| |unprotectedRemoveRedundantFactors| + |ratDsolve| |OMUnknownSymbol?| |alphabetic?| |curry| |rationalPoint?| + |clipPointsDefault| |polygon?| |delete| |primPartElseUnitCanonical| + |explicitlyEmpty?| |index| |rationalApproximation| |hitherPlane| + |leastPower| |arg1| |putGraph| |mapDown!| |e02agf| |objectOf| + |roughSubIdeal?| |increase| |const| |false| |sts2stst| |comparison| + |arg2| |f01brf| |univariate?| |algebraicSort| |strongGenerators| + |inputOutputBinaryFile| |d01amf| |df2st| |cotIfCan| |range| + |startTableGcd!| |algebraicOf| |selectODEIVPRoutines| |pair| |randnum| + |asechIfCan| |repeating?| |fortranDoubleComplex| |binomial| |padecf| + |rur| |conditions| |pmComplexintegrate| |externalList| |realRoots| EQ + |s18aff| |contractSolve| |distFact| |torsion?| |badValues| |value| + |sinh2csch| |match| |setScreenResolution| |selectsecond| + |LazardQuotient2| |cyclotomicDecomposition| |sumOfDivisors| + |irreducible?| |listexp| |heapSort| |#| |distdfact| |commutator| + |removeRedundantFactors| |result| |monicCompleteDecompose| |lintgcd| + |stoseInvertibleSetsqfreg| |iicoth| |indicialEquation| |ParCondList| + |limitPlus| |mathieu11| |supDimElseRittWu?| |groebner| + |LowTriBddDenomInv| |tab| |outputMeasure| |multinomial| + |palginfieldint| |rationalPoints| |polyPart| |orbits| |minset| + |binarySearchTree| |OMconnInDevice| |roughBasicSet| |reset| + |closedCurve?| |iiacot| |stopTableInvSet!| |OMopenString| |minrank| + |principalIdeal| |resultantReduit| |tubePlot| |sechIfCan| |charClass| + |represents| |lazyPseudoDivide| |upperCase!| |dualSignature| |column| + |factorAndSplit| |att2Result| |fprindINFO| |d03faf| |printInfo| + |wholeRadix| |write| |drawStyle| |rootKerSimp| |rischNormalize| + |selectOptimizationRoutines| |extractPoint| |identitySquareMatrix| + |e02baf| |limitedIntegrate| |linearlyDependent?| |save| |csc2sin| + |halfExtendedResultant2| |dictionary| |UP2ifCan| |computePowers| + |subResultantGcd| |branchPoint?| |sturmVariationsOf| |monicModulo| + |negative?| |plotPolar| |halfExtendedSubResultantGcd1| |push| |imagI| + |lepol| |e02adf| |categoryFrame| |sqfrFactor| |prime| |log10| + |oddintegers| |irreducibleFactor| |quasiComponent| |byteBuffer| + |subResultantGcdEuclidean| |OMgetEndApp| |zero?| |iiasech| |copyInto!| + |s19acf| |recur| |bitand| |gensym| |iiGamma| |elements| |variable?| + |deref| |particularSolution| |tubePointsDefault| |splitDenominator| + |recolor| |cyclotomic| |roughBase?| |Lazard| |bitior| |simpson| + |OMserve| |elliptic?| |cExp| |setTopPredicate| |isTerm| |taylorIfCan| + |problemPoints| |generator| |setleaves!| |palgextint| |pToDmp| + |tanSum| |directSum| |leftExactQuotient| |replace| |noKaratsuba| + |critpOrder| |generalInfiniteProduct| |rightMinimalPolynomial| + |hdmpToDmp| |multiple?| |zeroSetSplitIntoTriangularSystems| + |zeroMatrix| |lazyIntegrate| |submod| |push!| |createNormalElement| + |OMencodingXML| |forLoop| |csubst| |brillhartIrreducible?| |number?| + |SturmHabichtCoefficients| |generalizedContinuumHypothesisAssumed| + |reducedSystem| |cyclicCopy| |physicalLength!| |factorSquareFree| + |shellSort| |logIfCan| |wreath| |tryFunctionalDecomposition| + |denominators| |level| |viewpoint| |iterationVar| + |resultantReduitEuclidean| |charpol| |c06gcf| |f04arf| |subSet| |inf| + |odd?| |nextsubResultant2| |divisor| |complexEigenvectors| + |componentUpperBound| |d01ajf| + |rewriteSetByReducingWithParticularGenerators| |multiplyExponents| + |outputFloating| |aromberg| |positiveRemainder| |bubbleSort!| + |setFormula!| |palgintegrate| |bindings| |anticoord| |asinhIfCan| + |lineColorDefault| |integers| |e02ahf| |complexNormalize| |coerceP| + |fracPart| |internalInfRittWu?| |c05adf| |generalizedEigenvector| + |qroot| |noLinearFactor?| |mainPrimitivePart| |search| |c06fqf| + |selectSumOfSquaresRoutines| |outputSpacing| |composite| |e02daf| + |makeSin| |antisymmetric?| |ranges| |s13aaf| |matrix| |mdeg| |numer| + |outputAsTex| |lazyGintegrate| |singularAtInfinity?| |frobenius| + |elliptic| |oneDimensionalArray| |writeBytes!| |expressIdealMember| + |algDsolve| |rational?| |denom| |iisin| |findCycle| + |factorSquareFreeByRecursion| |RittWuCompare| |discriminantEuclidean| + |getStream| |c06gsf| |companionBlocks| |d02gbf| |e01bgf| |adjoint| + |slex| |graphs| |viewDefaults| |leftNorm| |delta| |bezoutResultant| + |FormatArabic| |stoseLastSubResultant| Y |complexLimit| |rCoord| |pi| + |rightExactQuotient| |initializeGroupForWordProblem| |e04naf| + |toseInvertibleSet| |iExquo| |coefChoose| |rotatez| |inconsistent?| + |pow| |startTableInvSet!| |infinity| |categories| |setAdaptive| + |expandTrigProducts| |modifyPoint| |cosSinInfo| |expint| F + |numberOfHues| |operations| |sizePascalTriangle| |idealSimplify| + |setProperty!| |move| |arbitrary| |c06fuf| |c06eaf| |fractRagits| + |localUnquote| |leadingIndex| |eigenMatrix| |diagonal?| |computeInt| + |changeNameToObjf| |child| |largest| |validExponential| |coerceImages| + |float?| |backOldPos| |shift| ~= |decrease| |headReduce| + |numberOfMonomials| |lastSubResultantElseSplit| |kernel| |null| + |paraboloidal| |BasicMethod| |nary?| |clipSurface| |biRank| + |polarCoordinates| |coerce| |select!| |predicates| |edf2fi| |mindeg| + |draw| |not| |reify| |usingTable?| |ocf2ocdf| |tube| |complexRoots| + |badNum| |construct| |reseed| |nullity| |exp1| |leadingExponent| |and| + |upperCase?| |relationsIdeal| |getBadValues| |conjugate| |pop!| + |lambda| |setRow!| |rightRankPolynomial| |collectQuasiMonic| |bits| + |lastSubResultant| |or| |zeroDimPrimary?| |supRittWu?| |dAndcExp| + |currentSubProgram| |makeop| |var2Steps| |fixPredicate| |totalDegree| + |curveColor| |radicalRoots| |xor| |leftGcd| |extendIfCan| + |principalAncestors| |complexIntegrate| + |rewriteIdealWithQuasiMonicGenerators| |prinshINFO| + |genericRightTraceForm| |bat1| |position!| |determinant| |showSummary| + |case| |dflist| |square?| |innerint| |blankSeparate| |bracket| + |cyclePartition| |imports| |resetVariableOrder| |rootNormalize| + |inGroundField?| |Zero| |makeYoungTableau| |outlineRender| + |internalIntegrate| |zeroSetSplit| |numberOfFractionalTerms| |obj| + |find| |isobaric?| |lhs| |conjugates| |unknownEndian| |isConnected?| + |showAttributes| |One| |linkToFortran| |OMclose| |basisOfLeftNucleus| + |internalAugment| |semiLastSubResultantEuclidean| |unaryFunction| + |e02bcf| |pr2dmp| |rhs| |initials| |lastSubResultantEuclidean| |cache| + |measure2Result| |firstDenom| |currentCategoryFrame| |commutative?| + |name| |cycleRagits| |splitSquarefree| |f02ajf| |preprocess| + |meshPar2Var| |po| |iifact| |factorPolynomial| |pseudoDivide| + |stopMusserTrials| |body| |lighting| |checkRur| + |univariatePolynomials| |evenlambert| |messagePrint| |intensity| + |iicos| |distance| |eulerE| |atanIfCan| |extendedIntegrate| + |insertionSort!| |s17dcf| |delay| |build| |writeByte!| + |dimensionOfIrreducibleRepresentation| |allRootsOf| + |resultantEuclidean| |minRowIndex| |primitivePart| |cRationalPower| + |semiResultantReduitEuclidean| |closed?| |addmod| |even?| |split| + |makingStats?| |cAcsch| |diagonals| |radicalEigenvalues| |ODESolve| + |aQuadratic| |inHallBasis?| |logpart| |central?| |tableau| + |OMgetEndBVar| |cschIfCan| |mainSquareFreePart| |vedf2vef| |depth| + |showIntensityFunctions| |cfirst| |iicot| |associates?| |setLength!| + |factorOfDegree| |ramified?| |tanhIfCan| |userOrdered?| + |showTheRoutinesTable| |denomLODE| |leadingCoefficientRicDE| |vspace| + |sinhIfCan| |matrixGcd| |f01maf| |port| |getPickedPoints| |sh| + |internalSubPolSet?| |Nul| |iitan| |tubeRadiusDefault| + |intermediateResultsIF| |leftFactorIfCan| |quadraticNorm| + |OMconnectTCP| |superHeight| F2FG |monomialIntegrate| |getCurve| + |finiteBasis| |univariatePolynomial| |Ci| |extendedint| |t| + |extractIfCan| |ldf2vmf| |exquo| |squareTop| |error| + |stoseInternalLastSubResultant| |stoseInvertible?| |testDim| |crest| + |explimitedint| |btwFact| |wrregime| |lifting| |div| |primitive?| + |nthFactor| |infinityNorm| |declare| |c05nbf| |region| |assert| + |output| |lowerCase?| |readBytes!| |rightScalarTimes!| |quo| + |superscript| |explicitEntries?| |redPo| |mappingAst| + |sortConstraints| GF2FG |calcRanges| |connectTo| |quatern| + |checkForZero| |ScanFloatIgnoreSpacesIfCan| |SturmHabicht| |setrest!| + |omError| |dfRange| |selectAndPolynomials| |rem| |coHeight| |e04ycf| + |setButtonValue| |pointColorPalette| |OMgetEndError| |fractionPart| + |s17aff| |digit| |head| |more?| |f04qaf| |critT| + |ScanFloatIgnoreSpaces| |call| |bandedJacobian| |isOpen?| + |positiveSolve| |cyclicParents| |fullPartialFraction| |tracePowMod| + |squareMatrix| |mapUp!| |firstUncouplingMatrix| |f02bbf| |iiasin| + |invertible?| |viewWriteAvailable| |varselect| |coefficient| + |cycleSplit!| |currentScope| |connect| |primitiveElement| + |hyperelliptic| |rightLcm| |binding| |pack!| |binaryFunction| + |rightFactorCandidate| |next| |genericLeftMinimalPolynomial| + |exactQuotient!| |rotate| |c06ekf| |tanNa| |getMultiplicationTable| + |linears| |sparsityIF| |mkAnswer| |tan2cot| |eigenvalues| + |rightQuotient| |floor| |lazyVariations| |trapezoidal| |finite?| + |leftCharacteristicPolynomial| |d02kef| |maxdeg| |numberOfOperations| + LODO2FUN |rootSimp| |postfix| |singular?| |sumSquares| |phiCoord| + |rename| |li| |solid?| |acosIfCan| |predicate| |cyclicEntries| |hcrf| + |midpoint| |numberOfPrimitivePoly| |virtualDegree| |semicolonSeparate| + |lquo| |ratpart| |setStatus| |prem| |null?| |bitCoef| |e02gaf| + |mapGen| |rowEchelonLocal| |mainContent| |groebner?| |entries| + |makeResult| |reciprocalPolynomial| |appendPoint| |remove!| |qfactor| + |roman| BY |zeroVector| |perfectSquare?| |leftFactor| |randomR| + |viewport3D| |basisOfCenter| |setMinPoints| |imagj| |OMsend| + |critBonD| |tableForDiscreteLogarithm| |c02aff| |normalizeIfCan| + |intChoose| |numberOfNormalPoly| |decompose| |htrigs| |pseudoQuotient| + |startStats!| |subTriSet?| |rightFactorIfCan| |diophantineSystem| + |generalPosition| |sizeLess?| |mathieu23| |hexDigit?| |rspace| + |localIntegralBasis| |pomopo!| |lfextlimint| |constantLeft| |char| + |constantKernel| |nextIrreduciblePoly| |every?| |lfextendedint| + |point?| |dec| |changeThreshhold| |e02ajf| |insert!| |associative?| + |purelyAlgebraicLeadingMonomial?| |subResultantsChain| |selectfirst| + |interReduce| |removeZero| |parameters| |f01bsf| + |SturmHabichtSequence| |dimensionsOf| |plusInfinity| + |fractionFreeGauss!| |lo| |OMbindTCP| |OMputEndAtp| |bivariate?| + |rightZero| |completeHensel| |radicalSolve| |minusInfinity| + |padicallyExpand| |setOrder| |romberg| |halfExtendedSubResultantGcd2| + NOT |divisors| |d01apf| |quadratic?| |less?| |cardinality| + |binaryTree| |coordinate| |partition| |incr| |geometric| OR |option?| + |imagi| |singularitiesOf| |deepestInitial| |makeGraphImage| + |lowerCase| |graphStates| |showTypeInOutput| |hi| |makeSeries| AND + |degree| |just| |removeSquaresIfCan| |OMputObject| |float| + |thenBranch| |constantToUnaryFunction| |rk4f| |returns| |mapExpon| + |primintegrate| |rewriteSetWithReduction| |d02raf| |OMreadStr| + |infix?| |seed| |conditionP| |ceiling| |fillPascalTriangle| + |solveLinearlyOverQ| |getSyntaxFormsFromFile| + |linearlyDependentOverZ?| |mergeFactors| |generic?| |sylvesterMatrix| + |mask| |print| |type| |pToHdmp| |minColIndex| |divideExponents| + |listOfLists| |space| |getOperator| |ffactor| |flatten| + |zeroSquareMatrix| |torsionIfCan| |resolve| |realElementary| |lookup| + |eyeDistance| |zoom| |addPointLast| |condition| |antiAssociative?| + |readUInt16!| |LiePoly| |primitivePart!| |nilFactor| |ksec| + |singleFactorBound| |genericLeftTraceForm| |intcompBasis| |subNode?| + |setClipValue| |rischDEsys| |leastAffineMultiple| |pushdown| |hasHi| + |revert| |duplicates| |pdf2ef| |initiallyReduce| |OMsupportsSymbol?| + |iiacosh| |rank| |s14abf| |mainValue| |divergence| |OMsetEncoding| + |twoFactor| |scalarTypeOf| |myDegree| |cycleEntry| + |removeRoughlyRedundantFactorsInPol| |routines| |s17akf| |normalise| + |euclideanNormalForm| |e02def| |bernoulliB| |f04mcf| + |createGenericMatrix| |credPol| |someBasis| |fortranReal| |setelt!| + |satisfy?| |contours| GE |comment| |clearTheSymbolTable| + |shallowExpand| |factorFraction| |inR?| |radPoly| |invmultisect| * + |index?| |s18acf| |extractProperty| GT |failed?| |linearMatrix| + |algSplitSimple| |subst| |lSpaceBasis| |basisOfLeftNucloid| + |normInvertible?| |orbit| |generalSqFr| |abelianGroup| LE |tan2trig| + |iiacsch| |argument| |modularGcdPrimitive| |generalizedEigenvectors| + |redPol| |pushdterm| |argumentListOf| |showAllElements| LT |cartesian| + |queue| |transcendentalDecompose| |semiSubResultantGcdEuclidean2| + |unitCanonical| |d01bbf| |patternVariable| = |squareFreeLexTriangular| + |e01bhf| |eigenvectors| |sizeMultiplication| |setFieldInfo| |simplify| + |lists| |denominator| |coleman| |listLoops| |maximumExponent| |imagJ| + |deleteRoutine!| |isList| |constant?| |generalLambert| + |genericLeftTrace| |hex| < |powern| |stoseInvertibleSetreg| + |transpose| |identityMatrix| |leftDiscriminant| |is?| + |leftAlternative?| |exponents| |createZechTable| > |symbolTableOf| + |leftMult| |LyndonWordsList1| |symmetricRemainder| + |radicalOfLeftTraceForm| |cSinh| |euler| |objects| |iidprod| |pade| + |separateDegrees| <= |genericLeftDiscriminant| |s21bdf| + |wordInStrongGenerators| |getButtonValue| |findConstructor| |base| + |acschIfCan| |integralMatrixAtInfinity| |nextPrimitivePoly| + |multMonom| >= |normal?| |radix| |mapUnivariate| + |mainDefiningPolynomial| |addPoint| |lift| |structuralConstants| + |compile| |univariatePolynomialsGcds| |inverseIntegralMatrix| |lfunc| + |d01alf| |tubeRadius| |lagrange| |factorials| |retract| |accuracyIF| + |hclf| |solve| |reduce| |lambert| |sup| |laguerreL| |chebyshevT| + |stoseIntegralLastSubResultant| |ode1| |property| |opeval| |fmecg| + |thetaCoord| |setref| |bumptab1| |powerSum| |absolutelyIrreducible?| + + |scan| |leftRegularRepresentation| |putColorInfo| |cyclic| + |generalizedInverse| |invertIfCan| |deepestTail| |ip4Address| + |nonLinearPart| |critMTonD1| |e02bbf| - |graphImage| |getGoodPrime| + |sort| |genericRightMinimalPolynomial| |merge!| |outputForm| + |aQuartic| |parents| |useNagFunctions| |e01sff| |diagonal| / + |wholePart| |toseSquareFreePart| |datalist| |units| |contract| + |numberOfDivisors| |nil?| |frst| |newSubProgram| |leftRank| + |completeHermite| |arrayStack| |pastel| |setchildren!| + |exprHasWeightCosWXorSinWX| |whatInfinity| |fixedPoint| + |createPrimitiveNormalPoly| |bag| |sech2cosh| |associatedSystem| + |OMgetObject| |top| |primeFrobenius| |OMwrite| |bright| |collectUnder| + |makeFloatFunction| |stFunc2| |swap!| |totalLex| |idealiser| |prime?| + |random| |writable?| |dihedralGroup| |mirror| |iitanh| |prinb| |plus| + |elColumn2!| |closeComponent| |compound?| |bandedHessian| |clearCache| + |list| |triangSolve| |prod| |subresultantVector| + |completeEchelonBasis| |iiasec| |bringDown| |point| |key| |generic| + |function| |Vectorise| |f02aaf| |code| |car| |integralAtInfinity?| + |zeroDim?| |birth| |previous| |lowerPolynomial| |acscIfCan| |totolex| + |monic?| |any?| |scripted?| |cdr| |factorSFBRlcUnit| + |basisOfRightNucleus| |extendedEuclidean| |showArrayValues| + |getIdentifier| |readInt8!| |lowerCase!| |iiabs| |eval| + |setDifference| |byte| |insertTop!| |elementary| |nthFractionalTerm| + |setErrorBound| |getProperties| |comp| |capacity| |series| + |genericRightNorm| |digits| |normalizedDivide| |times| |e02dcf| + |setIntersection| |isEquiv| |f02fjf| |OMgetEndObject| |initial| + |external?| |reverseLex| |partialQuotients| |derivationCoordinates| + |df2mf| |hostByteOrder| |processTemplate| |setUnion| |extend| |regime| + |polygon| |e02zaf| |viewSizeDefault| |antisymmetricTensors| + |stronglyReduced?| |s21bcf| |OMgetEndAtp| |digit?| |apply| + |semiResultantEuclidean2| |int| |commonDenominator| |mainForm| + |fortranTypeOf| |partialDenominators| |leviCivitaSymbol| |shiftRight| + |bfKeys| |janko2| |dom| |kmax| |bothWays| |atom?| |meshFun2Var| + |overbar| |OMgetEndBind| |sncndn| |min| |numericalOptimization| + |monom| |showTheIFTable| |getDatabase| |wordInGenerators| |size| + |zeroDimPrime?| |rowEchLocal| |imagk| |e01baf| |primextintfrac| + |edf2df| |decreasePrecision| |prevPrime| |rule| |getOperands| + |rowEchelon| |rightUnits| |restorePrecision| |boundOfCauchy| |ignore?| + |mix| |df2ef| |moduleSum| |extendedSubResultantGcd| |traceMatrix| + |complementaryBasis| |LiePolyIfCan| |numberOfCycles| |content| + |moebiusMu| |clearFortranOutputStack| |errorInfo| |common| + |flexibleArray| |bytes| |cross| |OMreadFile| |first| |leftZero| + |numberOfComponents| |nodeOf?| |nthCoef| |subNodeOf?| + |leftRankPolynomial| |leftLcm| |c05pbf| |dmp2rfi| |totalDifferential| + |title| |rest| |taylorQuoByVar| |f04faf| |quasiRegular| |children| + |e01bef| |secIfCan| |middle| |toroidal| |lcm| |PDESolve| |substitute| + |B1solve| |patternMatch| |failed| |addMatch| |updatF| |weierstrass| + |mainExpression| |expr| |dmpToHdmp| |initiallyReduced?| + |removeDuplicates| |stirling2| |fortranLiteral| |child?| |hdmpToP| + |cAcos| |swap| |pointColor| |normalElement| |inspect| |leaves| + |append| |d02bbf| |e| |stoseInvertibleSet| |lfintegrate| |schema| + |minordet| |setAdaptive3D| |quotedOperators| |d01aqf| |e01daf| + |inrootof| |gcd| |stopTableGcd!| |binary| |numFunEvals3D| + |radicalSimplify| |nthExponent| |getZechTable| |UpTriBddDenomInv| + |iiatan| |selectFiniteRoutines| |lexico| |isOr| + |selectMultiDimensionalRoutines| |mkPrim| |bombieriNorm| |rubiksGroup| + |e01sbf| |substring?| |leftRemainder| |variable| |getMatch| + |resetBadValues| |extension| |nothing| |trace2PowMod| |rationalPower| + |inverseColeman| |rootProduct| |brillhartTrials| |escape| |weight| + |diagonalProduct| |iterators| |leftExtendedGcd| |terms| |coerceS| + |d01anf| |cyclicEqual?| |cap| |palgint0| |ScanArabic| |suffix?| + |solveid| |modulus| |balancedBinaryTree| |localAbs| |hue| + |resultantnaif| |loopPoints| |youngGroup| |constantRight| + |jordanAdmissible?| |csch2sinh| |cPower| |integralLastSubResultant| + |prinpolINFO| |tanAn| |toseLastSubResultant| |setEmpty!| |nullary?| + |overset?| |e02bef| |prefix?| |rightDiscriminant| |atrapezoidal| + |s18adf| |npcoef| |parts| |extractTop!| |leftPower| |nextPartition| + |truncate| |mapCoef| |perfectSqrt| |countRealRootsMultiple| |domainOf| + |s17ahf| |invmod| |OMgetVariable| |e04gcf| |signAround| |nthRootIfCan| + |cAcsc| |typeList| |yCoordinates| |f01rcf| |realEigenvalues| |width| + |hermiteH| |alternatingGroup| |properties| |repeatUntilLoop| + |complexExpand| |magnitude| |setnext!| |OMgetAttr| |argumentList!| + |charthRoot| |drawCurves| |equality| |evenInfiniteProduct| |rightOne| + |continue| |xn| |lyndon| |coerceListOfPairs| |cAcoth| |translate| + |univariateSolve| |bipolarCylindrical| |complement| |antiCommutative?| + |exprToUPS| |block| |tree| |extractSplittingLeaf| |cosh2sech| |create| + |cothIfCan| |c06frf| |discriminant| |quasiRegular?| FG2F |printInfo!| + |ruleset| |rightNorm| |double?| |mulmod| |cSec| |curve| |ref| + |normalizedAssociate| |OMencodingBinary| |firstSubsetGray| + |LazardQuotient| |leftTraceMatrix| |tRange| |returnTypeOf| |e02akf| + |mvar| |hconcat| |expintegrate| |f07aef| |monicLeftDivide| |high| + |generalTwoFactor| |showFortranOutputStack| |leaf?| + |stiffnessAndStabilityFactor| |identity| |refine| + |irreducibleRepresentation| |simplifyLog| |complexForm| |stFunc1| + |suchThat| |replaceKthElement| |lflimitedint| |HermiteIntegrate| + |medialSet| |commutativeEquality| |infinite?| |leadingTerm| |cTanh| + |optional| |listYoungTableaus| |PollardSmallFactor| |nthr| |genus| + |infix| |iiperm| |gcdcofactprim| |beauzamyBound| |nlde| |module| + |FormatRoman| |movedPoints| |sign| |transcendenceDegree| + |characteristicPolynomial| |normalDeriv| |elRow2!| |quadratic| + |getOrder| |bernoulli| |shanksDiscLogAlgorithm| |over| + |clipParametric| |linearDependence| |stoseInvertible?reg| + |degreePartition| |shallowCopy| |spherical| |ReduceOrder| |interpret| + |stack| |fortranLiteralLine| |ridHack1| |numberOfImproperPartitions| + |fTable| |selectNonFiniteRoutines| |palgLODE0| |expenseOfEvaluationIF| + |aLinear| |e04jaf| |monomRDEsys| |invertibleSet| |Aleph| |graphState| + |arity| |color| |mr| |rightCharacteristicPolynomial| |exprex| + |complexElementary| |abs| |open?| |constant| + |constantCoefficientRicDE| |setVariableOrder| |product| |complexZeros| + |integralBasisAtInfinity| |tower| |symmetricTensors| |generate| + |makeCrit| |socf2socdf| |clikeUniv| |f2st| |OMlistSymbols| + |removeIrreducibleRedundantFactors| |front| |tensorProduct| + |squareFreePart| |log| |withPredicates| |viewDeltaYDefault| + |primlimintfrac| |f02adf| |numberOfIrreduciblePoly| |OMputEndBVar| + |triangulate| |mathieu22| |bottom!| |directory| |inRadical?| + |quasiAlgebraicSet| |readInt16!| |quartic| |setImagSteps| ~ |dim| + |incrementBy| |edf2efi| SEGMENT |setvalue!| |relativeApprox| + |leftTrace| |cot2tan| |laplace| |internalZeroSetSplit| |sample| + |createLowComplexityNormalBasis| |vertConcat| |expand| |equation| + |solveLinearPolynomialEquation| |unit| |cAsec| |ratDenom| + |internalSubQuasiComponent?| |write!| |showRegion| |squareFreePrim| + |perspective| |open| |makeCos| |filterWhile| |s17ajf| |dequeue| + |setScreenResolution3D| |numericIfCan| |prologue| |solveLinear| + |mapExponents| |adaptive?| |limitedint| |separateFactors| + |complexNumeric| |filterUntil| |tanh2trigh| |deleteProperty!| |iprint| + |binaryTournament| |order| |iflist2Result| |iiexp| |leadingIdeal| + |sumOfSquares| |OMconnOutDevice| |center| |select| |chiSquare1| + |inverseIntegralMatrixAtInfinity| |isTimes| |e02dff| |constDsolve| + |fibonacci| |squareFreePolynomial| |expIfCan| + |tryFunctionalDecomposition?| |rk4a| |kernels| |qqq| |tanQ| |sec2cos| + |continuedFraction| |minPoints| |screenResolution| |integralMatrix| + |buildSyntax| |readUInt32!| |repSq| |univariate| |lexGroebner| + |mainVariables| |newTypeLists| |matrixDimensions| |subset?| |yCoord| + |nextSubsetGray| |padicFraction| |elRow1!| |interpretString| |formula| + |nthFlag| |factorsOfCyclicGroupSize| |d01fcf| |f02xef| + |constantOperator| |nil| |concat| |unravel| |ScanRoman| |alternating| + |monomials| |mantissa| |callForm?| |minIndex| |f01qdf| |Beta| |cubic| + |OMputBind| |linear?| |getExplanations| |resultant| |factor| + |increment| |cylindrical| |rowEch| |computeCycleLength| |mpsode| + |collect| |Frobenius| |clearTheFTable| |d01asf| |sqrt| |makeRecord| + |changeName| |readByte!| |patternMatchTimes| |fintegrate| |status| + |OMputEndError| |approximate| |countable?| |rightMult| |nand| + |normalDenom| |nrows| |real| |sort!| |droot| |low| |infieldint| + |complex| |rangeIsFinite| |e01saf| |style| |nextPrimitiveNormalPoly| + |bitTruth| |semiSubResultantGcdEuclidean1| |ncols| |imag| + |integralCoordinates| |expenseOfEvaluation| |mathieu12| + |extensionDegree| |rootBound| |monomRDE| |primaryDecomp| |e04mbf| + |s17aef| |intersect| |directProduct| |compiledFunction| + |stosePrepareSubResAlgo| |split!| |computeBasis| |cTan| |isNot| + |subresultantSequence| |vark| |sinIfCan| |totalfract| |pushucoef| + |OMgetFloat| |internalDecompose| |screenResolution3D| |aCubic| + |pushup| |create3Space| |solid| |c02agf| |brace| + |nextNormalPrimitivePoly| |box| |changeWeightLevel| + |complexNumericIfCan| |singRicDE| |pseudoRemainder| |size?| |uniform| + |besselI| |GospersMethod| |qinterval| |destruct| |shrinkable| + |alphanumeric?| |f04adf| |simpleBounds?| |whileLoop| |setPoly| + |remove| |triangularSystems| |cCsc| |vconcat| |curveColorPalette| + |palgRDE0| |nodes| |linear| |karatsubaDivide| |bumptab| |cup| |rk4qc| + |functionIsFracPolynomial?| |atoms| |factorsOfDegree| |presub| + |unitsColorDefault| |s18aef| |mat| |reverse| |setCondition!| |makeSUP| + |last| |isAbsolutelyIrreducible?| |invertibleElseSplit?| + |mainMonomials| |mergeDifference| |OMputFloat| |signatureAst| + |polynomial| |coercePreimagesImages| |assoc| |fortranDouble| |top!| + |untab| |weakBiRank| |close!| |palgextint0| |monomial| |sdf2lst| + |pdf2df| |precision| |vector| |innerSolve1| |entry| |tValues| |limit| + |OMgetType| |firstNumer| |s20acf| |subscript| |multivariate| |iomode| + |differentiate| |seriesToOutputForm| |green| |reduceBasisAtInfinity| + |LyndonWordsList| |rightExtendedGcd| |iibinom| |countRealRoots| + |variables| |ideal| |createNormalPoly| |unexpand| + |genericRightDiscriminant| |key?| |purelyAlgebraic?| |headReduced?| + |f02aef| |indicialEquations| |flexible?| |definingInequation| |An| + |super| |multiset| |lazyPremWithDefault| |host| |unit?| |convergents| + |LagrangeInterpolation| |morphism| |leftQuotient| |deriv| |category| + |f04asf| |quoByVar| |homogeneous?| |cn| |updatD| |radicalEigenvector| + |operation| |OMputEndApp| |systemSizeIF| |basis| |domain| |primes| + |smith| |universe| |createThreeSpace| |subscriptedVariables| + |quotient| |permutationRepresentation| |f2df| |OMgetAtp| |package| + |radicalEigenvectors| |completeEval| |zerosOf| |d01gaf| + |topFortranOutputStack| |whitePoint| |show| |taylor| + |symmetricProduct| |setelt| |s18dcf| |writeInt8!| |e02bdf| + |minimumExponent| |meshPar1Var| |reduced?| |exptMod| |zCoord| + |laurent| |poisson| |commaSeparate| |divide| + |selectIntegrationRoutines| |laguerre| |OMgetSymbol| |epilogue| + |trace| |puiseux| |mesh?| |copy| |exponentialOrder| + |removeDuplicates!| |reducedForm| |tanIfCan| |polar| |readLine!| + |derivative| |lazyIrreducibleFactors| |rotatex| |univcase| |dark| + |prepareSubResAlgo| |factor1| |overlap| |karatsubaOnce| |update| + |sturmSequence| |pair?| |inv| |leadingSupport| |quoted?| |sincos| + |setPosition| |member?| |tablePow| |hessian| |ldf2lst| |bounds| + |ground?| |headRemainder| |autoCoerce| |jacobi| |ratPoly| |pile| + |quasiMonic?| |groebSolve| |times!| |ground| |any| |principal?| + |fullDisplay| |jacobian| |extract!| |randomLC| + |eisensteinIrreducible?| |moebius| |euclideanSize| |paren| + |leadingMonomial| |back| |OMputApp| |gcdPrimitive| |OMsupportsCD?| + |enqueue!| |cCsch| |e04ucf| |getMultiplicationMatrix| |readInt32!| + |leadingCoefficient| |hash| |mapSolve| |listConjugateBases| + |stopTable!| |numeric| |log2| |infieldIntegrate| |cyclicSubmodule| + |mainCharacterization| |position| |primitiveMonomials| |count| + |viewZoomDefault| |setProperty| |algebraicCoefficients?| |radical| + |makeMulti| |besselK| |match?| |semiResultantEuclideannaif| + |interpolate| |operators| |fortranCompilerName| |reductum| + |intPatternMatch| |plenaryPower| |iteratedInitials| + |variationOfParameters| |say| |curryRight| |gcdcofact| |d03edf| |rk4| + |lllp| |lexTriangular| |rst| |OMmakeConn| |f04maf| |fractRadix| + |pointLists| |rectangularMatrix| |rightRank| |innerEigenvectors| + |lieAlgebra?| |equiv| |axes| |rquo| |subQuasiComponent?| + |combineFeatureCompatibility| |quote| |regularRepresentation| |s14baf| + |normalized?| |basisOfCentroid| |algint| |indices| |OMopenFile| + |doubleDisc| |realZeros| |evaluate| |cycle| |minimize| |debug| + |measure| |shufflein| |squareFree| |iFTable| |lyndon?| |cSin| + |endOfFile?| |OMputEndBind| |subHeight| |skewSFunction| D + |reduceByQuasiMonic| |littleEndian| |internal?| |elem?| |Is| + |rational| |transcendent?| |goto| |numberOfComputedEntries| + |setLegalFortranSourceExtensions| |OMgetBind| |characteristicSerie| + |normalForm| |pol| |logGamma| |Si| |gcdprim| |belong?| + |readLineIfCan!| |differentialVariables| |compose| |gramschmidt| + |hspace| |s19adf| |OMcloseConn| |trigs2explogs| |c06ecf| |init| + |prolateSpheroidal| |defineProperty| |shiftLeft| + |linearAssociatedOrder| |removeSuperfluousCases| |lazyPquo| + |pushNewContour| |critB| |points| |viewDeltaXDefault| |divideIfCan!| + |dominantTerm| |slash| |insertBottom!| |trim| |upDateBranches| + |matrixConcat3D| |makeViewport2D| |cAsech| |OMgetBVar| |double| + |clearTable!| |multiEuclidean| |OMencodingSGML| |f07fdf| + |scanOneDimSubspaces| |f01qef| |assign| |symFunc| |has?| |f02aff| + |normalizeAtInfinity| |parametersOf| |critM| |linGenPos| |readUInt8!| + |expPot| |fixedDivisor| |outputAsScript| |lex| |rischDE| |zero| + |normalize| |iicosh| |wholeRagits| |coord| |froot| |makeSketch| + |modTree| |reflect| |length| |maxRowIndex| |enterInCache| + |selectOrPolynomials| |findBinding| |mapBivariate| |one?| |var1Steps| + |interval| |f02abf| |scripts| |showClipRegion| |And| + |useEisensteinCriterion?| |reducedQPowers| |c06ebf| |consnewpol| + |enterPointData| |nthRoot| |cAtanh| |createRandomElement| |d02bhf| + |Or| |palgRDE| |s17dgf| |integralBasis| |dihedral| |subCase?| |Ei| + |e02aef| |collectUpper| |se2rfi| |Not| |complex?| |heap| |sin2csc| + |minPol| |trigs| |errorKind| |factorSquareFreePolynomial| + |primPartElseUnitCanonical!| |declare!| |polynomialZeros| |/\\| + |oblateSpheroidal| |copy!| |stronglyReduce| |leftScalarTimes!| + |listRepresentation| |df2fi| |alphabetic| |setPredicates| + |printingInfo?| |\\/| |bivariateSLPEBR| |extractBottom!| |e01sef| + |midpoints| |cyclic?| |choosemon| |iroot| |getlo| |minus!| |s17dlf| + |mainKernel| |setClosed| |ramifiedAtInfinity?| |rightPower| |cot2trig| + |OMParseError?| |cyclicGroup| |createPrimitiveElement| + |definingEquations| |subMatrix| |debug3D| |innerSolve| |extractClosed| + |minPoints3D| |fi2df| |monomial?| |f02axf| |id| |weighted| + |parametric?| |infLex?| |hasPredicate?| |nextsousResultant2| + |unvectorise| |uncouplingMatrices| |nextSublist| |positive?| |f04mbf| + |bivariatePolynomials| |extractIndex| |plot| |inverse| |script| + |getCode| |dioSolve| |perfectNthRoot| |linearAssociatedLog| |s18def| + |table| |prepareDecompose| |monicDivide| |root| |probablyZeroDim?| + |splitLinear| |fortranCarriageReturn| |normal01| |segment| + |OMputEndObject| |insert| |new| |setOfMinN| + |stiffnessAndStabilityOfODEIF| |gderiv| |basisOfRightAnnihilator| + |addiag| |varList| |LyndonCoordinates| |numerators| |approximants| + |fortranCharacter| |rewriteIdealWithRemainder| |iipow| |schwerpunkt| + |f02awf| |solveLinearPolynomialEquationByRecursion| |tex| |iicsch| + |tanintegrate| |makeTerm| |expintfldpoly| |options| + |sumOfKthPowerDivisors| |laplacian| |viewWriteDefault| |setProperties| + |sin?| |BumInSepFFE| |sylvesterSequence| |stoseSquareFreePart| |latex| + |OMputVariable| |normDeriv2| |symmetricDifference| + |functionIsContinuousAtEndPoints| |bit?| |component| + |groebnerFactorize| |permanent| |palglimint| |getRef| + |linearPolynomials| |symbol?| |graeffe| |changeBase| |qPot| + |localReal?| |writeLine!| |d03eef| |string| |fglmIfCan| + |createMultiplicationMatrix| |subspace| |makeVariable| |OMgetApp| + |light| |neglist| |dmpToP| |autoReduced?| |retractIfCan| |meatAxe| + |cyclotomicFactorization| |sequence| |pascalTriangle| |taylorRep| + |ptFunc| |lifting1| |bsolve| |rename!| |solve1| |curryLeft| + |outputBinaryFile| |node?| |unrankImproperPartitions0| + |extendedResultant| |cAsin| |f01mcf| |pointColorDefault| + |loadNativeModule| |integral| |createMultiplicationTable| + |noncommutativeJordanAlgebra?| |factorial| |isAnd| |erf| |ptree| + |dimension| |upperCase| |laurentIfCan| |setProperties!| + |viewPhiDefault| |leftUnit| |testModulus| |linearAssociatedExp| + |coth2tanh| |minimalPolynomial| |exprHasAlgebraicWeight| + |semiDegreeSubResultantEuclidean| |semiResultantEuclidean1| |iiacos| + |left| |normFactors| |pureLex| |headAst| |listBranches| |acotIfCan| + |euclideanGroebner| |mainMonomial| |mapmult| |right| + |selectPDERoutines| |minimumDegree| |oddInfiniteProduct| + |solveLinearPolynomialEquationByFractions| |corrPoly| |dilog| |s20adf| + |basisOfLeftAnnihilator| |fixedPointExquo| |scale| |doubleRank| + |iisqrt3| |s17adf| |var1StepsDefault| |qelt| + |removeRedundantFactorsInContents| |sin| |numberOfVariables| + |constantOpIfCan| |certainlySubVariety?| |stripCommentsAndBlanks| + |qsetelt| |associatorDependence| |shuffle| |zag| |possiblyNewVariety?| + |isQuotient| |list?| |cos| |inc| |cosIfCan| |sqfree| |Hausdorff| + |makeObject| |composites| |basisOfCommutingElements| |makeEq| |map| + |HenselLift| |notelem| |xRange| |imagK| |tan| |acothIfCan| |ParCond| + |dot| |reverse!| |applyRules| |resetAttributeButtons| |s13adf| + |yRange| |ricDsolve| |removeZeroes| |currentEnv| |cot| |bigEndian| + |mathieu24| |degreeSubResultantEuclidean| |OMputBVar| |coef| |iisec| + |moduloP| |gethi| |lazyPseudoRemainder| |zRange| |merge| |sec| + |setsubMatrix!| |delete!| |printStatement| |irreducibleFactors| + |iisech| |d02gaf| |coefficients| |map!| |generateIrredPoly| |csc| + |setMaxPoints| |numberOfFactors| |exponential1| |indiceSubResultant| + |unary?| |insertRoot!| |qsetelt!| |height| |digamma| |endSubProgram| + |asin| |realSolve| |maxrank| |mainVariable?| |unmakeSUP| |convert| + |asecIfCan| |monicDecomposeIfCan| |eulerPhi| |cAcosh| |acos| + |elseBranch| |pushuconst| |maxPoints3D| |karatsuba| |ord| |mesh| + |basisOfRightNucloid| |s17agf| |atan| |aspFilename| |nextColeman| + |rightDivide| |elt| |symbol| |simplifyPower| |ran| |s13acf| + |generators| |acot| |clearDenominator| |moreAlgebraic?| |setEpilogue!| + |totalGroebner| |expression| |prindINFO| |wordsForStrongGenerators| + |s21baf| |toseInvertible?| |asec| |semiIndiceSubResultantEuclidean| + |partialNumerators| |getGraph| 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T) ((-23) . T) ((-25) . T) ((-38 #0=(-407 (-564))) -2750 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-38 |#1|) . T) ((-38 $) -2750 (|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#) -2750 (|has| |#1| (-349)) (|has| |#1| (-363))) ((-111 |#1| |#1|) . T) ((-111 $ $) . T) ((-131) . T) ((-145) -2750 (|has| |#1| (-349)) (|has| |#1| (-145))) ((-147) |has| |#1| (-147)) ((-614 #0#) -2750 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-349)) (|has| |#1| (-363))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 $) -2750 (|has| |#1| (-556)) (|has| |#1| (-349)) (|has| |#1| (-363)) (|has| |#1| (-307))) ((-611 (-858)) . T) ((-172) . T) ((-612 (-169 (-225))) |has| |#1| (-1018)) ((-612 (-169 (-379))) |has| |#1| (-1018)) ((-612 (-536)) |has| |#1| (-612 (-536))) ((-612 (-888 (-379))) |has| |#1| (-612 (-888 (-379)))) ((-612 (-888 (-564))) |has| |#1| (-612 (-888 (-564)))) ((-612 #1=(-1166 |#1|)) . 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(|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2797 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2797 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2797 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2797 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2797 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2797 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . 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T) ((-1266 |#2|) |has| |#2| (-363))) -((-3355 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-3255 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-3137 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) -(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -3355 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3255 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -3137 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) -((-3137 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-3255 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-3355 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) -(-10 -7 (-15 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(IF (|has| |t#2| (-722)) (PROGN (-6 (-722)) (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-368)) (-6 (-368)) |%noBranch|) (IF (|has| |t#2| (-172)) (PROGN (-6 (-38 |t#2|)) (-6 (-172))) |%noBranch|) (IF (|has| |t#2| (-6 -4403)) (-6 -4403) |%noBranch|) (IF (|has| |t#2| (-844)) (-6 (-844)) |%noBranch|) (IF (|has| |t#2| (-789)) (-6 (-789)) |%noBranch|) (IF (|has| |t#2| (-363)) (-6 (-1266 |t#2|)) |%noBranch|))) +(((-21) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-23) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-25) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-34) . T) ((-38 |#2|) |has| |#2| (-172)) ((-102) -2750 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-111 |#2| |#2|) -2750 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-111 $ $) |has| |#2| (-172)) ((-131) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131))) ((-614 #0=(-407 (-564))) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-614 (-564)) -2750 (|has| |#2| (-1045)) (-12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-614 |#2|) -2750 (|has| |#2| (-1094)) (|has| |#2| (-172))) ((-611 (-858)) -2750 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-611 (-858))) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-611 (-1259 |#2|)) . T) ((-172) |has| |#2| (-172)) ((-231 |#2|) |has| |#2| (-1045)) ((-233) -12 (|has| |#2| (-233)) (|has| |#2| (-1045))) ((-286 #1=(-564) |#2|) . T) ((-288 #1# |#2|) . T) ((-309 |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-368) |has| |#2| (-368)) ((-377 |#2|) |has| |#2| (-1045)) ((-411 |#2|) |has| |#2| (-1094)) ((-489 |#2|) . T) ((-602 #1# |#2|) . T) ((-514 |#2| |#2|) -12 (|has| |#2| (-309 |#2|)) (|has| |#2| (-1094))) ((-644 |#2|) -2750 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-644 $) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-637 (-564)) -12 (|has| |#2| (-637 (-564))) (|has| |#2| (-1045))) ((-637 |#2|) |has| |#2| (-1045)) ((-713 |#2|) -2750 (|has| |#2| (-363)) (|has| |#2| (-172))) ((-722) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-787) |has| |#2| (-844)) ((-788) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-789) |has| |#2| (-789)) ((-790) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-791) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-844) |has| |#2| (-844)) ((-846) -2750 (|has| |#2| (-844)) (|has| |#2| (-789))) ((-896 (-1170)) -12 (|has| |#2| (-896 (-1170))) (|has| |#2| (-1045))) ((-1034 #0#) -12 (|has| |#2| (-1034 (-407 (-564)))) (|has| |#2| (-1094))) ((-1034 (-564)) -12 (|has| |#2| (-1034 (-564))) (|has| |#2| (-1094))) ((-1034 |#2|) |has| |#2| (-1094)) ((-1051 |#2|) -2750 (|has| |#2| (-1045)) (|has| |#2| (-363)) (|has| |#2| (-172))) ((-1051 $) |has| |#2| (-172)) ((-1045) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1052) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-172))) ((-1106) -2750 (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-722)) (|has| |#2| (-172))) ((-1094) -2750 (|has| |#2| (-1094)) (|has| |#2| (-1045)) (|has| |#2| (-844)) (|has| |#2| (-789)) (|has| |#2| (-722)) (|has| |#2| (-368)) (|has| |#2| (-363)) (|has| |#2| (-172)) (|has| |#2| (-131)) (|has| |#2| (-25))) ((-1209) . T) ((-1266 |#2|) |has| |#2| (-363))) +((-2981 (((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 21)) (-2965 ((|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|) 23)) (-4289 (((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)) 18))) +(((-239 |#1| |#2| |#3|) (-10 -7 (-15 -2981 ((-240 |#1| |#3|) (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -2965 (|#3| (-1 |#3| |#2| |#3|) (-240 |#1| |#2|) |#3|)) (-15 -4289 ((-240 |#1| |#3|) (-1 |#3| |#2|) (-240 |#1| |#2|)))) (-767) (-1209) (-1209)) (T -239)) +((-4289 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *7 (-1209)) (-5 *2 (-240 *5 *7)) (-5 *1 (-239 *5 *6 *7)))) (-2965 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-240 *5 *6)) (-14 *5 (-767)) (-4 *6 (-1209)) (-4 *2 (-1209)) (-5 *1 (-239 *5 *6 *2)))) (-2981 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-240 *6 *7)) (-14 *6 (-767)) (-4 *7 (-1209)) (-4 *5 (-1209)) (-5 *2 (-240 *6 *5)) (-5 *1 (-239 *6 *7 *5))))) +(-10 -7 (-15 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T) ((-1213) |has| |#1| (-905))) -((-2331 (((-112) $ $) 19 (|has| |#1| (-1094)))) (-2188 ((|#1| $) 54)) (-1858 ((|#1| $) 44)) (-1555 (((-112) $ (-767)) 8)) (-2167 (($) 7 T CONST)) (-2329 (($ $) 60)) (-4178 (($ $) 48)) (-3396 ((|#1| |#1| $) 46)) (-4351 ((|#1| $) 45)) (-3554 (((-641 |#1|) $) 30 (|has| $ (-6 -4406)))) (-4374 (((-112) $ (-767)) 9)) (-4127 (((-641 |#1|) $) 29 (|has| $ (-6 -4406)))) (-1443 (((-112) |#1| $) 27 (-12 (|has| |#1| (-1094)) (|has| $ (-6 -4406))))) (-1455 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4407)))) (-3137 (($ (-1 |#1| |#1|) $) 35)) (-3964 (((-112) $ (-767)) 10)) (-1753 (((-767) $) 61)) (-4165 (((-1152) $) 22 (|has| |#1| (-1094)))) (-4012 ((|#1| $) 39)) (-1935 ((|#1| |#1| $) 52)) (-1461 ((|#1| |#1| $) 51)) (-3641 (($ |#1| $) 40)) (-3181 (((-767) $) 55)) (-3859 (((-1114) $) 21 (|has| |#1| (-1094)))) (-1535 ((|#1| $) 62)) (-1339 ((|#1| $) 50)) (-3202 ((|#1| $) 49)) (-4258 ((|#1| $) 41)) (-2212 (((-112) (-1 (-112) |#1|) $) 32 (|has| $ (-6 -4406)))) (-3115 (($ $ (-641 (-294 |#1|))) 26 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (($ $ (-294 |#1|)) 25 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (($ $ |#1| |#1|) 24 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094)))) (($ $ (-641 |#1|) (-641 |#1|)) 23 (-12 (|has| |#1| (-309 |#1|)) (|has| |#1| (-1094))))) (-1299 (((-112) $ $) 14)) (-1448 ((|#1| |#1| $) 58)) (-2771 (((-112) $) 11)) (-3787 (($) 12)) (-2665 ((|#1| $) 59)) (-3594 (($) 57) (($ (-641 |#1|)) 56)) (-1413 (((-767) $) 43)) (-3869 (((-767) (-1 (-112) |#1|) $) 31 (|has| $ (-6 -4406))) (((-767) |#1| $) 28 (-12 (|has| |#1| (-1094)) (|has| $ (-6 -4406))))) (-3796 (($ $) 13)) (-2345 (((-858) $) 18 (|has| |#1| (-611 (-858))))) (-3910 ((|#1| $) 53)) (-3359 (($ (-641 |#1|)) 42)) (-1756 ((|#1| $) 63)) (-3998 (((-112) (-1 (-112) |#1|) $) 33 (|has| $ (-6 -4406)))) (-2925 (((-112) $ $) 20 (|has| |#1| (-1094)))) (-2078 (((-767) $) 6 (|has| $ (-6 -4406))))) +((-4195 (*1 *2 *3) (-12 (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-1 *1 (-767))) (-4 *1 (-253 *4 *3 *5 *6)))) (-3970 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-641 *4)))) (-3533 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-767)))) (-3533 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-767)))) (-2762 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-767)))) (-1413 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-641 (-767))))) (-3268 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-767)))) (-1413 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-641 (-767))))) (-3268 (*1 *2 *1 *3) (-12 (-4 *1 (-253 *4 *3 *5 *6)) (-4 *4 (-1045)) (-4 *3 (-846)) (-4 *5 (-266 *3)) (-4 *6 (-789)) (-5 *2 (-767)))) (-2422 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *5 *6)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-112)))) (-1392 (*1 *2 *1) (-12 (-4 *1 (-253 *3 *4 *2 *5)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-789)) (-4 *2 (-266 *4)))) (-3104 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1045)) (-4 *3 (-846)) (-4 *4 (-266 *3)) (-4 *5 (-789)))) (-1986 (*1 *1 *1) (-12 (-4 *1 (-253 *2 *3 *4 *5)) (-4 *2 (-1045)) (-4 *3 (-846)) (-4 *4 (-266 *3)) (-4 *5 (-789)))) (-4195 (*1 *2 *1) (-12 (-4 *3 (-233)) (-4 *3 (-1045)) (-4 *4 (-846)) (-4 *5 (-266 *4)) (-4 *6 (-789)) (-5 *2 (-1 *1 (-767))) (-4 *1 (-253 *3 *4 *5 *6))))) +(-13 (-945 |t#1| |t#4| |t#3|) (-231 |t#1|) (-1034 |t#2|) (-10 -8 (-15 -4195 ((-1 $ (-767)) |t#2|)) (-15 -3970 ((-641 |t#2|) $)) (-15 -3533 ((-767) $ |t#2|)) (-15 -3533 ((-767) $)) (-15 -2762 ((-767) $ |t#2|)) (-15 -1413 ((-641 (-767)) $)) (-15 -3268 ((-767) $)) (-15 -1413 ((-641 (-767)) $ |t#2|)) (-15 -3268 ((-767) $ |t#2|)) (-15 -2422 ((-112) $)) (-15 -1392 (|t#3| $)) (-15 -3104 ($ $)) (-15 -1986 ($ $)) (IF (|has| |t#1| (-233)) (PROGN (-6 (-514 |t#2| |t#1|)) (-6 (-514 |t#2| $)) (-6 (-309 $)) (-15 -4195 ((-1 $ (-767)) $))) |%noBranch|))) +(((-21) . T) ((-23) . T) ((-47 |#1| |#4|) . T) ((-25) . T) ((-38 #0=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-102) . T) ((-111 #0# #0#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #0#) -2750 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 |#1|) . T) ((-614 |#2|) . T) ((-614 |#3|) . T) ((-614 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-611 (-858)) . T) ((-172) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| |#1| (-612 (-536))) (|has| |#3| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| |#1| (-612 (-888 (-379)))) (|has| |#3| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| |#1| (-612 (-888 (-564)))) (|has| |#3| (-612 (-888 (-564))))) ((-231 |#1|) . T) ((-233) |has| |#1| (-233)) ((-290) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-309 $) . T) ((-326 |#1| |#4|) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2750 (|has| |#1| (-905)) (|has| |#1| (-452))) ((-514 |#2| |#1|) |has| |#1| (-233)) ((-514 |#2| $) |has| |#1| (-233)) ((-514 |#3| |#1|) . T) ((-514 |#3| $) . T) ((-514 $ $) . T) ((-556) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452))) ((-644 #0#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . 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T) ((-302) . T) ((-363) |has| |#1| (-556)) ((-377 |#1|) |has| |#1| (-1045)) ((-400 |#1|) . T) ((-411 |#1|) . T) ((-452) |has| |#1| (-556)) ((-473) |has| |#1| (-473)) ((-514 (-610 $) $) . T) ((-514 $ $) . T) ((-556) |has| |#1| (-556)) ((-644 #0#) |has| |#1| (-556)) ((-644 |#1|) |has| |#1| (-172)) ((-644 $) -2797 (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-637 (-564)) -12 (|has| |#1| (-637 (-564))) (|has| |#1| (-1045))) ((-637 |#1|) |has| |#1| (-1045)) ((-713 #0#) |has| |#1| (-556)) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) |has| |#1| (-556)) ((-722) -2797 (|has| |#1| (-1106)) (|has| |#1| (-1045)) (|has| |#1| (-556)) (|has| |#1| (-473)) (|has| |#1| (-172)) (|has| |#1| (-147)) (|has| |#1| (-145))) ((-846) . T) ((-896 (-1170)) |has| |#1| (-1045)) ((-882 (-379)) |has| |#1| (-882 (-379))) ((-882 (-564)) |has| |#1| (-882 (-564))) ((-880 |#1|) . 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|notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) 27)) (-2538 (((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) 39)) (-2527 (((-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) 37)) (-2812 (((-1264)) 12))) -(((-559) (-10 -8 (-15 -3882 ($)) (-15 -2812 ((-1264))) (-15 -2850 ((-641 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) $)) (-15 -2795 ($ (-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3641 ($ (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-15 -2425 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-15 -2527 ((-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (-15 -2538 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))))) (T -559)) -((-2538 (*1 *2 *3) (-12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-559)))) (-2527 (*1 *2 *1) (-12 (-5 *2 (-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-559)))) (-2425 (*1 *2 *3) (|partial| -12 (-5 *3 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *2 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))) (-5 *1 (-559)))) (-3641 (*1 *1 *2) (-12 (-5 *2 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) (-5 *1 (-559)))) (-2795 (*1 *1 *2) (-12 (-5 *2 (-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-5 *1 (-559)))) (-2850 (*1 *2 *1) (-12 (-5 *2 (-641 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-5 *1 (-559)))) (-2812 (*1 *2) (-12 (-5 *2 (-1264)) (-5 *1 (-559)))) (-3882 (*1 *1) (-5 *1 (-559)))) -(-10 -8 (-15 -3882 ($)) (-15 -2812 ((-1264))) (-15 -2850 ((-641 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) $)) (-15 -2795 ($ (-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))))) (-15 -3641 ($ (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) (-15 -2425 ((-3 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225))))) (-15 -2527 ((-641 (-2 (|:| -3090 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| -2538 (-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $)) (-15 -2538 ((-2 (|:| |endPointContinuity| (-3 (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (-3 (|:| |str| (-1150 (-225))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| -1953 (-3 (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) -((-2362 (((-1166 (-407 (-1166 |#2|))) |#2| (-610 |#2|) (-610 |#2|) (-1166 |#2|)) 35)) (-1313 (((-3 (-2 (|:| |mainpart| |#2|) (|:| |limitedlogs| (-641 (-2 (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (-610 |#2|) (-610 |#2|) (-641 |#2|) (-610 |#2|) |#2| (-407 (-1166 |#2|))) 105) (((-3 (-2 (|:| |mainpart| |#2|) (|:| |limitedlogs| (-641 (-2 (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (-610 |#2|) (-610 |#2|) (-641 |#2|) |#2| (-1166 |#2|)) 115)) (-4322 (((-585 |#2|) |#2| (-610 |#2|) (-610 |#2|) (-610 |#2|) |#2| (-407 (-1166 |#2|))) 85) (((-585 |#2|) |#2| (-610 |#2|) (-610 |#2|) |#2| (-1166 |#2|)) 55)) (-1365 (((-3 (-2 (|:| -1886 |#2|) (|:| |coeff| |#2|)) "failed") |#2| (-610 |#2|) (-610 |#2|) |#2| (-610 |#2|) |#2| (-407 (-1166 |#2|))) 92) (((-3 (-2 (|:| -1886 |#2|) (|:| |coeff| |#2|)) "failed") |#2| (-610 |#2|) (-610 |#2|) |#2| |#2| (-1166 |#2|)) 114)) (-2502 (((-3 |#2| "failed") |#2| |#2| (-610 |#2|) (-610 |#2|) (-1 (-3 |#2| "failed") |#2| |#2| (-1170)) (-610 |#2|) |#2| (-407 (-1166 |#2|))) 110) (((-3 |#2| "failed") |#2| |#2| (-610 |#2|) (-610 |#2|) (-1 (-3 |#2| "failed") |#2| |#2| 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T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) -((-2560 (((-641 (-1076)) $) 34)) (-2730 (($ $) 31)) (-2533 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-2696 (($ $) 14)) (-2707 ((|#2| $) 12)) (-1595 ((|#3| $) 10))) -(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -2560 ((-641 (-1076)) |#1|)) (-15 -2533 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2533 (|#1| |#1| (-1076) |#3|)) (-15 -2730 (|#1| |#1|)) (-15 -2533 (|#1| |#2| |#3|)) (-15 -1595 (|#3| |#1|)) (-15 -2696 (|#1| |#1|)) (-15 -2707 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) -NIL -(-10 -8 (-15 -2560 ((-641 (-1076)) |#1|)) (-15 -2533 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -2533 (|#1| |#1| (-1076) |#3|)) (-15 -2730 (|#1| |#1|)) (-15 -2533 (|#1| |#2| |#3|)) (-15 -1595 (|#3| |#1|)) (-15 -2696 (|#1| |#1|)) (-15 -2707 (|#2| |#1|))) -((-2331 (((-112) $ $) 7)) (-4028 (((-112) $) 16)) (-2560 (((-641 (-1076)) $) 77)) (-3282 (((-1170) $) 106)) (-2698 (((-2 (|:| -2485 $) (|:| 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T) ((-23) . T) ((-47 |#1| #0=(-767)) . T) ((-25) . T) ((-38 #1=(-407 (-564))) |has| |#1| (-38 (-407 (-564)))) ((-38 |#1|) |has| |#1| (-172)) ((-38 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-102) . T) ((-111 #1# #1#) |has| |#1| (-38 (-407 (-564)))) ((-111 |#1| |#1|) . T) ((-111 $ $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-131) . T) ((-145) |has| |#1| (-145)) ((-147) |has| |#1| (-147)) ((-614 #1#) -2750 (|has| |#1| (-1034 (-407 (-564)))) (|has| |#1| (-38 (-407 (-564))))) ((-614 (-564)) . T) ((-614 #2=(-1076)) . T) ((-614 |#1|) . T) ((-614 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-611 (-858)) . T) ((-172) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-612 (-536)) -12 (|has| (-1076) (-612 (-536))) (|has| |#1| (-612 (-536)))) ((-612 (-888 (-379))) -12 (|has| (-1076) (-612 (-888 (-379)))) (|has| |#1| (-612 (-888 (-379))))) ((-612 (-888 (-564))) -12 (|has| (-1076) (-612 (-888 (-564)))) (|has| |#1| (-612 (-888 (-564))))) ((-231 |#1|) . T) ((-233) . T) ((-286 (-407 $) (-407 $)) |has| |#1| (-556)) ((-286 |#1| |#1|) . T) ((-286 $ $) . T) ((-290) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-307) |has| |#1| (-363)) ((-309 $) . T) ((-326 |#1| #0#) . T) ((-377 |#1|) . T) ((-411 |#1|) . T) ((-452) -2750 (|has| |#1| (-905)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-514 #2# |#1|) . T) ((-514 #2# $) . T) ((-514 $ $) . T) ((-556) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-644 #1#) |has| |#1| (-38 (-407 (-564)))) ((-644 |#1|) . T) ((-644 $) . T) ((-637 (-564)) |has| |#1| (-637 (-564))) ((-637 |#1|) . T) ((-713 #1#) |has| |#1| (-38 (-407 (-564)))) ((-713 |#1|) |has| |#1| (-172)) ((-713 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363))) ((-722) . T) ((-846) |has| |#1| (-846)) ((-896 #2#) . T) ((-896 (-1170)) |has| |#1| (-896 (-1170))) ((-882 (-379)) -12 (|has| (-1076) (-882 (-379))) (|has| |#1| (-882 (-379)))) ((-882 (-564)) -12 (|has| (-1076) (-882 (-564))) (|has| |#1| (-882 (-564)))) ((-945 |#1| #0# #2#) . T) ((-905) |has| |#1| (-905)) ((-916) |has| |#1| (-363)) ((-1034 (-407 (-564))) |has| |#1| (-1034 (-407 (-564)))) ((-1034 (-564)) |has| |#1| (-1034 (-564))) ((-1034 #2#) . T) ((-1034 |#1|) . T) ((-1051 #1#) |has| |#1| (-38 (-407 (-564)))) ((-1051 |#1|) . T) ((-1051 $) -2750 (|has| |#1| (-905)) (|has| |#1| (-556)) (|has| |#1| (-452)) (|has| |#1| (-363)) (|has| |#1| (-172))) ((-1045) . T) ((-1052) . T) ((-1106) . T) ((-1094) . T) ((-1145) |has| |#1| (-1145)) ((-1213) |has| |#1| (-905))) +((-3743 (((-641 (-1076)) $) 34)) (-3900 (($ $) 31)) (-3720 (($ |#2| |#3|) NIL) (($ $ (-1076) |#3|) 28) (($ $ (-641 (-1076)) (-641 |#3|)) 27)) (-3866 (($ $) 14)) (-3876 ((|#2| $) 12)) (-2762 ((|#3| $) 10))) +(((-1236 |#1| |#2| |#3|) (-10 -8 (-15 -3743 ((-641 (-1076)) |#1|)) (-15 -3720 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3720 (|#1| |#1| (-1076) |#3|)) (-15 -3900 (|#1| |#1|)) (-15 -3720 (|#1| |#2| |#3|)) (-15 -2762 (|#3| |#1|)) (-15 -3866 (|#1| |#1|)) (-15 -3876 (|#2| |#1|))) (-1237 |#2| |#3|) (-1045) (-788)) (T -1236)) +NIL +(-10 -8 (-15 -3743 ((-641 (-1076)) |#1|)) (-15 -3720 (|#1| |#1| (-641 (-1076)) (-641 |#3|))) (-15 -3720 (|#1| |#1| (-1076) |#3|)) (-15 -3900 (|#1| |#1|)) (-15 -3720 (|#1| |#2| |#3|)) (-15 -2762 (|#3| |#1|)) (-15 -3866 (|#1| |#1|)) (-15 -3876 (|#2| |#1|))) +((-2337 (((-112) $ $) 7)) (-2148 (((-112) $) 16)) (-3743 (((-641 (-1076)) $) 77)) (-3257 (((-1170) $) 106)) (-1850 (((-2 (|:| -3506 $) (|:| 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(-172) (-368) (-612 (-564)) (-1145)) @@ -5306,4 +5306,4 @@ NIL NIL NIL NIL -((-3 3198890 3198895 3198900 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3198875 3198880 3198885 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3198860 3198865 3198870 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3198845 3198850 3198855 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3198014 3198720 3198797 "ZMOD" 3198802 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3197124 3197288 3197497 "ZLINDEP" 3197846 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3186424 3188192 3190164 "ZDSOLVE" 3195254 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3185670 3185811 3186000 "YSTREAM" 3186270 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3183471 3184971 3185175 "XRPOLY" 3185513 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3180051 3181342 3181917 "XPR" 3182943 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3177799 3179382 3179586 "XPOLY" 3179882 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3175582 3176924 3176979 "XPOLYC" 3177267 NIL XPOLYC (NIL T T) -9 NIL 3177380 NIL) (-1279 3171985 3174099 3174487 "XPBWPOLY" 3175240 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3167888 3170148 3170190 "XF" 3170811 NIL XF (NIL T) -9 NIL 3171211 NIL) (-1277 3167509 3167597 3167766 "XF-" 3167771 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3162835 3164098 3164153 "XFALG" 3166325 NIL XFALG (NIL T T) -9 NIL 3167114 NIL) (-1275 3161968 3162072 3162277 "XEXPPKG" 3162727 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3160104 3161818 3161914 "XDPOLY" 3161919 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159041 3159615 3159658 "XALG" 3159663 NIL XALG (NIL T) -9 NIL 3159774 NIL) (-1272 3152510 3157018 3157512 "WUTSET" 3158633 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3150793 3151562 3151885 "WP" 3152321 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3150422 3150615 3150685 "WHILEAST" 3150745 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3149921 3150139 3150233 "WHEREAST" 3150350 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3148807 3149005 3149300 "WFFINTBS" 3149718 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3146711 3147138 3147600 "WEIER" 3148379 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3145858 3146282 3146324 "VSPACE" 3146460 NIL VSPACE (NIL T) -9 NIL 3146534 NIL) (-1265 3145696 3145723 3145814 "VSPACE-" 3145819 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3145504 3145547 3145615 "VOID" 3145650 T VOID (NIL) -8 NIL NIL NIL) (-1263 3143640 3143999 3144405 "VIEW" 3145120 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140064 3140703 3141440 "VIEWDEF" 3142925 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3129395 3131612 3133785 "VIEW3D" 3137913 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3121673 3123306 3124885 "VIEW2D" 3127838 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117075 3121443 3121535 "VECTOR" 3121616 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3115652 3115911 3116229 "VECTOR2" 3116805 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3109179 3113436 3113479 "VECTCAT" 3114472 NIL VECTCAT (NIL T) -9 NIL 3115058 NIL) (-1256 3108193 3108447 3108837 "VECTCAT-" 3108842 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3107674 3107844 3107964 "VARIABLE" 3108108 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3107607 3107612 3107642 "UTYPE" 3107647 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3106437 3106591 3106853 "UTSODETL" 3107433 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3103877 3104337 3104861 "UTSODE" 3105978 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3095741 3101503 3101992 "UTS" 3103446 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3086976 3092308 3092351 "UTSCAT" 3093463 NIL UTSCAT (NIL T) -9 NIL 3094220 NIL) (-1249 3084324 3085046 3086035 "UTSCAT-" 3086040 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3083951 3083994 3084127 "UTS2" 3084275 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3078224 3080789 3080832 "URAGG" 3082902 NIL URAGG (NIL T) -9 NIL 3083625 NIL) (-1246 3075163 3076026 3077149 "URAGG-" 3077154 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3070879 3073777 3074249 "UPXSSING" 3074827 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3062972 3070126 3070399 "UPXS" 3070664 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056072 3062876 3062948 "UPXSCONS" 3062953 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3046309 3053067 3053129 "UPXSCCA" 3053703 NIL UPXSCCA (NIL T T) -9 NIL 3053936 NIL) (-1241 3045947 3046032 3046206 "UPXSCCA-" 3046211 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036037 3042568 3042611 "UPXSCAT" 3043259 NIL UPXSCAT (NIL T) -9 NIL 3043867 NIL) (-1239 3035467 3035546 3035725 "UPXS2" 3035952 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3034121 3034374 3034725 "UPSQFREE" 3035210 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3027901 3030923 3030978 "UPSCAT" 3032139 NIL UPSCAT (NIL T T) -9 NIL 3032913 NIL) (-1236 3027105 3027312 3027639 "UPSCAT-" 3027644 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3012947 3020953 3020996 "UPOLYC" 3023097 NIL UPOLYC (NIL T) -9 NIL 3024318 NIL) (-1234 3004275 3006701 3009848 "UPOLYC-" 3009853 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3003902 3003945 3004078 "UPOLYC2" 3004226 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2995468 3003585 3003714 "UP" 3003821 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2994807 2994914 2995078 "UPMP" 2995357 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2994360 2994441 2994580 "UPDIVP" 2994720 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2992928 2993177 2993493 "UPDECOMP" 2994109 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2992163 2992275 2992460 "UPCDEN" 2992812 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2991682 2991751 2991900 "UP2" 2992088 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2990197 2990886 2991163 "UNISEG" 2991440 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2989412 2989539 2989744 "UNISEG2" 2990040 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2988472 2988652 2988878 "UNIFACT" 2989228 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2972431 2987649 2987900 "ULS" 2988279 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2960457 2972335 2972407 "ULSCONS" 2972412 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943065 2955015 2955077 "ULSCCAT" 2955715 NIL ULSCCAT (NIL T T) -9 NIL 2956003 NIL) (-1220 2942115 2942360 2942748 "ULSCCAT-" 2942753 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2931982 2938427 2938470 "ULSCAT" 2939333 NIL ULSCAT (NIL T) -9 NIL 2940063 NIL) (-1218 2931412 2931491 2931670 "ULS2" 2931897 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2930529 2931012 2931119 "UINT8" 2931230 T UINT8 (NIL) -8 NIL NIL 2931315) (-1216 2929645 2930128 2930235 "UINT64" 2930346 T UINT64 (NIL) -8 NIL NIL 2930431) (-1215 2928761 2929244 2929351 "UINT32" 2929462 T UINT32 (NIL) -8 NIL NIL 2929547) (-1214 2927877 2928360 2928467 "UINT16" 2928578 T UINT16 (NIL) -8 NIL NIL 2928663) (-1213 2926272 2927203 2927233 "UFD" 2927445 T UFD (NIL) -9 NIL 2927559 NIL) (-1212 2926066 2926112 2926207 "UFD-" 2926212 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2925148 2925331 2925547 "UDVO" 2925872 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2922964 2923373 2923844 "UDPO" 2924712 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2922897 2922902 2922932 "TYPE" 2922937 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2922684 2922852 2922883 "TYPEAST" 2922888 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2921655 2921857 2922097 "TWOFACT" 2922478 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2920726 2921064 2921299 "TUPLE" 2921455 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2918417 2918936 2919475 "TUBETOOL" 2920209 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2917266 2917471 2917712 "TUBE" 2918210 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912022 2916238 2916521 "TS" 2917018 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2900689 2904781 2904878 "TSETCAT" 2910147 NIL TSETCAT (NIL T T T T) -9 NIL 2911678 NIL) (-1201 2895421 2897021 2898912 "TSETCAT-" 2898917 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2889683 2890530 2891472 "TRMANIP" 2894557 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2889124 2889187 2889350 "TRIMAT" 2889615 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2886919 2887157 2887521 "TRIGMNIP" 2888873 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2886439 2886552 2886582 "TRIGCAT" 2886795 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2886108 2886187 2886328 "TRIGCAT-" 2886333 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883001 2884966 2885247 "TREE" 2885862 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2882275 2882803 2882833 "TRANFUN" 2882868 T TRANFUN (NIL) -9 NIL 2882934 NIL) (-1193 2881554 2881745 2882025 "TRANFUN-" 2882030 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2881358 2881390 2881451 "TOPSP" 2881515 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2880706 2880821 2880975 "TOOLSIGN" 2881239 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2879367 2879883 2880122 "TEXTFILE" 2880489 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2877306 2877820 2878249 "TEX" 2878960 T TEX (NIL) -8 NIL NIL NIL) (-1188 2877087 2877118 2877190 "TEX1" 2877269 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2876735 2876798 2876888 "TEMUTL" 2877019 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2874889 2875169 2875494 "TBCMPPK" 2876458 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2866777 2873049 2873105 "TBAGG" 2873505 NIL TBAGG (NIL T T) -9 NIL 2873716 NIL) (-1184 2861847 2863335 2865089 "TBAGG-" 2865094 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2861231 2861338 2861483 "TANEXP" 2861736 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2854732 2861088 2861181 "TABLE" 2861186 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2854144 2854243 2854381 "TABLEAU" 2854629 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2848752 2849972 2851220 "TABLBUMP" 2852930 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2847974 2848121 2848302 "SYSTEM" 2848593 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2844433 2845132 2845915 "SYSSOLP" 2847225 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2843467 2843945 2844064 "SYSNNI" 2844250 NIL SYSNNI (NIL NIL) -8 NIL NIL 2844335) (-1176 2842764 2843196 2843275 "SYSINT" 2843335 NIL SYSINT (NIL NIL) -8 NIL NIL 2843380) (-1175 2839123 2840042 2840752 "SYNTAX" 2842076 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2836281 2836883 2837515 "SYMTAB" 2838513 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2831530 2832432 2833415 "SYMS" 2835320 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2828792 2830988 2831218 "SYMPOLY" 2831335 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2828309 2828384 2828507 "SYMFUNC" 2828704 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2824355 2825621 2826434 "SYMBOL" 2827518 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2817894 2819583 2821303 "SWITCH" 2822657 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2811155 2816715 2817018 "SUTS" 2817649 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2803248 2810402 2810675 "SUPXS" 2810940 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2794763 2802866 2802992 "SUP" 2803157 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2793922 2794049 2794266 "SUPFRACF" 2794631 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2793543 2793602 2793715 "SUP2" 2793857 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2791956 2792230 2792593 "SUMRF" 2793242 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2791270 2791336 2791535 "SUMFS" 2791877 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2775264 2790447 2790698 "SULS" 2791077 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2774893 2775086 2775156 "SUCHTAST" 2775216 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2774215 2774418 2774558 "SUCH" 2774801 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2768109 2769121 2770080 "SUBSPACE" 2773303 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2767539 2767629 2767793 "SUBRESP" 2767997 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2760904 2762204 2763515 "STTF" 2766275 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755077 2756197 2757344 "STTFNC" 2759804 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2746388 2748259 2750053 "STTAYLOR" 2753318 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2739632 2746252 2746335 "STRTBL" 2746340 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735023 2739587 2739618 "STRING" 2739623 T STRING (NIL) -8 NIL NIL NIL) (-1151 2729911 2734396 2734426 "STRICAT" 2734485 T STRICAT (NIL) -9 NIL 2734547 NIL) (-1150 2722714 2727530 2728141 "STREAM" 2729335 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2722224 2722301 2722445 "STREAM3" 2722631 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2721206 2721389 2721624 "STREAM2" 2722037 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2720894 2720946 2721039 "STREAM1" 2721148 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2719910 2720091 2720322 "STINPROD" 2720710 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2719488 2719672 2719702 "STEP" 2719782 T STEP (NIL) -9 NIL 2719860 NIL) (-1144 2713031 2719387 2719464 "STBL" 2719469 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2708205 2712252 2712295 "STAGG" 2712448 NIL STAGG (NIL T) -9 NIL 2712537 NIL) (-1142 2705907 2706509 2707381 "STAGG-" 2707386 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2704102 2705677 2705769 "STACK" 2705850 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2696825 2702243 2702699 "SREGSET" 2703732 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2689250 2690619 2692132 "SRDCMPK" 2695431 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2682217 2686690 2686720 "SRAGG" 2688023 T SRAGG (NIL) -9 NIL 2688631 NIL) (-1137 2681234 2681489 2681868 "SRAGG-" 2681873 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2675721 2680181 2680602 "SQMATRIX" 2680860 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2669468 2672439 2673166 "SPLTREE" 2675066 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2665458 2666124 2666770 "SPLNODE" 2668894 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2664505 2664738 2664768 "SPFCAT" 2665212 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2663242 2663452 2663716 "SPECOUT" 2664263 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2654894 2656638 2656668 "SPADXPT" 2661060 T SPADXPT (NIL) -9 NIL 2663094 NIL) (-1130 2654655 2654695 2654764 "SPADPRSR" 2654847 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2652837 2654610 2654641 "SPADAST" 2654646 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2644808 2646555 2646598 "SPACEC" 2650971 NIL SPACEC (NIL T) -9 NIL 2652787 NIL) (-1127 2642965 2644740 2644789 "SPACE3" 2644794 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2641717 2641888 2642179 "SORTPAK" 2642770 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2639767 2640070 2640489 "SOLVETRA" 2641381 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2638778 2639000 2639274 "SOLVESER" 2639540 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2633989 2634879 2635881 "SOLVERAD" 2637830 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2629804 2630413 2631142 "SOLVEFOR" 2633356 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2624101 2629153 2629250 "SNTSCAT" 2629255 NIL SNTSCAT (NIL T T T T) -9 NIL 2629325 NIL) (-1120 2618234 2622424 2622815 "SMTS" 2623791 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2612674 2618122 2618199 "SMP" 2618204 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2610833 2611134 2611532 "SMITH" 2612371 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2603720 2607884 2607987 "SMATCAT" 2609338 NIL SMATCAT (NIL NIL T T T) -9 NIL 2609888 NIL) (-1116 2600660 2601483 2602661 "SMATCAT-" 2602666 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2598373 2599896 2599939 "SKAGG" 2600200 NIL SKAGG (NIL T) -9 NIL 2600335 NIL) (-1114 2594708 2597789 2597984 "SINT" 2598171 T SINT (NIL) -8 NIL NIL 2598344) (-1113 2594480 2594518 2594584 "SIMPAN" 2594664 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2593786 2594015 2594155 "SIG" 2594362 T SIG (NIL) -8 NIL NIL NIL) (-1111 2592624 2592845 2593120 "SIGNRF" 2593545 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2591429 2591580 2591871 "SIGNEF" 2592453 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2590762 2591012 2591136 "SIGAST" 2591327 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2588452 2588906 2589412 "SHP" 2590303 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2582352 2588353 2588429 "SHDP" 2588434 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2581951 2582117 2582147 "SGROUP" 2582240 T SGROUP (NIL) -9 NIL 2582302 NIL) (-1105 2581809 2581835 2581908 "SGROUP-" 2581913 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2578644 2579342 2580065 "SGCF" 2581108 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573039 2578091 2578188 "SFRTCAT" 2578193 NIL SFRTCAT (NIL T T T T) -9 NIL 2578232 NIL) (-1102 2566460 2567478 2568614 "SFRGCD" 2572022 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2559587 2560659 2561845 "SFQCMPK" 2565393 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559209 2559298 2559408 "SFORT" 2559528 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2558354 2559049 2559170 "SEXOF" 2559175 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2557488 2558235 2558303 "SEX" 2558308 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553027 2553716 2553811 "SEXCAT" 2556748 NIL SEXCAT (NIL T T T T T) -9 NIL 2557326 NIL) (-1096 2550207 2552961 2553009 "SET" 2553014 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2548458 2548920 2549225 "SETMN" 2549948 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548064 2548190 2548220 "SETCAT" 2548337 T SETCAT (NIL) -9 NIL 2548422 NIL) (-1093 2547844 2547896 2547995 "SETCAT-" 2548000 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2544231 2546305 2546348 "SETAGG" 2547218 NIL SETAGG (NIL T) -9 NIL 2547558 NIL) (-1091 2543689 2543805 2544042 "SETAGG-" 2544047 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2543159 2543385 2543486 "SEQAST" 2543610 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2542358 2542652 2542713 "SEGXCAT" 2542999 NIL SEGXCAT (NIL T T) -9 NIL 2543119 NIL) (-1088 2541412 2542024 2542206 "SEG" 2542211 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2540391 2540605 2540648 "SEGCAT" 2541170 NIL SEGCAT (NIL T) -9 NIL 2541391 NIL) (-1086 2539440 2539770 2539970 "SEGBIND" 2540226 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539061 2539120 2539233 "SEGBIND2" 2539375 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2538661 2538862 2538939 "SEGAST" 2539006 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2537880 2538006 2538210 "SEG2" 2538505 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2537317 2537815 2537862 "SDVAR" 2537867 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2529599 2537087 2537217 "SDPOL" 2537222 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2528192 2528458 2528777 "SCPKG" 2529314 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2527356 2527528 2527720 "SCOPE" 2528022 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2526576 2526710 2526889 "SCACHE" 2527211 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2526248 2526408 2526438 "SASTCAT" 2526443 T SASTCAT (NIL) -9 NIL 2526456 NIL) (-1076 2525762 2526083 2526159 "SAOS" 2526194 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2525327 2525362 2525535 "SAERFFC" 2525721 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2519293 2525224 2525304 "SAE" 2525309 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2518886 2518921 2519080 "SAEFACT" 2519252 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2517207 2517521 2517922 "RURPK" 2518552 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2515843 2516122 2516434 "RULESET" 2517041 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513030 2513533 2513998 "RULE" 2515524 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2512669 2512824 2512907 "RULECOLD" 2512982 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2512459 2512487 2512558 "RTVALUE" 2512620 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2511957 2512176 2512270 "RSTRCAST" 2512387 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2506805 2507600 2508520 "RSETGCD" 2511156 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496062 2501114 2501211 "RSETCAT" 2505330 NIL RSETCAT (NIL T T T T) -9 NIL 2506427 NIL) (-1064 2493989 2494528 2495352 "RSETCAT-" 2495357 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486374 2487751 2489271 "RSDCMPK" 2492588 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484379 2484820 2484894 "RRCC" 2485980 NIL RRCC (NIL T T) -9 NIL 2486324 NIL) (-1061 2483730 2483904 2484183 "RRCC-" 2484188 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483200 2483426 2483527 "RPTAST" 2483651 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457198 2466793 2466860 "RPOLCAT" 2477524 NIL RPOLCAT (NIL T T T) -9 NIL 2480683 NIL) (-1058 2448696 2451036 2454158 "RPOLCAT-" 2454163 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2439743 2446907 2447389 "ROUTINE" 2448236 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2436568 2439369 2439509 "ROMAN" 2439625 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2434839 2435428 2435688 "ROIRC" 2436373 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431224 2433475 2433505 "RNS" 2433809 T RNS (NIL) -9 NIL 2434082 NIL) (-1053 2429733 2430116 2430650 "RNS-" 2430725 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429182 2429564 2429594 "RNG" 2429599 T RNG (NIL) -9 NIL 2429620 NIL) (-1051 2428574 2428936 2428979 "RMODULE" 2429041 NIL RMODULE (NIL T) -9 NIL 2429083 NIL) (-1050 2427410 2427504 2427840 "RMCAT2" 2428475 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424287 2426756 2427053 "RMATRIX" 2427172 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417229 2419463 2419578 "RMATCAT" 2422937 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2423919 NIL) (-1047 2416604 2416751 2417058 "RMATCAT-" 2417063 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416171 2416246 2416374 "RINTERP" 2416523 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415290 2415818 2415848 "RING" 2415904 T RING (NIL) -9 NIL 2415996 NIL) (-1044 2415082 2415126 2415223 "RING-" 2415228 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2413923 2414160 2414418 "RIDIST" 2414846 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405239 2413391 2413597 "RGCHAIN" 2413771 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2404615 2404995 2405036 "RGBCSPC" 2405094 NIL RGBCSPC (NIL T) -9 NIL 2405146 NIL) (-1040 2403799 2404154 2404195 "RGBCMDL" 2404427 NIL RGBCMDL (NIL T) -9 NIL 2404541 NIL) (-1039 2400793 2401407 2402077 "RF" 2403163 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400439 2400502 2400605 "RFFACTOR" 2400724 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400164 2400199 2400296 "RFFACT" 2400398 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398281 2398645 2399027 "RFDIST" 2399804 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2397734 2397826 2397989 "RETSOL" 2398183 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397370 2397450 2397493 "RETRACT" 2397626 NIL RETRACT (NIL T) -9 NIL 2397713 NIL) (-1033 2397219 2397244 2397331 "RETRACT-" 2397336 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2396848 2397041 2397111 "RETAST" 2397171 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2389702 2396501 2396628 "RESULT" 2396743 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388320 2388971 2389170 "RESRING" 2389605 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2387956 2388005 2388103 "RESLATC" 2388257 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2387661 2387696 2387803 "REPSQ" 2387915 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385083 2385663 2386265 "REP" 2387081 T REP (NIL) -7 NIL NIL NIL) (-1026 2384780 2384815 2384926 "REPDB" 2385042 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2378680 2380069 2381292 "REP2" 2383592 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375057 2375738 2376546 "REP1" 2377907 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2367780 2373198 2373654 "REGSET" 2374687 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2366593 2366928 2367178 "REF" 2367565 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2365970 2366073 2366240 "REDORDER" 2366477 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2361965 2365183 2365410 "RECLOS" 2365798 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361017 2361198 2361413 "REALSOLV" 2361772 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2360863 2360904 2360934 "REAL" 2360939 T REAL (NIL) -9 NIL 2360974 NIL) (-1017 2357346 2358148 2359032 "REAL0Q" 2360028 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2352947 2353935 2354996 "REAL0" 2356327 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352445 2352664 2352758 "RDUCEAST" 2352875 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2351850 2351922 2352129 "RDIV" 2352367 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2350918 2351092 2351305 "RDIST" 2351672 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349515 2349802 2350174 "RDETRS" 2350626 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347327 2347781 2348319 "RDETR" 2349057 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2345938 2346216 2346620 "RDEEFS" 2347043 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344433 2344739 2345171 "RDEEF" 2345626 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2338686 2341569 2341599 "RCFIELD" 2342894 T RCFIELD (NIL) -9 NIL 2343624 NIL) (-1007 2336750 2337254 2337950 "RCFIELD-" 2338025 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333066 2334851 2334894 "RCAGG" 2335978 NIL RCAGG (NIL T) -9 NIL 2336443 NIL) (-1005 2332694 2332788 2332951 "RCAGG-" 2332956 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332029 2332141 2332306 "RATRET" 2332578 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2331582 2331649 2331770 "RATFACT" 2331957 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2330890 2331010 2331162 "RANDSRC" 2331452 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2330624 2330668 2330741 "RADUTIL" 2330839 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2323767 2329457 2329767 "RADIX" 2330348 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315415 2323611 2323739 "RADFF" 2323744 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315067 2315142 2315170 "RADCAT" 2315327 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2314852 2314900 2314997 "RADCAT-" 2315002 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313003 2314627 2314716 "QUEUE" 2314796 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2309571 2312940 2312985 "QUAT" 2312990 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309209 2309252 2309379 "QUATCT2" 2309522 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2302948 2306258 2306298 "QUATCAT" 2307078 NIL QUATCAT (NIL T) -9 NIL 2307844 NIL) (-992 2299092 2300129 2301516 "QUATCAT-" 2301610 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2296612 2298176 2298217 "QUAGG" 2298592 NIL QUAGG (NIL T) -9 NIL 2298767 NIL) (-990 2296244 2296437 2296505 "QQUTAST" 2296564 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295169 2295642 2295814 "QFORM" 2296116 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286373 2291586 2291626 "QFCAT" 2292284 NIL QFCAT (NIL T) -9 NIL 2293285 NIL) (-987 2281945 2283146 2284737 "QFCAT-" 2284831 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2281583 2281626 2281753 "QFCAT2" 2281896 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281043 2281153 2281283 "QEQUAT" 2281473 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274190 2275262 2276446 "QCMPACK" 2279976 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2271766 2272187 2272615 "QALGSET" 2273845 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271011 2271185 2271417 "QALGSET2" 2271586 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2269701 2269925 2270242 "PWFFINTB" 2270784 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2267883 2268051 2268405 "PUSHVAR" 2269515 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2263801 2264855 2264896 "PTRANFN" 2266780 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262203 2262494 2262816 "PTPACK" 2263512 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2261835 2261892 2262001 "PTFUNC2" 2262140 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256362 2260707 2260748 "PTCAT" 2261044 NIL PTCAT (NIL T) -9 NIL 2261197 NIL) (-975 2256020 2256055 2256179 "PSQFR" 2256321 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2254615 2254913 2255247 "PSEUDLIN" 2255718 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241378 2243749 2246073 "PSETPK" 2252375 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234422 2237136 2237232 "PSETCAT" 2240253 NIL PSETCAT (NIL T T T T) -9 NIL 2241067 NIL) (-971 2232258 2232892 2233713 "PSETCAT-" 2233718 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2231607 2231772 2231800 "PSCURVE" 2232068 T PSCURVE (NIL) -9 NIL 2232235 NIL) (-969 2227955 2229445 2229510 "PSCAT" 2230354 NIL PSCAT (NIL T T T) -9 NIL 2230594 NIL) (-968 2227018 2227234 2227634 "PSCAT-" 2227639 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2225750 2226383 2226588 "PRTITION" 2226833 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225252 2225471 2225563 "PRTDAST" 2225678 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214342 2216556 2218744 "PRS" 2223114 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212200 2213692 2213732 "PRQAGG" 2213915 NIL PRQAGG (NIL T) -9 NIL 2214017 NIL) (-963 2211586 2211815 2211843 "PROPLOG" 2212028 T PROPLOG (NIL) -9 NIL 2212150 NIL) (-962 2210094 2210537 2210794 "PROPFRML" 2211362 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2209563 2209670 2209798 "PROPERTY" 2209986 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2203648 2207729 2208549 "PRODUCT" 2208789 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2200953 2203106 2203340 "PR" 2203459 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2200749 2200781 2200840 "PRINT" 2200914 T PRINT (NIL) -7 NIL NIL NIL) (-957 2200089 2200206 2200358 "PRIMES" 2200629 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2198154 2198555 2199021 "PRIMELT" 2199668 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2197883 2197932 2197960 "PRIMCAT" 2198084 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2194046 2197821 2197866 "PRIMARR" 2197871 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2193053 2193231 2193459 "PRIMARR2" 2193864 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2192696 2192752 2192863 "PREASSOC" 2192991 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2192171 2192304 2192332 "PPCURVE" 2192537 T PPCURVE (NIL) -9 NIL 2192673 NIL) (-950 2191793 2191966 2192049 "PORTNUM" 2192108 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2189152 2189551 2190143 "POLYROOT" 2191374 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2183089 2188756 2188916 "POLY" 2189025 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2182472 2182530 2182764 "POLYLIFT" 2183025 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2178747 2179196 2179825 "POLYCATQ" 2182017 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2165556 2170922 2170987 "POLYCAT" 2174501 NIL POLYCAT (NIL T T T) -9 NIL 2176429 NIL) (-944 2159005 2160867 2163251 "POLYCAT-" 2163256 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2158592 2158660 2158780 "POLY2UP" 2158931 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2158224 2158281 2158390 "POLY2" 2158529 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2156909 2157148 2157424 "POLUTIL" 2157998 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2155264 2155541 2155872 "POLTOPOL" 2156631 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2150779 2155200 2155246 "POINT" 2155251 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2148966 2149323 2149698 "PNTHEORY" 2150424 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2147385 2147682 2148094 "PMTOOLS" 2148664 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2146978 2147056 2147173 "PMSYM" 2147301 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2146488 2146557 2146731 "PMQFCAT" 2146903 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2145843 2145953 2146109 "PMPRED" 2146365 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2145239 2145325 2145486 "PMPREDFS" 2145744 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2143882 2144090 2144475 "PMPLCAT" 2145001 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2143414 2143493 2143645 "PMLSAGG" 2143797 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2142889 2142965 2143146 "PMKERNEL" 2143332 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2142506 2142581 2142694 "PMINS" 2142808 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2141934 2142003 2142219 "PMFS" 2142431 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2141162 2141280 2141485 "PMDOWN" 2141811 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2140329 2140487 2140668 "PMASS" 2141001 T PMASS (NIL) -7 NIL NIL NIL) (-925 2139607 2139717 2139879 "PMASSFS" 2140216 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2139262 2139330 2139424 "PLOTTOOL" 2139533 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2133869 2135073 2136221 "PLOT" 2138134 T PLOT (NIL) -8 NIL NIL NIL) (-922 2129673 2130717 2131638 "PLOT3D" 2132968 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2128585 2128762 2128997 "PLOT1" 2129477 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2103974 2108651 2113502 "PLEQN" 2123851 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2103292 2103414 2103594 "PINTERP" 2103839 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2102985 2103032 2103135 "PINTERPA" 2103239 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2102233 2102754 2102841 "PI" 2102881 T PI (NIL) -8 NIL NIL 2102948) (-916 2100622 2101571 2101599 "PID" 2101781 T PID (NIL) -9 NIL 2101915 NIL) (-915 2100347 2100384 2100472 "PICOERCE" 2100579 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2099667 2099806 2099982 "PGROEB" 2100203 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2095254 2096068 2096973 "PGE" 2098782 T PGE (NIL) -7 NIL NIL NIL) (-912 2093377 2093624 2093990 "PGCD" 2094971 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2092715 2092818 2092979 "PFRPAC" 2093261 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2089383 2091263 2091616 "PFR" 2092394 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2087772 2088016 2088341 "PFOTOOLS" 2089130 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2086305 2086544 2086895 "PFOQ" 2087529 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2084778 2084990 2085353 "PFO" 2086089 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2081358 2084667 2084736 "PF" 2084741 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2078784 2080029 2080057 "PFECAT" 2080642 T PFECAT (NIL) -9 NIL 2081026 NIL) (-904 2078229 2078383 2078597 "PFECAT-" 2078602 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2076832 2077084 2077385 "PFBRU" 2077978 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2074697 2075050 2075482 "PFBR" 2076483 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2070606 2072073 2072749 "PERM" 2074054 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2065867 2066813 2067683 "PERMGRP" 2069769 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2063999 2064930 2064971 "PERMCAT" 2065417 NIL PERMCAT (NIL T) -9 NIL 2065722 NIL) (-898 2063652 2063693 2063817 "PERMAN" 2063952 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2061188 2063317 2063439 "PENDTREE" 2063563 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2059273 2060015 2060056 "PDRING" 2060713 NIL PDRING (NIL T) -9 NIL 2060999 NIL) (-895 2058376 2058594 2058956 "PDRING-" 2058961 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2055618 2056369 2057037 "PDEPROB" 2057728 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2053163 2053667 2054222 "PDEPACK" 2055083 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2052075 2052265 2052516 "PDECOMP" 2052962 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2049680 2050497 2050525 "PDECAT" 2051312 T PDECAT (NIL) -9 NIL 2052025 NIL) (-890 2049431 2049464 2049554 "PCOMP" 2049641 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2047636 2048232 2048529 "PBWLB" 2049160 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2040136 2041709 2043047 "PATTERN" 2046319 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2039768 2039825 2039934 "PATTERN2" 2040073 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2037525 2037913 2038370 "PATTERN1" 2039357 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2034920 2035474 2035955 "PATRES" 2037090 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2034484 2034551 2034683 "PATRES2" 2034847 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2032367 2032772 2033179 "PATMATCH" 2034151 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2031903 2032086 2032127 "PATMAB" 2032234 NIL PATMAB (NIL T) -9 NIL 2032317 NIL) (-881 2030448 2030757 2031015 "PATLRES" 2031708 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2029994 2030117 2030158 "PATAB" 2030163 NIL PATAB (NIL T) -9 NIL 2030335 NIL) (-879 2027475 2028007 2028580 "PARTPERM" 2029441 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2027096 2027159 2027261 "PARSURF" 2027406 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2026728 2026785 2026894 "PARSU2" 2027033 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2026492 2026532 2026599 "PARSER" 2026681 T PARSER (NIL) -7 NIL NIL NIL) (-875 2026113 2026176 2026278 "PARSCURV" 2026423 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2025745 2025802 2025911 "PARSC2" 2026050 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2025384 2025442 2025539 "PARPCURV" 2025681 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2025016 2025073 2025182 "PARPC2" 2025321 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2024536 2024622 2024741 "PAN2EXPR" 2024917 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2023340 2023657 2023885 "PALETTE" 2024328 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2021808 2022345 2022705 "PAIR" 2023026 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2015705 2021067 2021261 "PADICRC" 2021663 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2008961 2015051 2015235 "PADICRAT" 2015553 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2007303 2008898 2008943 "PADIC" 2008948 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2004505 2006043 2006083 "PADICCT" 2006664 NIL PADICCT (NIL NIL) -9 NIL 2006946 NIL) (-864 2003462 2003662 2003930 "PADEPAC" 2004292 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2002674 2002807 2003013 "PADE" 2003324 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2001088 2001882 2002162 "OWP" 2002478 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2000608 2000794 2000891 "OVERSET" 2001011 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1999681 2000213 2000385 "OVAR" 2000476 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1998945 1999066 1999227 "OUT" 1999540 T OUT (NIL) -7 NIL NIL NIL) (-858 1987843 1990054 1992254 "OUTFORM" 1996765 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1987179 1987440 1987567 "OUTBFILE" 1987736 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1986486 1986651 1986679 "OUTBCON" 1986997 T OUTBCON (NIL) -9 NIL 1987163 NIL) (-855 1986087 1986199 1986356 "OUTBCON-" 1986361 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1985494 1985816 1985905 "OSI" 1986018 T OSI (NIL) -8 NIL NIL NIL) (-853 1985050 1985362 1985390 "OSGROUP" 1985395 T OSGROUP (NIL) -9 NIL 1985417 NIL) (-852 1983795 1984022 1984307 "ORTHPOL" 1984797 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1981373 1983630 1983751 "OREUP" 1983756 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1978803 1981064 1981191 "ORESUP" 1981315 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1976331 1976831 1977392 "OREPCTO" 1978292 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1970147 1972322 1972363 "OREPCAT" 1974711 NIL OREPCAT (NIL T) -9 NIL 1975815 NIL) (-847 1967294 1968076 1969134 "OREPCAT-" 1969139 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1966471 1966743 1966771 "ORDSET" 1967080 T ORDSET (NIL) -9 NIL 1967244 NIL) (-845 1965990 1966112 1966305 "ORDSET-" 1966310 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1964616 1965381 1965409 "ORDRING" 1965611 T ORDRING (NIL) -9 NIL 1965736 NIL) (-843 1964261 1964355 1964499 "ORDRING-" 1964504 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1963667 1964104 1964132 "ORDMON" 1964137 T ORDMON (NIL) -9 NIL 1964158 NIL) (-841 1962829 1962976 1963171 "ORDFUNS" 1963516 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1962193 1962586 1962614 "ORDFIN" 1962679 T ORDFIN (NIL) -9 NIL 1962753 NIL) (-839 1958779 1960779 1961188 "ORDCOMP" 1961817 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1958045 1958172 1958358 "ORDCOMP2" 1958639 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954653 1955536 1956350 "OPTPROB" 1957251 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1951455 1952094 1952798 "OPTPACK" 1953969 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1949168 1949908 1949936 "OPTCAT" 1950755 T OPTCAT (NIL) -9 NIL 1951405 NIL) (-834 1948611 1948845 1948950 "OPSIG" 1949083 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1948379 1948418 1948484 "OPQUERY" 1948565 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1945537 1946690 1947194 "OP" 1947908 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1945072 1945243 1945284 "OPERCAT" 1945419 NIL OPERCAT (NIL T) -9 NIL 1945487 NIL) (-830 1944918 1944945 1945031 "OPERCAT-" 1945036 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1941757 1943715 1944084 "ONECOMP" 1944582 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1941062 1941177 1941351 "ONECOMP2" 1941629 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1940481 1940587 1940717 "OMSERVER" 1940952 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1937369 1939921 1939961 "OMSAGG" 1940022 NIL OMSAGG (NIL T) -9 NIL 1940086 NIL) (-825 1935992 1936255 1936537 "OMPKG" 1937107 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1935422 1935525 1935553 "OM" 1935852 T OM (NIL) -9 NIL NIL NIL) (-823 1933996 1934971 1935140 "OMLO" 1935303 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1932921 1933068 1933295 "OMEXPR" 1933822 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1932239 1932467 1932603 "OMERR" 1932805 T OMERR (NIL) -8 NIL NIL NIL) (-820 1931417 1931660 1931820 "OMERRK" 1932099 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1930895 1931094 1931202 "OMENC" 1931329 T OMENC (NIL) -8 NIL NIL NIL) (-818 1924790 1925975 1927146 "OMDEV" 1929744 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1923859 1924030 1924224 "OMCONN" 1924616 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1922472 1923422 1923450 "OINTDOM" 1923455 T OINTDOM (NIL) -9 NIL 1923476 NIL) (-815 1918278 1919462 1920178 "OFMONOID" 1921788 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1917716 1918215 1918260 "ODVAR" 1918265 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1915166 1917461 1917616 "ODR" 1917621 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1907502 1914942 1915068 "ODPOL" 1915073 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1901372 1907374 1907479 "ODP" 1907484 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1900138 1900353 1900628 "ODETOOLS" 1901146 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1897105 1897763 1898479 "ODESYS" 1899471 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1891987 1892895 1893920 "ODERTRIC" 1896180 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1891413 1891495 1891689 "ODERED" 1891899 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1888301 1888849 1889526 "ODERAT" 1890836 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1885258 1885725 1886322 "ODEPRRIC" 1887830 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1883228 1883797 1884283 "ODEPROB" 1884792 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1879748 1880233 1880880 "ODEPRIM" 1882707 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1878997 1879099 1879359 "ODEPAL" 1879640 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1875159 1875950 1876814 "ODEPACK" 1878153 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1874192 1874299 1874528 "ODEINT" 1875048 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1868293 1869718 1871165 "ODEIFTBL" 1872765 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1863628 1864414 1865373 "ODEEF" 1867452 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1862963 1863052 1863282 "ODECONST" 1863533 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1861114 1861749 1861777 "ODECAT" 1862382 T ODECAT (NIL) -9 NIL 1862913 NIL) (-795 1858013 1860826 1860945 "OCT" 1861027 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1857651 1857694 1857821 "OCTCT2" 1857964 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1852417 1854825 1854865 "OC" 1855962 NIL OC (NIL T) -9 NIL 1856820 NIL) (-792 1849644 1850392 1851382 "OC-" 1851476 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1849022 1849464 1849492 "OCAMON" 1849497 T OCAMON (NIL) -9 NIL 1849518 NIL) (-790 1848579 1848894 1848922 "OASGP" 1848927 T OASGP (NIL) -9 NIL 1848947 NIL) (-789 1847866 1848329 1848357 "OAMONS" 1848397 T OAMONS (NIL) -9 NIL 1848440 NIL) (-788 1847306 1847713 1847741 "OAMON" 1847746 T OAMON (NIL) -9 NIL 1847766 NIL) (-787 1846610 1847102 1847130 "OAGROUP" 1847135 T OAGROUP (NIL) -9 NIL 1847155 NIL) (-786 1846300 1846350 1846438 "NUMTUBE" 1846554 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1839873 1841391 1842927 "NUMQUAD" 1844784 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1835629 1836617 1837642 "NUMODE" 1838868 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1833010 1833864 1833892 "NUMINT" 1834815 T NUMINT (NIL) -9 NIL 1835579 NIL) (-782 1831958 1832155 1832373 "NUMFMT" 1832812 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1818317 1821262 1823794 "NUMERIC" 1829465 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1812714 1817766 1817861 "NTSCAT" 1817866 NIL NTSCAT (NIL T T T T) -9 NIL 1817905 NIL) (-779 1811908 1812073 1812266 "NTPOLFN" 1812553 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1799740 1808733 1809545 "NSUP" 1811129 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1799372 1799429 1799538 "NSUP2" 1799677 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1789355 1799146 1799279 "NSMP" 1799284 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1787787 1788088 1788445 "NREP" 1789043 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1786378 1786630 1786988 "NPCOEF" 1787530 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1785444 1785559 1785775 "NORMRETR" 1786259 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1783485 1783775 1784184 "NORMPK" 1785152 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1783170 1783198 1783322 "NORMMA" 1783451 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1782997 1783127 1783156 "NONE" 1783161 T NONE (NIL) -8 NIL NIL NIL) (-769 1782786 1782815 1782884 "NONE1" 1782961 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1782269 1782331 1782517 "NODE1" 1782718 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1780539 1781363 1781618 "NNI" 1781965 T NNI (NIL) -8 NIL NIL 1782200) (-766 1778959 1779272 1779636 "NLINSOL" 1780207 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1775227 1776195 1777094 "NIPROB" 1778080 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1773984 1774218 1774520 "NFINTBAS" 1774989 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1773158 1773634 1773675 "NETCLT" 1773847 NIL NETCLT (NIL T) -9 NIL 1773929 NIL) (-762 1771866 1772097 1772378 "NCODIV" 1772926 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1771628 1771665 1771740 "NCNTFRAC" 1771823 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1769808 1770172 1770592 "NCEP" 1771253 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1768705 1769452 1769480 "NASRING" 1769590 T NASRING (NIL) -9 NIL 1769670 NIL) (-758 1768500 1768544 1768638 "NASRING-" 1768643 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1767653 1768152 1768180 "NARNG" 1768297 T NARNG (NIL) -9 NIL 1768388 NIL) (-756 1767345 1767412 1767546 "NARNG-" 1767551 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1766224 1766431 1766666 "NAGSP" 1767130 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1757496 1759180 1760853 "NAGS" 1764571 T NAGS (NIL) -7 NIL NIL NIL) (-753 1756044 1756352 1756683 "NAGF07" 1757185 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1750582 1751873 1753180 "NAGF04" 1754757 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1743550 1745164 1746797 "NAGF02" 1748969 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1738774 1739874 1740991 "NAGF01" 1742453 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1732402 1733968 1735553 "NAGE04" 1737209 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1723571 1725692 1727822 "NAGE02" 1730292 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1719524 1720471 1721435 "NAGE01" 1722627 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1717319 1717853 1718411 "NAGD03" 1718986 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1709069 1710997 1712951 "NAGD02" 1715385 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1702880 1704305 1705745 "NAGD01" 1707649 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1699089 1699911 1700748 "NAGC06" 1702063 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1697554 1697886 1698242 "NAGC05" 1698753 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1696930 1697049 1697193 "NAGC02" 1697430 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1695990 1696547 1696587 "NAALG" 1696666 NIL NAALG (NIL T) -9 NIL 1696727 NIL) (-739 1695825 1695854 1695944 "NAALG-" 1695949 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1689775 1690883 1692070 "MULTSQFR" 1694721 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1689094 1689169 1689353 "MULTFACT" 1689687 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1682179 1686057 1686110 "MTSCAT" 1687180 NIL MTSCAT (NIL T T) -9 NIL 1687694 NIL) (-735 1681891 1681945 1682037 "MTHING" 1682119 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1681683 1681716 1681776 "MSYSCMD" 1681851 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1677792 1680438 1680758 "MSET" 1681396 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1674887 1677353 1677394 "MSETAGG" 1677399 NIL MSETAGG (NIL T) -9 NIL 1677433 NIL) (-731 1670755 1672266 1673011 "MRING" 1674187 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1670321 1670388 1670519 "MRF2" 1670682 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1669939 1669974 1670118 "MRATFAC" 1670280 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1667551 1667846 1668277 "MPRFF" 1669644 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1661603 1667405 1667502 "MPOLY" 1667507 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1661093 1661128 1661336 "MPCPF" 1661562 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1660607 1660650 1660834 "MPC3" 1661044 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1659802 1659883 1660104 "MPC2" 1660522 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1658103 1658440 1658830 "MONOTOOL" 1659462 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1657354 1657645 1657673 "MONOID" 1657892 T MONOID (NIL) -9 NIL 1658039 NIL) (-721 1656900 1657019 1657200 "MONOID-" 1657205 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1647751 1653667 1653726 "MONOGEN" 1654400 NIL MONOGEN (NIL T T) -9 NIL 1654856 NIL) (-719 1644969 1645704 1646704 "MONOGEN-" 1646823 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1643828 1644248 1644276 "MONADWU" 1644668 T MONADWU (NIL) -9 NIL 1644906 NIL) (-717 1643200 1643359 1643607 "MONADWU-" 1643612 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1642585 1642803 1642831 "MONAD" 1643038 T MONAD (NIL) -9 NIL 1643150 NIL) (-715 1642270 1642348 1642480 "MONAD-" 1642485 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1640586 1641183 1641462 "MOEBIUS" 1642023 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1639978 1640356 1640396 "MODULE" 1640401 NIL MODULE (NIL T) -9 NIL 1640427 NIL) (-712 1639546 1639642 1639832 "MODULE-" 1639837 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1637253 1637910 1638237 "MODRING" 1639370 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1634224 1635358 1635879 "MODOP" 1636782 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1632839 1633291 1633568 "MODMONOM" 1634087 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1622636 1631130 1631544 "MODMON" 1632476 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1619819 1621480 1621756 "MODFIELD" 1622511 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1618823 1619100 1619290 "MMLFORM" 1619649 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1618349 1618392 1618571 "MMAP" 1618774 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1616558 1617299 1617340 "MLO" 1617763 NIL MLO (NIL T) -9 NIL 1618005 NIL) (-703 1613924 1614440 1615042 "MLIFT" 1616039 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1613315 1613399 1613553 "MKUCFUNC" 1613835 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1612914 1612984 1613107 "MKRECORD" 1613238 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1611961 1612123 1612351 "MKFUNC" 1612725 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1611349 1611453 1611609 "MKFLCFN" 1611844 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610626 1610728 1610913 "MKBCFUNC" 1611242 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607360 1610180 1610316 "MINT" 1610510 T MINT (NIL) -8 NIL NIL NIL) (-696 1606172 1606415 1606692 "MHROWRED" 1607115 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601579 1604707 1605112 "MFLOAT" 1605787 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600936 1601012 1601183 "MFINFACT" 1601491 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597251 1598099 1598983 "MESH" 1600072 T MESH (NIL) -7 NIL NIL NIL) (-692 1595641 1595953 1596306 "MDDFACT" 1596938 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592483 1594800 1594841 "MDAGG" 1595096 NIL MDAGG (NIL T) -9 NIL 1595239 NIL) (-690 1582253 1591776 1591983 "MCMPLX" 1592296 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581394 1581540 1581740 "MCDEN" 1582102 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579284 1579554 1579934 "MCALCFN" 1581124 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578209 1578449 1578682 "MAYBE" 1579090 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575821 1576344 1576906 "MATSTOR" 1577680 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571826 1575193 1575441 "MATRIX" 1575606 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567590 1568299 1569035 "MATLIN" 1571183 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557744 1560882 1560959 "MATCAT" 1565839 NIL MATCAT (NIL T T T) -9 NIL 1567256 NIL) (-682 1554100 1555121 1556477 "MATCAT-" 1556482 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552694 1552847 1553180 "MATCAT2" 1553935 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550806 1551130 1551514 "MAPPKG3" 1552369 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549787 1549960 1550182 "MAPPKG2" 1550630 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548286 1548570 1548897 "MAPPKG1" 1549493 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547392 1547692 1547869 "MAPPAST" 1548129 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1547003 1547061 1547184 "MAPHACK3" 1547328 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546595 1546656 1546770 "MAPHACK2" 1546935 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1546032 1546136 1546278 "MAPHACK1" 1546486 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544138 1544732 1545036 "MAGMA" 1545760 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543644 1543862 1543953 "MACROAST" 1544067 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1540110 1541883 1542344 "M3D" 1543216 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534264 1538479 1538520 "LZSTAGG" 1539302 NIL LZSTAGG (NIL T) -9 NIL 1539597 NIL) (-669 1530221 1531395 1532852 "LZSTAGG-" 1532857 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527335 1528112 1528599 "LWORD" 1529766 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526938 1527139 1527214 "LSTAST" 1527280 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1520131 1526709 1526843 "LSQM" 1526848 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519355 1519494 1519722 "LSPP" 1519986 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517167 1517468 1517924 "LSMP" 1519044 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513946 1514620 1515350 "LSMP1" 1516469 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507871 1513113 1513154 "LSAGG" 1513216 NIL LSAGG (NIL T) -9 NIL 1513294 NIL) (-661 1504566 1505490 1506703 "LSAGG-" 1506708 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502192 1503710 1503959 "LPOLY" 1504361 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501774 1501859 1501982 "LPEFRAC" 1502101 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1500121 1500868 1501121 "LO" 1501606 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499773 1499885 1499913 "LOGIC" 1500024 T LOGIC (NIL) -9 NIL 1500105 NIL) (-656 1499635 1499658 1499729 "LOGIC-" 1499734 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498828 1498968 1499161 "LODOOPS" 1499491 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496278 1498744 1498810 "LODO" 1498815 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494816 1495051 1495404 "LODOF" 1496025 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491164 1493569 1493610 "LODOCAT" 1494048 NIL LODOCAT (NIL T) -9 NIL 1494259 NIL) (-651 1490897 1490955 1491082 "LODOCAT-" 1491087 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488244 1490738 1490856 "LODO2" 1490861 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485706 1488181 1488226 "LODO1" 1488231 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484566 1484731 1485043 "LODEEF" 1485529 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479852 1482696 1482737 "LNAGG" 1483684 NIL LNAGG (NIL T) -9 NIL 1484128 NIL) (-646 1478999 1479213 1479555 "LNAGG-" 1479560 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475162 1475924 1476563 "LMOPS" 1478414 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474557 1474919 1474960 "LMODULE" 1475021 NIL LMODULE (NIL T) -9 NIL 1475063 NIL) (-643 1471803 1474202 1474325 "LMDICT" 1474467 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471529 1471711 1471771 "LITERAL" 1471776 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464760 1470475 1470773 "LIST" 1471264 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464285 1464359 1464498 "LIST3" 1464680 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463292 1463470 1463698 "LIST2" 1464103 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461426 1461738 1462137 "LIST2MAP" 1462939 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460148 1460792 1460833 "LINEXP" 1461088 NIL LINEXP (NIL T) -9 NIL 1461237 NIL) (-636 1458795 1459055 1459352 "LINDEP" 1459900 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455562 1456281 1457058 "LIMITRF" 1458050 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453837 1454133 1454549 "LIMITPS" 1455257 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448292 1453348 1453576 "LIE" 1453658 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447341 1447784 1447824 "LIECAT" 1447964 NIL LIECAT (NIL T) -9 NIL 1448115 NIL) (-631 1447182 1447209 1447297 "LIECAT-" 1447302 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439794 1446631 1446796 "LIB" 1447037 T LIB (NIL) -8 NIL NIL NIL) (-629 1435429 1436312 1437247 "LGROBP" 1438911 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433295 1433569 1433931 "LF" 1435150 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432135 1432827 1432855 "LFCAT" 1433062 T LFCAT (NIL) -9 NIL 1433201 NIL) (-626 1429037 1429667 1430355 "LEXTRIPK" 1431499 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425808 1426607 1427110 "LEXP" 1428617 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425311 1425529 1425621 "LETAST" 1425736 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423709 1424022 1424423 "LEADCDET" 1424993 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422899 1422973 1423202 "LAZM3PK" 1423630 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417843 1420976 1421514 "LAUPOL" 1422411 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417408 1417452 1417620 "LAPLACE" 1417793 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415374 1416509 1416760 "LA" 1417241 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414447 1415005 1415046 "LALG" 1415108 NIL LALG (NIL T) -9 NIL 1415167 NIL) (-617 1414161 1414220 1414356 "LALG-" 1414361 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413996 1414020 1414061 "KVTFROM" 1414123 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412796 1413213 1413442 "KTVLOGIC" 1413787 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412631 1412655 1412696 "KRCFROM" 1412758 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411535 1411722 1412021 "KOVACIC" 1412431 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411370 1411394 1411435 "KONVERT" 1411497 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411205 1411229 1411270 "KOERCE" 1411332 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408938 1409699 1410092 "KERNEL" 1410844 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408440 1408521 1408651 "KERNEL2" 1408852 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402291 1406979 1407033 "KDAGG" 1407410 NIL KDAGG (NIL T T) -9 NIL 1407616 NIL) (-607 1401820 1401944 1402149 "KDAGG-" 1402154 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394995 1401481 1401636 "KAFILE" 1401698 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389450 1394506 1394734 "JORDAN" 1394816 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388856 1389099 1389220 "JOINAST" 1389349 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388702 1388761 1388816 "JAVACODE" 1388821 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1385001 1386907 1386961 "IXAGG" 1387890 NIL IXAGG (NIL T T) -9 NIL 1388349 NIL) (-601 1383920 1384226 1384645 "IXAGG-" 1384650 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379500 1383842 1383901 "IVECTOR" 1383906 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378266 1378503 1378769 "ITUPLE" 1379267 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376702 1376879 1377185 "ITRIGMNP" 1378088 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375447 1375651 1375934 "ITFUN3" 1376478 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1375079 1375136 1375245 "ITFUN2" 1375384 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372908 1373941 1374240 "ITAYLOR" 1374813 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361880 1367045 1368208 "ISUPS" 1371778 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360984 1361124 1361360 "ISUMP" 1361727 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356248 1360785 1360864 "ISTRING" 1360937 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355751 1355969 1356061 "ISAST" 1356176 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354961 1355042 1355258 "IRURPK" 1355665 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353897 1354098 1354338 "IRSN" 1354741 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351926 1352281 1352717 "IRRF2F" 1353535 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351673 1351711 1351787 "IRREDFFX" 1351882 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350288 1350547 1350846 "IROOT" 1351406 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346919 1347972 1348664 "IR" 1349628 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344532 1345027 1345593 "IR2" 1346397 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343604 1343717 1343938 "IR2F" 1344415 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343395 1343429 1343489 "IPRNTPK" 1343564 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1340002 1343284 1343353 "IPF" 1343358 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338356 1339927 1339984 "IPADIC" 1339989 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337695 1337916 1338046 "IP4ADDR" 1338246 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337195 1337399 1337509 "IOMODE" 1337605 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336268 1336792 1336919 "IOBFILE" 1337088 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335756 1336172 1336200 "IOBCON" 1336205 T IOBCON (NIL) -9 NIL 1336226 NIL) (-575 1335253 1335311 1335501 "INVLAPLA" 1335692 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324901 1327255 1329641 "INTTR" 1332917 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321245 1321987 1322851 "INTTOOLS" 1324086 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320831 1320922 1321039 "INTSLPE" 1321148 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318812 1320754 1320813 "INTRVL" 1320818 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316414 1316926 1317501 "INTRF" 1318297 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315825 1315922 1316064 "INTRET" 1316312 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313822 1314211 1314681 "INTRAT" 1315433 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1311050 1311633 1312259 "INTPM" 1313307 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307752 1308352 1309097 "INTPAF" 1310436 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302931 1303893 1304944 "INTPACK" 1306721 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299835 1302660 1302787 "INT" 1302824 T INT (NIL) -8 NIL NIL NIL) (-563 1299087 1299239 1299447 "INTHERTR" 1299677 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298526 1298606 1298794 "INTHERAL" 1299001 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296372 1296815 1297272 "INTHEORY" 1298089 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287680 1289301 1291080 "INTG0" 1294724 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268253 1273043 1277853 "INTFTBL" 1282890 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267502 1267640 1267813 "INTFACT" 1268112 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264887 1265333 1265897 "INTEF" 1267056 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263346 1264059 1264087 "INTDOM" 1264388 T INTDOM (NIL) -9 NIL 1264595 NIL) (-555 1262715 1262889 1263131 "INTDOM-" 1263136 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259202 1261099 1261153 "INTCAT" 1261952 NIL INTCAT (NIL T) -9 NIL 1262272 NIL) (-553 1258674 1258777 1258905 "INTBIT" 1259094 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257345 1257499 1257813 "INTALG" 1258519 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256802 1256892 1257062 "INTAF" 1257249 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250256 1256612 1256752 "INTABL" 1256757 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249587 1250026 1250091 "INT8" 1250125 T INT8 (NIL) -8 NIL NIL 1250170) (-548 1248917 1249356 1249421 "INT64" 1249455 T INT64 (NIL) -8 NIL NIL 1249500) (-547 1248247 1248686 1248751 "INT32" 1248785 T INT32 (NIL) -8 NIL NIL 1248830) (-546 1247577 1248016 1248081 "INT16" 1248115 T INT16 (NIL) -8 NIL NIL 1248160) (-545 1242584 1245266 1245294 "INS" 1246228 T INS (NIL) -9 NIL 1246893 NIL) (-544 1239824 1240595 1241569 "INS-" 1241642 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238599 1238826 1239124 "INPSIGN" 1239577 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237717 1237834 1238031 "INPRODPF" 1238479 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236611 1236728 1236965 "INPRODFF" 1237597 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235611 1235763 1236023 "INNMFACT" 1236447 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234808 1234905 1235093 "INMODGCD" 1235510 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233316 1233561 1233885 "INFSP" 1234553 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232500 1232617 1232800 "INFPROD0" 1233196 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229382 1230565 1231080 "INFORM" 1231993 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228992 1229052 1229150 "INFORM1" 1229317 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228515 1228604 1228718 "INFINITY" 1228898 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227691 1228235 1228336 "INETCLTS" 1228434 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226307 1226557 1226878 "INEP" 1227439 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225583 1226204 1226269 "INDE" 1226274 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225147 1225215 1225332 "INCRMAPS" 1225510 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223965 1224416 1224622 "INBFILE" 1224961 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219265 1220201 1221145 "INBFF" 1223053 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218173 1218442 1218470 "INBCON" 1218983 T INBCON (NIL) -9 NIL 1219249 NIL) (-526 1217425 1217648 1217924 "INBCON-" 1217929 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216931 1217149 1217240 "INAST" 1217354 T INAST (NIL) -8 NIL NIL NIL) (-524 1216385 1216610 1216716 "IMPTAST" 1216845 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212879 1216229 1216333 "IMATRIX" 1216338 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211591 1211714 1212029 "IMATQF" 1212735 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209811 1210038 1210375 "IMATLIN" 1211347 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204437 1209735 1209793 "ILIST" 1209798 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202390 1204297 1204410 "IIARRAY2" 1204415 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197815 1202301 1202365 "IFF" 1202370 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197189 1197432 1197548 "IFAST" 1197719 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192232 1196481 1196669 "IFARRAY" 1197046 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191439 1192136 1192209 "IFAMON" 1192214 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1191023 1191088 1191142 "IEVALAB" 1191349 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190698 1190766 1190926 "IEVALAB-" 1190931 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190356 1190612 1190675 "IDPO" 1190680 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189633 1190245 1190320 "IDPOAMS" 1190325 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188967 1189522 1189597 "IDPOAM" 1189602 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1188052 1188302 1188355 "IDPC" 1188768 NIL IDPC (NIL T T) -9 NIL 1188917 NIL) (-508 1187548 1187944 1188017 "IDPAM" 1188022 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186951 1187440 1187513 "IDPAG" 1187518 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186623 1186787 1186862 "IDENT" 1186896 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182878 1183726 1184621 "IDECOMP" 1185780 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175742 1176801 1177848 "IDEAL" 1181914 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174906 1175018 1175217 "ICDEN" 1175626 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1174004 1174386 1174533 "ICARD" 1174779 T ICARD (NIL) -8 NIL NIL NIL) (-501 1172064 1172377 1172782 "IBPTOOLS" 1173681 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167698 1171684 1171797 "IBITS" 1171983 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164421 1164997 1165692 "IBATOOL" 1167115 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162200 1162662 1163195 "IBACHIN" 1163956 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1160077 1162046 1162149 "IARRAY2" 1162154 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156231 1160003 1160060 "IARRAY1" 1160065 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150215 1154643 1155124 "IAN" 1155770 T IAN (NIL) -8 NIL NIL NIL) (-494 1149726 1149783 1149956 "IALGFACT" 1150152 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149254 1149367 1149395 "HYPCAT" 1149602 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148792 1148909 1149095 "HYPCAT-" 1149100 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148414 1148587 1148670 "HOSTNAME" 1148729 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148259 1148296 1148337 "HOMOTOP" 1148342 NIL HOMOTOP (NIL T) -9 NIL 1148375 NIL) (-489 1144938 1146269 1146310 "HOAGG" 1147291 NIL HOAGG (NIL T) -9 NIL 1147970 NIL) (-488 1143532 1143931 1144457 "HOAGG-" 1144462 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137563 1143127 1143276 "HEXADEC" 1143403 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136311 1136533 1136796 "HEUGCD" 1137340 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135414 1136148 1136278 "HELLFDIV" 1136283 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133641 1135191 1135279 "HEAP" 1135358 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132931 1133193 1133327 "HEADAST" 1133527 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126845 1132846 1132908 "HDP" 1132913 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120588 1126480 1126632 "HDMP" 1126746 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119912 1120052 1120216 "HB" 1120444 T HB (NIL) -7 NIL NIL NIL) (-479 1113409 1119758 1119862 "HASHTBL" 1119867 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112912 1113130 1113222 "HASAST" 1113337 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110717 1112534 1112716 "HACKPI" 1112750 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106412 1110570 1110683 "GTSET" 1110688 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099938 1106290 1106388 "GSTBL" 1106393 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092243 1098969 1099234 "GSERIES" 1099729 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091410 1091801 1091829 "GROUP" 1092032 T GROUP (NIL) -9 NIL 1092166 NIL) (-472 1090776 1090935 1091186 "GROUP-" 1091191 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089143 1089464 1089851 "GROEBSOL" 1090453 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088083 1088345 1088396 "GRMOD" 1088925 NIL GRMOD (NIL T T) -9 NIL 1089093 NIL) (-469 1087851 1087887 1088015 "GRMOD-" 1088020 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083168 1084205 1085205 "GRIMAGE" 1086871 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081634 1081895 1082219 "GRDEF" 1082864 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081078 1081194 1081335 "GRAY" 1081513 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080291 1080671 1080722 "GRALG" 1080875 NIL GRALG (NIL T T) -9 NIL 1080968 NIL) (-464 1079952 1080025 1080188 "GRALG-" 1080193 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076756 1079537 1079715 "GPOLSET" 1079859 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076110 1076167 1076425 "GOSPER" 1076693 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071869 1072548 1073074 "GMODPOL" 1075809 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070874 1071058 1071296 "GHENSEL" 1071681 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064925 1065768 1066795 "GENUPS" 1069958 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064622 1064673 1064762 "GENUFACT" 1064868 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064034 1064111 1064276 "GENPGCD" 1064540 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063508 1063543 1063756 "GENMFACT" 1063993 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062074 1062331 1062638 "GENEEZ" 1063251 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055975 1061685 1061847 "GDMP" 1061997 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045344 1049746 1050852 "GCNAALG" 1054958 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043763 1044599 1044627 "GCDDOM" 1044882 T GCDDOM (NIL) -9 NIL 1045039 NIL) (-451 1043233 1043360 1043575 "GCDDOM-" 1043580 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041905 1042090 1042394 "GB" 1043012 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030521 1032851 1035243 "GBINTERN" 1039596 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028358 1028650 1029071 "GBF" 1030196 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027139 1027304 1027571 "GBEUCLID" 1028174 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026488 1026613 1026762 "GAUSSFAC" 1027010 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024855 1025157 1025471 "GALUTIL" 1026207 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023163 1023437 1023761 "GALPOLYU" 1024582 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020528 1020818 1021225 "GALFACTU" 1022860 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012334 1013833 1015441 "GALFACT" 1018960 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009722 1010380 1010408 "FVFUN" 1011564 T FVFUN (NIL) -9 NIL 1012284 NIL) (-440 1008988 1009170 1009198 "FVC" 1009489 T FVC (NIL) -9 NIL 1009672 NIL) (-439 1008658 1008813 1008881 "FUNDESC" 1008940 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008300 1008455 1008536 "FUNCTION" 1008610 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006071 1006622 1007088 "FT" 1007854 T FT (NIL) -8 NIL NIL NIL) (-436 1004889 1005372 1005575 "FTEM" 1005888 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003145 1003434 1003838 "FSUPFACT" 1004580 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001542 1001831 1002163 "FST" 1002833 T FST (NIL) -8 NIL NIL NIL) (-433 1000713 1000819 1001014 "FSRED" 1001424 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999391 999647 1000001 "FSPRMELT" 1000428 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996476 996914 997413 "FSPECF" 998954 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978530 986979 987019 "FS" 990867 NIL FS (NIL T) -9 NIL 993156 NIL) (-429 967177 970170 974226 "FS-" 974523 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966691 966745 966922 "FSINT" 967118 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 965010 965684 965987 "FSERIES" 966470 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 964024 964140 964371 "FSCINT" 964890 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960258 962968 963009 "FSAGG" 963379 NIL FSAGG (NIL T) -9 NIL 963638 NIL) (-424 958020 958621 959417 "FSAGG-" 959512 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 957062 957205 957432 "FSAGG2" 957873 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954716 954996 955550 "FS2UPS" 956780 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954298 954341 954496 "FS2" 954667 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953155 953326 953635 "FS2EXPXP" 954123 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952581 952696 952848 "FRUTIL" 953035 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944021 948076 949434 "FR" 951255 NIL FR (NIL T) -8 NIL NIL NIL) (-417 939096 941739 941779 "FRNAALG" 943175 NIL FRNAALG (NIL T) -9 NIL 943782 NIL) (-416 934769 935845 937120 "FRNAALG-" 937870 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934407 934450 934577 "FRNAAF2" 934720 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932814 933261 933556 "FRMOD" 934219 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930592 931197 931514 "FRIDEAL" 932605 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929787 929874 930163 "FRIDEAL2" 930499 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928920 929334 929375 "FRETRCT" 929380 NIL FRETRCT (NIL T) -9 NIL 929556 NIL) (-410 928032 928263 928614 "FRETRCT-" 928619 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925236 926420 926479 "FRAMALG" 927361 NIL FRAMALG (NIL T T) -9 NIL 927653 NIL) (-408 923370 923825 924455 "FRAMALG-" 924678 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917318 922845 923121 "FRAC" 923126 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916954 917011 917118 "FRAC2" 917255 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916590 916647 916754 "FR2" 916891 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911255 914115 914143 "FPS" 915262 T FPS (NIL) -9 NIL 915819 NIL) (-403 910704 910813 910977 "FPS-" 911123 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908150 909793 909821 "FPC" 910046 T FPC (NIL) -9 NIL 910188 NIL) (-401 907943 907983 908080 "FPC-" 908085 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906821 907431 907472 "FPATMAB" 907477 NIL FPATMAB (NIL T) -9 NIL 907629 NIL) (-399 904521 904997 905423 "FPARFRAC" 906458 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899914 900413 901095 "FORTRAN" 903953 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897630 898130 898669 "FORT" 899395 T FORT (NIL) -7 NIL NIL NIL) (-396 895306 895868 895896 "FORTFN" 896956 T FORTFN (NIL) -9 NIL 897580 NIL) (-395 895070 895120 895148 "FORTCAT" 895207 T FORTCAT (NIL) -9 NIL 895269 NIL) (-394 893203 893686 894076 "FORMULA" 894700 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892991 893021 893090 "FORMULA1" 893167 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892514 892566 892739 "FORDER" 892933 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891610 891774 891967 "FOP" 892341 T FOP (NIL) -7 NIL NIL NIL) (-390 890218 890890 891064 "FNLA" 891492 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888973 889362 889390 "FNCAT" 889850 T FNCAT (NIL) -9 NIL 890110 NIL) (-388 888539 888932 888960 "FNAME" 888965 T FNAME (NIL) -8 NIL NIL NIL) (-387 887194 888131 888159 "FMTC" 888164 T FMTC (NIL) -9 NIL 888200 NIL) (-386 883554 884717 885346 "FMONOID" 886598 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882773 883296 883445 "FM" 883450 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880197 880843 880871 "FMFUN" 882015 T FMFUN (NIL) -9 NIL 882723 NIL) (-383 879466 879647 879675 "FMC" 879965 T FMC (NIL) -9 NIL 880147 NIL) (-382 876660 877494 877548 "FMCAT" 878743 NIL FMCAT (NIL T T) -9 NIL 879238 NIL) (-381 875553 876426 876526 "FM1" 876605 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873327 873743 874237 "FLOATRP" 875104 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866928 871056 871677 "FLOAT" 872726 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864366 864866 865444 "FLOATCP" 866395 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863167 863979 864020 "FLINEXP" 864025 NIL FLINEXP (NIL T) -9 NIL 864118 NIL) (-376 862321 862556 862884 "FLINEXP-" 862889 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861397 861541 861765 "FLASORT" 862173 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858614 859456 859508 "FLALG" 860735 NIL FLALG (NIL T T) -9 NIL 861202 NIL) (-373 852398 856100 856141 "FLAGG" 857403 NIL FLAGG (NIL T) -9 NIL 858055 NIL) (-372 851124 851463 851953 "FLAGG-" 851958 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850166 850309 850536 "FLAGG2" 850977 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847133 848115 848174 "FINRALG" 849302 NIL FINRALG (NIL T T) -9 NIL 849810 NIL) (-369 846293 846522 846861 "FINRALG-" 846866 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845699 845912 845940 "FINITE" 846136 T FINITE (NIL) -9 NIL 846243 NIL) (-367 838157 840318 840358 "FINAALG" 844025 NIL FINAALG (NIL T) -9 NIL 845478 NIL) (-366 833489 834539 835683 "FINAALG-" 837062 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832884 833244 833347 "FILE" 833419 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831568 831880 831934 "FILECAT" 832618 NIL FILECAT (NIL T T) -9 NIL 832834 NIL) (-363 829428 830930 830958 "FIELD" 830998 T FIELD (NIL) -9 NIL 831078 NIL) (-362 828048 828433 828944 "FIELD-" 828949 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825925 826683 827030 "FGROUP" 827734 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825015 825179 825399 "FGLMICPK" 825757 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820874 824940 824997 "FFX" 825002 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820475 820536 820671 "FFSLPE" 820807 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816464 817247 818043 "FFPOLY" 819711 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815968 816004 816213 "FFPOLY2" 816422 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811838 815887 815950 "FFP" 815955 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807263 811749 811813 "FF" 811818 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802416 806606 806796 "FFNBX" 807117 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797372 801551 801809 "FFNBP" 802270 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792032 796656 796867 "FFNB" 797205 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790864 791062 791377 "FFINTBAS" 791829 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787084 789271 789299 "FFIELDC" 789919 T FFIELDC (NIL) -9 NIL 790295 NIL) (-348 785746 786117 786614 "FFIELDC-" 786619 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785315 785361 785485 "FFHOM" 785688 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783010 783497 784014 "FFF" 784830 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778655 782752 782853 "FFCGX" 782953 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774303 778387 778494 "FFCGP" 778598 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769513 774030 774138 "FFCG" 774239 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751338 760384 760470 "FFCAT" 765635 NIL FFCAT (NIL T T T) -9 NIL 767086 NIL) (-341 746536 747583 748897 "FFCAT-" 750127 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745947 745990 746225 "FFCAT2" 746487 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735144 738919 740139 "FEXPR" 744799 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734144 734579 734620 "FEVALAB" 734704 NIL FEVALAB (NIL T) -9 NIL 734965 NIL) (-337 733303 733513 733851 "FEVALAB-" 733856 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731896 732686 732889 "FDIV" 733202 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728962 729677 729792 "FDIVCAT" 731360 NIL FDIVCAT (NIL T T T T) -9 NIL 731797 NIL) (-334 728724 728751 728921 "FDIVCAT-" 728926 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727944 728031 728308 "FDIV2" 728631 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726630 726889 727178 "FCPAK1" 727675 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725756 726130 726271 "FCOMP" 726521 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709485 712906 716444 "FC" 722238 T FC (NIL) -8 NIL NIL NIL) (-329 702056 706049 706089 "FAXF" 707891 NIL FAXF (NIL T) -9 NIL 708583 NIL) (-328 699332 699990 700815 "FAXF-" 701280 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694432 698708 698884 "FARRAY" 699189 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689677 691717 691770 "FAMR" 692793 NIL FAMR (NIL T T) -9 NIL 693253 NIL) (-325 688567 688869 689304 "FAMR-" 689309 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687763 688489 688542 "FAMONOID" 688547 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685575 686259 686312 "FAMONC" 687253 NIL FAMONC (NIL T T) -9 NIL 687639 NIL) (-322 684267 685329 685466 "FAGROUP" 685471 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682062 682381 682784 "FACUTIL" 683948 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681161 681346 681568 "FACTFUNC" 681872 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673558 680412 680624 "EXPUPXS" 681017 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671041 671581 672167 "EXPRTUBE" 672992 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667235 667827 668564 "EXPRODE" 670380 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652601 665890 666318 "EXPR" 666839 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647008 647595 648408 "EXPR2UPS" 651899 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646644 646701 646808 "EXPR2" 646945 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638041 645776 646073 "EXPEXPAN" 646481 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637868 637998 638027 "EXIT" 638032 T EXIT (NIL) -8 NIL NIL NIL) (-311 637375 637592 637683 "EXITAST" 637797 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637002 637064 637177 "EVALCYC" 637307 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636543 636661 636702 "EVALAB" 636872 NIL EVALAB (NIL T) -9 NIL 636976 NIL) (-308 636024 636146 636367 "EVALAB-" 636372 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633484 634760 634788 "EUCDOM" 635343 T EUCDOM (NIL) -9 NIL 635693 NIL) (-306 631889 632331 632921 "EUCDOM-" 632926 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619427 622187 624937 "ESTOOLS" 629159 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619059 619116 619225 "ESTOOLS2" 619364 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618810 618852 618932 "ESTOOLS1" 619011 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612715 614443 614471 "ES" 617239 T ES (NIL) -9 NIL 618648 NIL) (-301 607662 608949 610766 "ES-" 610930 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604036 604797 605577 "ESCONT" 606902 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603781 603813 603895 "ESCONT1" 603998 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603456 603506 603606 "ES2" 603725 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603086 603144 603253 "ES1" 603392 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602302 602431 602607 "ERROR" 602930 T ERROR (NIL) -7 NIL NIL NIL) (-295 595805 602161 602252 "EQTBL" 602257 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588356 591119 592568 "EQ" 594389 NIL -2064 (NIL T) -8 NIL NIL NIL) (-293 587988 588045 588154 "EQ2" 588293 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583277 584326 585419 "EP" 586927 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581877 582168 582474 "ENV" 582991 T ENV (NIL) -8 NIL NIL NIL) (-290 581048 581576 581604 "ENTIRER" 581609 T ENTIRER (NIL) -9 NIL 581655 NIL) (-289 577542 579003 579373 "EMR" 580847 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576686 576871 576925 "ELTAGG" 577305 NIL ELTAGG (NIL T T) -9 NIL 577516 NIL) (-287 576405 576467 576608 "ELTAGG-" 576613 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576194 576223 576277 "ELTAB" 576361 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575320 575466 575665 "ELFUTS" 576045 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575062 575118 575146 "ELEMFUN" 575251 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574932 574953 575021 "ELEMFUN-" 575026 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569823 573032 573073 "ELAGG" 574013 NIL ELAGG (NIL T) -9 NIL 574476 NIL) (-281 568108 568542 569205 "ELAGG-" 569210 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566773 567051 567344 "ELABEXPR" 567835 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559637 561440 562267 "EFUPXS" 566049 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553087 554888 555698 "EFULS" 558913 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550509 550867 551346 "EFSTRUC" 552719 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539580 541146 542706 "EF" 549024 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538681 539065 539214 "EAB" 539451 T EAB (NIL) -8 NIL NIL NIL) (-274 537890 538640 538668 "E04UCFA" 538673 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537099 537849 537877 "E04NAFA" 537882 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536308 537058 537086 "E04MBFA" 537091 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535517 536267 536295 "E04JAFA" 536300 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534728 535476 535504 "E04GCFA" 535509 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533939 534687 534715 "E04FDFA" 534720 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533148 533898 533926 "E04DGFA" 533931 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527321 528673 530037 "E04AGNT" 531804 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526027 526507 526547 "DVARCAT" 527022 NIL DVARCAT (NIL T) -9 NIL 527221 NIL) (-265 525231 525443 525757 "DVARCAT-" 525762 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518123 525030 525159 "DSMP" 525164 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512932 514068 515136 "DROPT" 517075 T DROPT (NIL) -8 NIL NIL NIL) (-262 512597 512656 512754 "DROPT1" 512867 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507712 508838 509975 "DROPT0" 511480 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506057 506382 506768 "DRAWPT" 507346 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500644 501567 502646 "DRAW" 505031 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500277 500330 500448 "DRAWHACK" 500585 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499008 499277 499568 "DRAWCX" 500006 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498523 498592 498743 "DRAWCURV" 498934 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488991 490953 493068 "DRAWCFUN" 496428 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485804 487686 487727 "DQAGG" 488356 NIL DQAGG (NIL T) -9 NIL 488629 NIL) (-253 474075 480782 480865 "DPOLCAT" 482717 NIL DPOLCAT (NIL T T T T) -9 NIL 483262 NIL) (-252 468911 470260 472218 "DPOLCAT-" 472223 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 462060 468772 468870 "DPMO" 468875 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 455112 461840 462007 "DPMM" 462012 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454744 455031 455079 "DOMCTOR" 455084 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454039 454266 454403 "DOMAIN" 454627 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447782 453674 453826 "DMP" 453940 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447382 447438 447582 "DLP" 447720 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441252 446709 446899 "DLIST" 447224 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 438096 440105 440146 "DLAGG" 440696 NIL DLAGG (NIL T) -9 NIL 440926 NIL) (-243 436901 437539 437567 "DIVRING" 437659 T DIVRING (NIL) -9 NIL 437742 NIL) (-242 436138 436328 436628 "DIVRING-" 436633 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434240 434597 435003 "DISPLAY" 435752 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428176 434154 434217 "DIRPROD" 434222 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 427024 427227 427492 "DIRPROD2" 427969 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416281 422239 422292 "DIRPCAT" 422702 NIL DIRPCAT (NIL NIL T) -9 NIL 423542 NIL) (-237 413607 414249 415130 "DIRPCAT-" 415467 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412894 413054 413240 "DIOSP" 413441 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409596 411806 411847 "DIOPS" 412281 NIL DIOPS (NIL T) -9 NIL 412510 NIL) (-234 409145 409259 409450 "DIOPS-" 409455 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408029 408631 408659 "DIFRING" 408846 T DIFRING (NIL) -9 NIL 408956 NIL) (-232 407675 407752 407904 "DIFRING-" 407909 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405472 406718 406759 "DIFEXT" 407122 NIL DIFEXT (NIL T) -9 NIL 407416 NIL) (-230 403757 404185 404851 "DIFEXT-" 404856 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401079 403289 403330 "DIAGG" 403335 NIL DIAGG (NIL T) -9 NIL 403355 NIL) (-228 400463 400620 400872 "DIAGG-" 400877 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395928 399422 399699 "DHMATRIX" 400232 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391540 392449 393459 "DFSFUN" 394938 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386645 390471 390783 "DFLOAT" 391248 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384873 385154 385550 "DFINTTLS" 386353 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381929 382894 383294 "DERHAM" 384539 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379778 381704 381793 "DEQUEUE" 381873 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378993 379126 379322 "DEGRED" 379640 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375388 376133 376986 "DEFINTRF" 378221 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372915 373384 373983 "DEFINTEF" 374907 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372292 372535 372650 "DEFAST" 372820 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366323 371887 372036 "DECIMAL" 372163 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363833 364293 364799 "DDFACT" 365867 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363429 363472 363623 "DBLRESP" 363784 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361328 361662 362022 "DBASE" 363196 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360597 360808 360954 "DATAARY" 361227 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359730 360556 360584 "D03FAFA" 360589 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358864 359689 359717 "D03EEFA" 359722 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356814 357280 357769 "D03AGNT" 358395 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356130 356773 356801 "D02EJFA" 356806 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355446 356089 356117 "D02CJFA" 356122 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354762 355405 355433 "D02BHFA" 355438 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354078 354721 354749 "D02BBFA" 354754 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347275 348864 350470 "D02AGNT" 352492 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345043 345566 346112 "D01WGTS" 346749 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344137 345002 345030 "D01TRNS" 345035 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343232 344096 344124 "D01GBFA" 344129 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342327 343191 343219 "D01FCFA" 343224 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341422 342286 342314 "D01ASFA" 342319 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340517 341381 341409 "D01AQFA" 341414 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339612 340476 340504 "D01APFA" 340509 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338707 339571 339599 "D01ANFA" 339604 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337802 338666 338694 "D01AMFA" 338699 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336897 337761 337789 "D01ALFA" 337794 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335992 336856 336884 "D01AKFA" 336889 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335087 335951 335979 "D01AJFA" 335984 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328382 329935 331496 "D01AGNT" 333546 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327719 327847 327999 "CYCLOTOM" 328250 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324454 325167 325894 "CYCLES" 327012 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323766 323900 324071 "CVMP" 324315 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321537 321795 322171 "CTRIGMNP" 323494 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321032 321331 321404 "CTOR" 321484 T CTOR (NIL) -8 NIL NIL NIL) (-186 320568 320763 320864 "CTORKIND" 320951 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319916 320175 320203 "CTORCAT" 320385 T CTORCAT (NIL) -9 NIL 320498 NIL) (-184 319514 319625 319784 "CTORCAT-" 319789 NIL CTORCAT- (NIL T) -8 NIL NIL NIL) (-183 319030 319217 319315 "CTORCALL" 319436 T CTORCALL (NIL) -8 NIL NIL NIL) (-182 318404 318503 318656 "CSTTOOLS" 318927 NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-181 314203 314860 315618 "CRFP" 317716 NIL CRFP (NIL T T) -7 NIL NIL NIL) (-180 313705 313924 314016 "CRCEAST" 314131 T CRCEAST (NIL) -8 NIL NIL NIL) (-179 312752 312937 313165 "CRAPACK" 313509 NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-178 312136 312237 312441 "CPMATCH" 312628 NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-177 311861 311889 311995 "CPIMA" 312102 NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-176 308225 308897 309615 "COORDSYS" 311196 NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-175 307637 307758 307900 "CONTOUR" 308103 T CONTOUR (NIL) -8 NIL NIL NIL) (-174 303555 305640 306132 "CONTFRAC" 307177 NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-173 303435 303456 303484 "CONDUIT" 303521 T CONDUIT (NIL) -9 NIL NIL NIL) (-172 302600 303128 303156 "COMRING" 303161 T COMRING (NIL) -9 NIL 303213 NIL) (-171 301681 301958 302142 "COMPPROP" 302436 T COMPPROP (NIL) -8 NIL NIL NIL) (-170 301342 301377 301505 "COMPLPAT" 301640 NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-169 291391 301151 301260 "COMPLEX" 301265 NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-168 291027 291084 291191 "COMPLEX2" 291328 NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-167 290745 290780 290878 "COMPFACT" 290986 NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-166 274899 285127 285167 "COMPCAT" 286171 NIL COMPCAT (NIL T) -9 NIL 287567 NIL) (-165 264410 267338 270965 "COMPCAT-" 271321 NIL COMPCAT- (NIL T T) -8 NIL NIL NIL) (-164 264139 264167 264270 "COMMUPC" 264376 NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-163 263933 263967 264026 "COMMONOP" 264100 T COMMONOP (NIL) -7 NIL NIL NIL) (-162 263516 263684 263771 "COMM" 263866 T COMM (NIL) -8 NIL NIL NIL) (-161 263119 263320 263395 "COMMAAST" 263461 T COMMAAST (NIL) -8 NIL NIL NIL) (-160 262368 262562 262590 "COMBOPC" 262928 T COMBOPC (NIL) -9 NIL 263103 NIL) (-159 261264 261474 261716 "COMBINAT" 262158 NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-158 257461 258035 258675 "COMBF" 260686 NIL COMBF (NIL T T) -7 NIL NIL NIL) (-157 256246 256577 256812 "COLOR" 257246 T COLOR (NIL) -8 NIL NIL NIL) (-156 255749 255967 256059 "COLONAST" 256174 T COLONAST (NIL) -8 NIL NIL NIL) (-155 255389 255436 255561 "CMPLXRT" 255696 NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-154 254864 255089 255188 "CLLCTAST" 255310 T CLLCTAST (NIL) -8 NIL NIL NIL) (-153 250364 251394 252474 "CLIP" 253804 T CLIP (NIL) -7 NIL NIL NIL) (-152 248737 249470 249709 "CLIF" 250191 NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-151 244959 246883 246924 "CLAGG" 247853 NIL CLAGG (NIL T) -9 NIL 248389 NIL) (-150 243381 243838 244421 "CLAGG-" 244426 NIL CLAGG- (NIL T T) -8 NIL NIL NIL) (-149 242925 243010 243150 "CINTSLPE" 243290 NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-148 240426 240897 241445 "CHVAR" 242453 NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-147 239661 240189 240217 "CHARZ" 240222 T CHARZ (NIL) -9 NIL 240237 NIL) (-146 239415 239455 239533 "CHARPOL" 239615 NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-145 238534 239095 239123 "CHARNZ" 239170 T CHARNZ (NIL) -9 NIL 239226 NIL) (-144 236523 237224 237559 "CHAR" 238219 T CHAR (NIL) -8 NIL NIL NIL) (-143 236249 236310 236338 "CFCAT" 236449 T CFCAT (NIL) -9 NIL NIL NIL) (-142 235494 235605 235787 "CDEN" 236133 NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-141 231486 234647 234927 "CCLASS" 235234 T CCLASS (NIL) -8 NIL NIL NIL) (-140 230793 230936 231099 "CATEGORY" 231343 T -10 (NIL) -8 NIL NIL NIL) (-139 230425 230712 230760 "CATCTOR" 230765 T CATCTOR (NIL) -8 NIL NIL NIL) (-138 229903 230128 230226 "CATAST" 230347 T CATAST (NIL) -8 NIL NIL NIL) (-137 229406 229624 229716 "CASEAST" 229831 T CASEAST (NIL) -8 NIL NIL NIL) (-136 224442 225435 226188 "CARTEN" 228709 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-135 223550 223698 223919 "CARTEN2" 224289 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-134 221892 222700 222957 "CARD" 223313 T CARD (NIL) -8 NIL NIL NIL) (-133 221495 221696 221771 "CAPSLAST" 221837 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220867 221195 221223 "CACHSET" 221355 T CACHSET (NIL) -9 NIL 221432 NIL) (-131 220363 220659 220687 "CABMON" 220737 T CABMON (NIL) -9 NIL 220793 NIL) (-130 219863 220067 220177 "BYTEORD" 220273 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218866 219397 219539 "BYTE" 219702 T BYTE (NIL) -8 NIL NIL 219824) (-128 214266 218371 218543 "BYTEBUF" 218714 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211823 213958 214065 "BTREE" 214192 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209320 211471 211593 "BTOURN" 211733 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206737 208790 208831 "BTCAT" 208899 NIL BTCAT (NIL T) -9 NIL 208976 NIL) (-124 206404 206484 206633 "BTCAT-" 206638 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201696 205547 205575 "BTAGG" 205797 T BTAGG (NIL) -9 NIL 205958 NIL) (-122 201186 201311 201517 "BTAGG-" 201522 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198229 200464 200679 "BSTREE" 201003 NIL BSTREE (NIL T) -8 NIL NIL NIL) (-120 197367 197493 197677 "BRILL" 198085 NIL BRILL (NIL T) -7 NIL NIL NIL) (-119 194066 196093 196134 "BRAGG" 196783 NIL BRAGG (NIL T) -9 NIL 197041 NIL) (-118 192595 193001 193556 "BRAGG-" 193561 NIL BRAGG- (NIL T T) -8 NIL NIL NIL) (-117 185851 191941 192125 "BPADICRT" 192443 NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-116 184193 185788 185833 "BPADIC" 185838 NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-115 183891 183921 184035 "BOUNDZRO" 184157 NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-114 179011 180181 181124 "BOP" 182968 T BOP (NIL) -8 NIL NIL NIL) (-113 176632 177076 177596 "BOP1" 178524 NIL BOP1 (NIL T) -7 NIL NIL NIL) (-112 175334 176056 176249 "BOOLEAN" 176459 T BOOLEAN (NIL) -8 NIL NIL NIL) (-111 174696 175074 175128 "BMODULE" 175133 NIL BMODULE (NIL T T) -9 NIL 175198 NIL) (-110 170524 174494 174567 "BITS" 174643 T BITS (NIL) -8 NIL NIL NIL) (-109 169945 170064 170204 "BINDING" 170404 T BINDING (NIL) -8 NIL NIL NIL) (-108 163979 169542 169690 "BINARY" 169817 T BINARY (NIL) -8 NIL NIL NIL) (-107 161806 163234 163275 "BGAGG" 163535 NIL BGAGG (NIL T) -9 NIL 163672 NIL) (-106 161637 161669 161760 "BGAGG-" 161765 NIL BGAGG- (NIL T T) -8 NIL NIL NIL) (-105 160735 161021 161226 "BFUNCT" 161452 T BFUNCT (NIL) -8 NIL NIL NIL) (-104 159425 159603 159891 "BEZOUT" 160559 NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-103 155942 158277 158607 "BBTREE" 159128 NIL BBTREE (NIL T) -8 NIL NIL NIL) (-102 155676 155729 155757 "BASTYPE" 155876 T BASTYPE (NIL) -9 NIL NIL NIL) (-101 155529 155557 155630 "BASTYPE-" 155635 NIL BASTYPE- (NIL T) -8 NIL NIL NIL) (-100 154963 155039 155191 "BALFACT" 155440 NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-99 153846 154378 154564 "AUTOMOR" 154808 NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-98 153572 153577 153603 "ATTREG" 153608 T ATTREG (NIL) -9 NIL NIL NIL) (-97 151851 152269 152621 "ATTRBUT" 153238 T ATTRBUT (NIL) -8 NIL NIL NIL) (-96 151486 151679 151745 "ATTRAST" 151803 T ATTRAST (NIL) -8 NIL NIL NIL) (-95 151022 151135 151161 "ATRIG" 151362 T ATRIG (NIL) -9 NIL NIL NIL) (-94 150831 150872 150959 "ATRIG-" 150964 NIL ATRIG- (NIL T) -8 NIL NIL NIL) (-93 150502 150662 150688 "ASTCAT" 150693 T ASTCAT (NIL) -9 NIL 150723 NIL) (-92 150229 150288 150407 "ASTCAT-" 150412 NIL ASTCAT- (NIL T) -8 NIL NIL NIL) (-91 148426 150005 150093 "ASTACK" 150172 NIL ASTACK (NIL T) -8 NIL NIL NIL) (-90 146931 147228 147593 "ASSOCEQ" 148108 NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-89 145963 146590 146714 "ASP9" 146838 NIL ASP9 (NIL NIL) -8 NIL NIL NIL) (-88 145726 145911 145950 "ASP8" 145955 NIL ASP8 (NIL NIL) -8 NIL NIL NIL) (-87 144594 145331 145473 "ASP80" 145615 NIL ASP80 (NIL NIL) -8 NIL NIL NIL) (-86 143492 144229 144361 "ASP7" 144493 NIL ASP7 (NIL NIL) -8 NIL NIL NIL) (-85 142446 143169 143287 "ASP78" 143405 NIL ASP78 (NIL NIL) -8 NIL NIL NIL) (-84 141415 142126 142243 "ASP77" 142360 NIL ASP77 (NIL NIL) -8 NIL NIL NIL) (-83 140327 141053 141184 "ASP74" 141315 NIL ASP74 (NIL NIL) -8 NIL NIL NIL) (-82 139227 139962 140094 "ASP73" 140226 NIL ASP73 (NIL NIL) -8 NIL NIL NIL) (-81 138331 139053 139153 "ASP6" 139158 NIL ASP6 (NIL NIL) -8 NIL NIL NIL) (-80 137275 138008 138126 "ASP55" 138244 NIL ASP55 (NIL NIL) -8 NIL NIL NIL) (-79 136224 136949 137068 "ASP50" 137187 NIL ASP50 (NIL NIL) -8 NIL NIL NIL) (-78 135312 135925 136035 "ASP4" 136145 NIL ASP4 (NIL NIL) -8 NIL NIL NIL) (-77 134400 135013 135123 "ASP49" 135233 NIL ASP49 (NIL NIL) -8 NIL NIL NIL) (-76 133184 133939 134107 "ASP42" 134289 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-75 131960 132717 132887 "ASP41" 133071 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL NIL) (-74 130910 131637 131755 "ASP35" 131873 NIL ASP35 (NIL NIL) -8 NIL NIL NIL) (-73 130675 130858 130897 "ASP34" 130902 NIL ASP34 (NIL NIL) -8 NIL NIL NIL) (-72 130412 130479 130555 "ASP33" 130630 NIL ASP33 (NIL NIL) -8 NIL NIL NIL) (-71 129305 130047 130179 "ASP31" 130311 NIL ASP31 (NIL NIL) -8 NIL NIL NIL) (-70 129070 129253 129292 "ASP30" 129297 NIL ASP30 (NIL NIL) -8 NIL NIL NIL) (-69 128805 128874 128950 "ASP29" 129025 NIL ASP29 (NIL NIL) -8 NIL NIL NIL) (-68 128570 128753 128792 "ASP28" 128797 NIL ASP28 (NIL NIL) -8 NIL NIL NIL) (-67 128335 128518 128557 "ASP27" 128562 NIL ASP27 (NIL NIL) -8 NIL NIL NIL) (-66 127419 128033 128144 "ASP24" 128255 NIL ASP24 (NIL NIL) -8 NIL NIL NIL) (-65 126495 127221 127333 "ASP20" 127338 NIL ASP20 (NIL NIL) -8 NIL NIL NIL) (-64 125583 126196 126306 "ASP1" 126416 NIL ASP1 (NIL NIL) -8 NIL NIL NIL) (-63 124525 125257 125376 "ASP19" 125495 NIL ASP19 (NIL NIL) -8 NIL NIL NIL) (-62 124262 124329 124405 "ASP12" 124480 NIL ASP12 (NIL NIL) -8 NIL NIL NIL) (-61 123114 123861 124005 "ASP10" 124149 NIL ASP10 (NIL NIL) -8 NIL NIL NIL) (-60 121013 122958 123049 "ARRAY2" 123054 NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 116826 120661 120775 "ARRAY1" 120930 NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-58 115858 116031 116252 "ARRAY12" 116649 NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-57 110217 112088 112163 "ARR2CAT" 114793 NIL ARR2CAT (NIL T T T) -9 NIL 115551 NIL) (-56 107651 108395 109349 "ARR2CAT-" 109354 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL NIL) (-55 106995 107278 107403 "ARITY" 107544 T ARITY (NIL) -8 NIL NIL NIL) (-54 105743 105895 106201 "APPRULE" 106831 NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 105394 105442 105561 "APPLYORE" 105689 NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 104368 104659 104854 "ANY" 105217 T ANY (NIL) -8 NIL NIL NIL) (-51 103646 103769 103926 "ANY1" 104242 NIL ANY1 (NIL T) -7 NIL NIL NIL) (-50 101203 102083 102410 "ANTISYM" 103370 NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 100722 100910 101006 "ANON" 101125 T ANON (NIL) -8 NIL NIL NIL) (-48 94846 99261 99715 "AN" 100286 T AN (NIL) -8 NIL NIL NIL) (-47 91094 92456 92507 "AMR" 93255 NIL AMR (NIL T T) -9 NIL 93855 NIL) (-46 90206 90427 90790 "AMR-" 90795 NIL AMR- (NIL T T T) -8 NIL NIL NIL) (-45 74756 90123 90184 "ALIST" 90189 NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 71585 74350 74519 "ALGSC" 74674 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 68140 68695 69302 "ALGPKG" 71025 NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 67417 67518 67702 "ALGMFACT" 68026 NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 63155 63841 64496 "ALGMANIP" 66940 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 3198891 3198896 3198901 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-2 3198876 3198881 3198886 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1 3198861 3198866 3198871 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (0 3198846 3198851 3198856 NIL NIL NIL NIL (NIL) -8 NIL NIL NIL) (-1287 3198015 3198721 3198798 "ZMOD" 3198803 NIL ZMOD (NIL NIL) -8 NIL NIL NIL) (-1286 3197125 3197289 3197498 "ZLINDEP" 3197847 NIL ZLINDEP (NIL T) -7 NIL NIL NIL) (-1285 3186425 3188193 3190165 "ZDSOLVE" 3195255 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL NIL) (-1284 3185671 3185812 3186001 "YSTREAM" 3186271 NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1283 3183472 3184972 3185176 "XRPOLY" 3185514 NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1282 3180052 3181343 3181918 "XPR" 3182944 NIL XPR (NIL T T) -8 NIL NIL NIL) (-1281 3177800 3179383 3179587 "XPOLY" 3179883 NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1280 3175583 3176925 3176980 "XPOLYC" 3177268 NIL XPOLYC (NIL T T) -9 NIL 3177381 NIL) (-1279 3171986 3174100 3174488 "XPBWPOLY" 3175241 NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1278 3167889 3170149 3170191 "XF" 3170812 NIL XF (NIL T) -9 NIL 3171212 NIL) (-1277 3167510 3167598 3167767 "XF-" 3167772 NIL XF- (NIL T T) -8 NIL NIL NIL) (-1276 3162836 3164099 3164154 "XFALG" 3166326 NIL XFALG (NIL T T) -9 NIL 3167115 NIL) (-1275 3161969 3162073 3162278 "XEXPPKG" 3162728 NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1274 3160105 3161819 3161915 "XDPOLY" 3161920 NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1273 3159042 3159616 3159659 "XALG" 3159664 NIL XALG (NIL T) -9 NIL 3159775 NIL) (-1272 3152511 3157019 3157513 "WUTSET" 3158634 NIL WUTSET (NIL T T T T) -8 NIL NIL NIL) (-1271 3150794 3151563 3151886 "WP" 3152322 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL NIL) (-1270 3150423 3150616 3150686 "WHILEAST" 3150746 T WHILEAST (NIL) -8 NIL NIL NIL) (-1269 3149922 3150140 3150234 "WHEREAST" 3150351 T WHEREAST (NIL) -8 NIL NIL NIL) (-1268 3148808 3149006 3149301 "WFFINTBS" 3149719 NIL WFFINTBS (NIL T T T T) -7 NIL NIL NIL) (-1267 3146712 3147139 3147601 "WEIER" 3148380 NIL WEIER (NIL T) -7 NIL NIL NIL) (-1266 3145859 3146283 3146325 "VSPACE" 3146461 NIL VSPACE (NIL T) -9 NIL 3146535 NIL) (-1265 3145697 3145724 3145815 "VSPACE-" 3145820 NIL VSPACE- (NIL T T) -8 NIL NIL NIL) (-1264 3145505 3145548 3145616 "VOID" 3145651 T VOID (NIL) -8 NIL NIL NIL) (-1263 3143641 3144000 3144406 "VIEW" 3145121 T VIEW (NIL) -7 NIL NIL NIL) (-1262 3140065 3140704 3141441 "VIEWDEF" 3142926 T VIEWDEF (NIL) -7 NIL NIL NIL) (-1261 3129396 3131613 3133786 "VIEW3D" 3137914 T VIEW3D (NIL) -8 NIL NIL NIL) (-1260 3121674 3123307 3124886 "VIEW2D" 3127839 T VIEW2D (NIL) -8 NIL NIL NIL) (-1259 3117076 3121444 3121536 "VECTOR" 3121617 NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1258 3115653 3115912 3116230 "VECTOR2" 3116806 NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1257 3109180 3113437 3113480 "VECTCAT" 3114473 NIL VECTCAT (NIL T) -9 NIL 3115059 NIL) (-1256 3108194 3108448 3108838 "VECTCAT-" 3108843 NIL VECTCAT- (NIL T T) -8 NIL NIL NIL) (-1255 3107675 3107845 3107965 "VARIABLE" 3108109 NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1254 3107608 3107613 3107643 "UTYPE" 3107648 T UTYPE (NIL) -9 NIL NIL NIL) (-1253 3106438 3106592 3106854 "UTSODETL" 3107434 NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1252 3103878 3104338 3104862 "UTSODE" 3105979 NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1251 3095742 3101504 3101993 "UTS" 3103447 NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1250 3086977 3092309 3092352 "UTSCAT" 3093464 NIL UTSCAT (NIL T) -9 NIL 3094221 NIL) (-1249 3084325 3085047 3086036 "UTSCAT-" 3086041 NIL UTSCAT- (NIL T T) -8 NIL NIL NIL) (-1248 3083952 3083995 3084128 "UTS2" 3084276 NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1247 3078225 3080790 3080833 "URAGG" 3082903 NIL URAGG (NIL T) -9 NIL 3083626 NIL) (-1246 3075164 3076027 3077150 "URAGG-" 3077155 NIL URAGG- (NIL T T) -8 NIL NIL NIL) (-1245 3070880 3073778 3074250 "UPXSSING" 3074828 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1244 3062973 3070127 3070400 "UPXS" 3070665 NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1243 3056073 3062877 3062949 "UPXSCONS" 3062954 NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1242 3046310 3053068 3053130 "UPXSCCA" 3053704 NIL UPXSCCA (NIL T T) -9 NIL 3053937 NIL) (-1241 3045948 3046033 3046207 "UPXSCCA-" 3046212 NIL UPXSCCA- (NIL T T T) -8 NIL NIL NIL) (-1240 3036038 3042569 3042612 "UPXSCAT" 3043260 NIL UPXSCAT (NIL T) -9 NIL 3043868 NIL) (-1239 3035468 3035547 3035726 "UPXS2" 3035953 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1238 3034122 3034375 3034726 "UPSQFREE" 3035211 NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1237 3027902 3030924 3030979 "UPSCAT" 3032140 NIL UPSCAT (NIL T T) -9 NIL 3032914 NIL) (-1236 3027106 3027313 3027640 "UPSCAT-" 3027645 NIL UPSCAT- (NIL T T T) -8 NIL NIL NIL) (-1235 3012948 3020954 3020997 "UPOLYC" 3023098 NIL UPOLYC (NIL T) -9 NIL 3024319 NIL) (-1234 3004276 3006702 3009849 "UPOLYC-" 3009854 NIL UPOLYC- (NIL T T) -8 NIL NIL NIL) (-1233 3003903 3003946 3004079 "UPOLYC2" 3004227 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1232 2995469 3003586 3003715 "UP" 3003822 NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1231 2994808 2994915 2995079 "UPMP" 2995358 NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1230 2994361 2994442 2994581 "UPDIVP" 2994721 NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1229 2992929 2993178 2993494 "UPDECOMP" 2994110 NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1228 2992164 2992276 2992461 "UPCDEN" 2992813 NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1227 2991683 2991752 2991901 "UP2" 2992089 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1226 2990198 2990887 2991164 "UNISEG" 2991441 NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1225 2989413 2989540 2989745 "UNISEG2" 2990041 NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1224 2988473 2988653 2988879 "UNIFACT" 2989229 NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1223 2972432 2987650 2987901 "ULS" 2988280 NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1222 2960458 2972336 2972408 "ULSCONS" 2972413 NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1221 2943066 2955016 2955078 "ULSCCAT" 2955716 NIL ULSCCAT (NIL T T) -9 NIL 2956004 NIL) (-1220 2942116 2942361 2942749 "ULSCCAT-" 2942754 NIL ULSCCAT- (NIL T T T) -8 NIL NIL NIL) (-1219 2931983 2938428 2938471 "ULSCAT" 2939334 NIL ULSCAT (NIL T) -9 NIL 2940064 NIL) (-1218 2931413 2931492 2931671 "ULS2" 2931898 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1217 2930530 2931013 2931120 "UINT8" 2931231 T UINT8 (NIL) -8 NIL NIL 2931316) (-1216 2929646 2930129 2930236 "UINT64" 2930347 T UINT64 (NIL) -8 NIL NIL 2930432) (-1215 2928762 2929245 2929352 "UINT32" 2929463 T UINT32 (NIL) -8 NIL NIL 2929548) (-1214 2927878 2928361 2928468 "UINT16" 2928579 T UINT16 (NIL) -8 NIL NIL 2928664) (-1213 2926273 2927204 2927234 "UFD" 2927446 T UFD (NIL) -9 NIL 2927560 NIL) (-1212 2926067 2926113 2926208 "UFD-" 2926213 NIL UFD- (NIL T) -8 NIL NIL NIL) (-1211 2925149 2925332 2925548 "UDVO" 2925873 T UDVO (NIL) -7 NIL NIL NIL) (-1210 2922965 2923374 2923845 "UDPO" 2924713 NIL UDPO (NIL T) -7 NIL NIL NIL) (-1209 2922898 2922903 2922933 "TYPE" 2922938 T TYPE (NIL) -9 NIL NIL NIL) (-1208 2922685 2922853 2922884 "TYPEAST" 2922889 T TYPEAST (NIL) -8 NIL NIL NIL) (-1207 2921656 2921858 2922098 "TWOFACT" 2922479 NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1206 2920727 2921065 2921300 "TUPLE" 2921456 NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1205 2918418 2918937 2919476 "TUBETOOL" 2920210 T TUBETOOL (NIL) -7 NIL NIL NIL) (-1204 2917267 2917472 2917713 "TUBE" 2918211 NIL TUBE (NIL T) -8 NIL NIL NIL) (-1203 2912023 2916239 2916522 "TS" 2917019 NIL TS (NIL T) -8 NIL NIL NIL) (-1202 2900690 2904782 2904879 "TSETCAT" 2910148 NIL TSETCAT (NIL T T T T) -9 NIL 2911679 NIL) (-1201 2895422 2897022 2898913 "TSETCAT-" 2898918 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1200 2889684 2890531 2891473 "TRMANIP" 2894558 NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1199 2889125 2889188 2889351 "TRIMAT" 2889616 NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1198 2886920 2887158 2887522 "TRIGMNIP" 2888874 NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1197 2886440 2886553 2886583 "TRIGCAT" 2886796 T TRIGCAT (NIL) -9 NIL NIL NIL) (-1196 2886109 2886188 2886329 "TRIGCAT-" 2886334 NIL TRIGCAT- (NIL T) -8 NIL NIL NIL) (-1195 2883002 2884967 2885248 "TREE" 2885863 NIL TREE (NIL T) -8 NIL NIL NIL) (-1194 2882276 2882804 2882834 "TRANFUN" 2882869 T TRANFUN (NIL) -9 NIL 2882935 NIL) (-1193 2881555 2881746 2882026 "TRANFUN-" 2882031 NIL TRANFUN- (NIL T) -8 NIL NIL NIL) (-1192 2881359 2881391 2881452 "TOPSP" 2881516 T TOPSP (NIL) -7 NIL NIL NIL) (-1191 2880707 2880822 2880976 "TOOLSIGN" 2881240 NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1190 2879368 2879884 2880123 "TEXTFILE" 2880490 T TEXTFILE (NIL) -8 NIL NIL NIL) (-1189 2877307 2877821 2878250 "TEX" 2878961 T TEX (NIL) -8 NIL NIL NIL) (-1188 2877088 2877119 2877191 "TEX1" 2877270 NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1187 2876736 2876799 2876889 "TEMUTL" 2877020 T TEMUTL (NIL) -7 NIL NIL NIL) (-1186 2874890 2875170 2875495 "TBCMPPK" 2876459 NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1185 2866778 2873050 2873106 "TBAGG" 2873506 NIL TBAGG (NIL T T) -9 NIL 2873717 NIL) (-1184 2861848 2863336 2865090 "TBAGG-" 2865095 NIL TBAGG- (NIL T T T) -8 NIL NIL NIL) (-1183 2861232 2861339 2861484 "TANEXP" 2861737 NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1182 2854733 2861089 2861182 "TABLE" 2861187 NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1181 2854145 2854244 2854382 "TABLEAU" 2854630 NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1180 2848753 2849973 2851221 "TABLBUMP" 2852931 NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1179 2847975 2848122 2848303 "SYSTEM" 2848594 T SYSTEM (NIL) -8 NIL NIL NIL) (-1178 2844434 2845133 2845916 "SYSSOLP" 2847226 NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1177 2843468 2843946 2844065 "SYSNNI" 2844251 NIL SYSNNI (NIL NIL) -8 NIL NIL 2844336) (-1176 2842765 2843197 2843276 "SYSINT" 2843336 NIL SYSINT (NIL NIL) -8 NIL NIL 2843381) (-1175 2839124 2840043 2840753 "SYNTAX" 2842077 T SYNTAX (NIL) -8 NIL NIL NIL) (-1174 2836282 2836884 2837516 "SYMTAB" 2838514 T SYMTAB (NIL) -8 NIL NIL NIL) (-1173 2831531 2832433 2833416 "SYMS" 2835321 T SYMS (NIL) -8 NIL NIL NIL) (-1172 2828793 2830989 2831219 "SYMPOLY" 2831336 NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1171 2828310 2828385 2828508 "SYMFUNC" 2828705 NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1170 2824356 2825622 2826435 "SYMBOL" 2827519 T SYMBOL (NIL) -8 NIL NIL NIL) (-1169 2817895 2819584 2821304 "SWITCH" 2822658 T SWITCH (NIL) -8 NIL NIL NIL) (-1168 2811156 2816716 2817019 "SUTS" 2817650 NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1167 2803249 2810403 2810676 "SUPXS" 2810941 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1166 2794764 2802867 2802993 "SUP" 2803158 NIL SUP (NIL T) -8 NIL NIL NIL) (-1165 2793923 2794050 2794267 "SUPFRACF" 2794632 NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1164 2793544 2793603 2793716 "SUP2" 2793858 NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1163 2791957 2792231 2792594 "SUMRF" 2793243 NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1162 2791271 2791337 2791536 "SUMFS" 2791878 NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1161 2775265 2790448 2790699 "SULS" 2791078 NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2774894 2775087 2775157 "SUCHTAST" 2775217 T SUCHTAST (NIL) -8 NIL NIL NIL) (-1159 2774216 2774419 2774559 "SUCH" 2774802 NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1158 2768110 2769122 2770081 "SUBSPACE" 2773304 NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1157 2767540 2767630 2767794 "SUBRESP" 2767998 NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1156 2760905 2762205 2763516 "STTF" 2766276 NIL STTF (NIL T) -7 NIL NIL NIL) (-1155 2755078 2756198 2757345 "STTFNC" 2759805 NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1154 2746389 2748260 2750054 "STTAYLOR" 2753319 NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1153 2739633 2746253 2746336 "STRTBL" 2746341 NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1152 2735024 2739588 2739619 "STRING" 2739624 T STRING (NIL) -8 NIL NIL NIL) (-1151 2729912 2734397 2734427 "STRICAT" 2734486 T STRICAT (NIL) -9 NIL 2734548 NIL) (-1150 2722715 2727531 2728142 "STREAM" 2729336 NIL STREAM (NIL T) -8 NIL NIL NIL) (-1149 2722225 2722302 2722446 "STREAM3" 2722632 NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1148 2721207 2721390 2721625 "STREAM2" 2722038 NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1147 2720895 2720947 2721040 "STREAM1" 2721149 NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1146 2719911 2720092 2720323 "STINPROD" 2720711 NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1145 2719489 2719673 2719703 "STEP" 2719783 T STEP (NIL) -9 NIL 2719861 NIL) (-1144 2713032 2719388 2719465 "STBL" 2719470 NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1143 2708206 2712253 2712296 "STAGG" 2712449 NIL STAGG (NIL T) -9 NIL 2712538 NIL) (-1142 2705908 2706510 2707382 "STAGG-" 2707387 NIL STAGG- (NIL T T) -8 NIL NIL NIL) (-1141 2704103 2705678 2705770 "STACK" 2705851 NIL STACK (NIL T) -8 NIL NIL NIL) (-1140 2696826 2702244 2702700 "SREGSET" 2703733 NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1139 2689251 2690620 2692133 "SRDCMPK" 2695432 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1138 2682218 2686691 2686721 "SRAGG" 2688024 T SRAGG (NIL) -9 NIL 2688632 NIL) (-1137 2681235 2681490 2681869 "SRAGG-" 2681874 NIL SRAGG- (NIL T) -8 NIL NIL NIL) (-1136 2675722 2680182 2680603 "SQMATRIX" 2680861 NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1135 2669469 2672440 2673167 "SPLTREE" 2675067 NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1134 2665459 2666125 2666771 "SPLNODE" 2668895 NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1133 2664506 2664739 2664769 "SPFCAT" 2665213 T SPFCAT (NIL) -9 NIL NIL NIL) (-1132 2663243 2663453 2663717 "SPECOUT" 2664264 T SPECOUT (NIL) -7 NIL NIL NIL) (-1131 2654895 2656639 2656669 "SPADXPT" 2661061 T SPADXPT (NIL) -9 NIL 2663095 NIL) (-1130 2654656 2654696 2654765 "SPADPRSR" 2654848 T SPADPRSR (NIL) -7 NIL NIL NIL) (-1129 2652838 2654611 2654642 "SPADAST" 2654647 T SPADAST (NIL) -8 NIL NIL NIL) (-1128 2644809 2646556 2646599 "SPACEC" 2650972 NIL SPACEC (NIL T) -9 NIL 2652788 NIL) (-1127 2642966 2644741 2644790 "SPACE3" 2644795 NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1126 2641718 2641889 2642180 "SORTPAK" 2642771 NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1125 2639768 2640071 2640490 "SOLVETRA" 2641382 NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1124 2638779 2639001 2639275 "SOLVESER" 2639541 NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1123 2633990 2634880 2635882 "SOLVERAD" 2637831 NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1122 2629805 2630414 2631143 "SOLVEFOR" 2633357 NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1121 2624102 2629154 2629251 "SNTSCAT" 2629256 NIL SNTSCAT (NIL T T T T) -9 NIL 2629326 NIL) (-1120 2618235 2622425 2622816 "SMTS" 2623792 NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1119 2612675 2618123 2618200 "SMP" 2618205 NIL SMP (NIL T T) -8 NIL NIL NIL) (-1118 2610834 2611135 2611533 "SMITH" 2612372 NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1117 2603721 2607885 2607988 "SMATCAT" 2609339 NIL SMATCAT (NIL NIL T T T) -9 NIL 2609889 NIL) (-1116 2600661 2601484 2602662 "SMATCAT-" 2602667 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL NIL) (-1115 2598374 2599897 2599940 "SKAGG" 2600201 NIL SKAGG (NIL T) -9 NIL 2600336 NIL) (-1114 2594709 2597790 2597985 "SINT" 2598172 T SINT (NIL) -8 NIL NIL 2598345) (-1113 2594481 2594519 2594585 "SIMPAN" 2594665 T SIMPAN (NIL) -7 NIL NIL NIL) (-1112 2593787 2594016 2594156 "SIG" 2594363 T SIG (NIL) -8 NIL NIL NIL) (-1111 2592625 2592846 2593121 "SIGNRF" 2593546 NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1110 2591430 2591581 2591872 "SIGNEF" 2592454 NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1109 2590763 2591013 2591137 "SIGAST" 2591328 T SIGAST (NIL) -8 NIL NIL NIL) (-1108 2588453 2588907 2589413 "SHP" 2590304 NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1107 2582353 2588354 2588430 "SHDP" 2588435 NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1106 2581952 2582118 2582148 "SGROUP" 2582241 T SGROUP (NIL) -9 NIL 2582303 NIL) (-1105 2581810 2581836 2581909 "SGROUP-" 2581914 NIL SGROUP- (NIL T) -8 NIL NIL NIL) (-1104 2578645 2579343 2580066 "SGCF" 2581109 T SGCF (NIL) -7 NIL NIL NIL) (-1103 2573040 2578092 2578189 "SFRTCAT" 2578194 NIL SFRTCAT (NIL T T T T) -9 NIL 2578233 NIL) (-1102 2566461 2567479 2568615 "SFRGCD" 2572023 NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1101 2559588 2560660 2561846 "SFQCMPK" 2565394 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1100 2559210 2559299 2559409 "SFORT" 2559529 NIL SFORT (NIL T T) -8 NIL NIL NIL) (-1099 2558355 2559050 2559171 "SEXOF" 2559176 NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1098 2557489 2558236 2558304 "SEX" 2558309 T SEX (NIL) -8 NIL NIL NIL) (-1097 2553028 2553717 2553812 "SEXCAT" 2556749 NIL SEXCAT (NIL T T T T T) -9 NIL 2557327 NIL) (-1096 2550208 2552962 2553010 "SET" 2553015 NIL SET (NIL T) -8 NIL NIL NIL) (-1095 2548459 2548921 2549226 "SETMN" 2549949 NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1094 2548065 2548191 2548221 "SETCAT" 2548338 T SETCAT (NIL) -9 NIL 2548423 NIL) (-1093 2547845 2547897 2547996 "SETCAT-" 2548001 NIL SETCAT- (NIL T) -8 NIL NIL NIL) (-1092 2544232 2546306 2546349 "SETAGG" 2547219 NIL SETAGG (NIL T) -9 NIL 2547559 NIL) (-1091 2543690 2543806 2544043 "SETAGG-" 2544048 NIL SETAGG- (NIL T T) -8 NIL NIL NIL) (-1090 2543160 2543386 2543487 "SEQAST" 2543611 T SEQAST (NIL) -8 NIL NIL NIL) (-1089 2542359 2542653 2542714 "SEGXCAT" 2543000 NIL SEGXCAT (NIL T T) -9 NIL 2543120 NIL) (-1088 2541413 2542025 2542207 "SEG" 2542212 NIL SEG (NIL T) -8 NIL NIL NIL) (-1087 2540392 2540606 2540649 "SEGCAT" 2541171 NIL SEGCAT (NIL T) -9 NIL 2541392 NIL) (-1086 2539441 2539771 2539971 "SEGBIND" 2540227 NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1085 2539062 2539121 2539234 "SEGBIND2" 2539376 NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1084 2538662 2538863 2538940 "SEGAST" 2539007 T SEGAST (NIL) -8 NIL NIL NIL) (-1083 2537881 2538007 2538211 "SEG2" 2538506 NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1082 2537318 2537816 2537863 "SDVAR" 2537868 NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1081 2529600 2537088 2537218 "SDPOL" 2537223 NIL SDPOL (NIL T) -8 NIL NIL NIL) (-1080 2528193 2528459 2528778 "SCPKG" 2529315 NIL SCPKG (NIL T) -7 NIL NIL NIL) (-1079 2527357 2527529 2527721 "SCOPE" 2528023 T SCOPE (NIL) -8 NIL NIL NIL) (-1078 2526577 2526711 2526890 "SCACHE" 2527212 NIL SCACHE (NIL T) -7 NIL NIL NIL) (-1077 2526249 2526409 2526439 "SASTCAT" 2526444 T SASTCAT (NIL) -9 NIL 2526457 NIL) (-1076 2525763 2526084 2526160 "SAOS" 2526195 T SAOS (NIL) -8 NIL NIL NIL) (-1075 2525328 2525363 2525536 "SAERFFC" 2525722 NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-1074 2519294 2525225 2525305 "SAE" 2525310 NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-1073 2518887 2518922 2519081 "SAEFACT" 2519253 NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-1072 2517208 2517522 2517923 "RURPK" 2518553 NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-1071 2515844 2516123 2516435 "RULESET" 2517042 NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-1070 2513031 2513534 2513999 "RULE" 2515525 NIL RULE (NIL T T T) -8 NIL NIL NIL) (-1069 2512670 2512825 2512908 "RULECOLD" 2512983 NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-1068 2512460 2512488 2512559 "RTVALUE" 2512621 T RTVALUE (NIL) -8 NIL NIL NIL) (-1067 2511958 2512177 2512271 "RSTRCAST" 2512388 T RSTRCAST (NIL) -8 NIL NIL NIL) (-1066 2506806 2507601 2508521 "RSETGCD" 2511157 NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-1065 2496063 2501115 2501212 "RSETCAT" 2505331 NIL RSETCAT (NIL T T T T) -9 NIL 2506428 NIL) (-1064 2493990 2494529 2495353 "RSETCAT-" 2495358 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-1063 2486375 2487752 2489272 "RSDCMPK" 2492589 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1062 2484380 2484821 2484895 "RRCC" 2485981 NIL RRCC (NIL T T) -9 NIL 2486325 NIL) (-1061 2483731 2483905 2484184 "RRCC-" 2484189 NIL RRCC- (NIL T T T) -8 NIL NIL NIL) (-1060 2483201 2483427 2483528 "RPTAST" 2483652 T RPTAST (NIL) -8 NIL NIL NIL) (-1059 2457199 2466794 2466861 "RPOLCAT" 2477525 NIL RPOLCAT (NIL T T T) -9 NIL 2480684 NIL) (-1058 2448697 2451037 2454159 "RPOLCAT-" 2454164 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL NIL) (-1057 2439744 2446908 2447390 "ROUTINE" 2448237 T ROUTINE (NIL) -8 NIL NIL NIL) (-1056 2436569 2439370 2439510 "ROMAN" 2439626 T ROMAN (NIL) -8 NIL NIL NIL) (-1055 2434840 2435429 2435689 "ROIRC" 2436374 NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-1054 2431225 2433476 2433506 "RNS" 2433810 T RNS (NIL) -9 NIL 2434083 NIL) (-1053 2429734 2430117 2430651 "RNS-" 2430726 NIL RNS- (NIL T) -8 NIL NIL NIL) (-1052 2429183 2429565 2429595 "RNG" 2429600 T RNG (NIL) -9 NIL 2429621 NIL) (-1051 2428575 2428937 2428980 "RMODULE" 2429042 NIL RMODULE (NIL T) -9 NIL 2429084 NIL) (-1050 2427411 2427505 2427841 "RMCAT2" 2428476 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-1049 2424288 2426757 2427054 "RMATRIX" 2427173 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-1048 2417230 2419464 2419579 "RMATCAT" 2422938 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2423920 NIL) (-1047 2416605 2416752 2417059 "RMATCAT-" 2417064 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL NIL) (-1046 2416172 2416247 2416375 "RINTERP" 2416524 NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-1045 2415291 2415819 2415849 "RING" 2415905 T RING (NIL) -9 NIL 2415997 NIL) (-1044 2415083 2415127 2415224 "RING-" 2415229 NIL RING- (NIL T) -8 NIL NIL NIL) (-1043 2413924 2414161 2414419 "RIDIST" 2414847 T RIDIST (NIL) -7 NIL NIL NIL) (-1042 2405240 2413392 2413598 "RGCHAIN" 2413772 NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-1041 2404616 2404996 2405037 "RGBCSPC" 2405095 NIL RGBCSPC (NIL T) -9 NIL 2405147 NIL) (-1040 2403800 2404155 2404196 "RGBCMDL" 2404428 NIL RGBCMDL (NIL T) -9 NIL 2404542 NIL) (-1039 2400794 2401408 2402078 "RF" 2403164 NIL RF (NIL T) -7 NIL NIL NIL) (-1038 2400440 2400503 2400606 "RFFACTOR" 2400725 NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-1037 2400165 2400200 2400297 "RFFACT" 2400399 NIL RFFACT (NIL T) -7 NIL NIL NIL) (-1036 2398282 2398646 2399028 "RFDIST" 2399805 T RFDIST (NIL) -7 NIL NIL NIL) (-1035 2397735 2397827 2397990 "RETSOL" 2398184 NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-1034 2397371 2397451 2397494 "RETRACT" 2397627 NIL RETRACT (NIL T) -9 NIL 2397714 NIL) (-1033 2397220 2397245 2397332 "RETRACT-" 2397337 NIL RETRACT- (NIL T T) -8 NIL NIL NIL) (-1032 2396849 2397042 2397112 "RETAST" 2397172 T RETAST (NIL) -8 NIL NIL NIL) (-1031 2389703 2396502 2396629 "RESULT" 2396744 T RESULT (NIL) -8 NIL NIL NIL) (-1030 2388321 2388972 2389171 "RESRING" 2389606 NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-1029 2387957 2388006 2388104 "RESLATC" 2388258 NIL RESLATC (NIL T) -7 NIL NIL NIL) (-1028 2387662 2387697 2387804 "REPSQ" 2387916 NIL REPSQ (NIL T) -7 NIL NIL NIL) (-1027 2385084 2385664 2386266 "REP" 2387082 T REP (NIL) -7 NIL NIL NIL) (-1026 2384781 2384816 2384927 "REPDB" 2385043 NIL REPDB (NIL T) -7 NIL NIL NIL) (-1025 2378681 2380070 2381293 "REP2" 2383593 NIL REP2 (NIL T) -7 NIL NIL NIL) (-1024 2375058 2375739 2376547 "REP1" 2377908 NIL REP1 (NIL T) -7 NIL NIL NIL) (-1023 2367781 2373199 2373655 "REGSET" 2374688 NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-1022 2366594 2366929 2367179 "REF" 2367566 NIL REF (NIL T) -8 NIL NIL NIL) (-1021 2365971 2366074 2366241 "REDORDER" 2366478 NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-1020 2361966 2365184 2365411 "RECLOS" 2365799 NIL RECLOS (NIL T) -8 NIL NIL NIL) (-1019 2361018 2361199 2361414 "REALSOLV" 2361773 T REALSOLV (NIL) -7 NIL NIL NIL) (-1018 2360864 2360905 2360935 "REAL" 2360940 T REAL (NIL) -9 NIL 2360975 NIL) (-1017 2357347 2358149 2359033 "REAL0Q" 2360029 NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-1016 2352948 2353936 2354997 "REAL0" 2356328 NIL REAL0 (NIL T) -7 NIL NIL NIL) (-1015 2352446 2352665 2352759 "RDUCEAST" 2352876 T RDUCEAST (NIL) -8 NIL NIL NIL) (-1014 2351851 2351923 2352130 "RDIV" 2352368 NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-1013 2350919 2351093 2351306 "RDIST" 2351673 NIL RDIST (NIL T) -7 NIL NIL NIL) (-1012 2349516 2349803 2350175 "RDETRS" 2350627 NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-1011 2347328 2347782 2348320 "RDETR" 2349058 NIL RDETR (NIL T T) -7 NIL NIL NIL) (-1010 2345939 2346217 2346621 "RDEEFS" 2347044 NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-1009 2344434 2344740 2345172 "RDEEF" 2345627 NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-1008 2338687 2341570 2341600 "RCFIELD" 2342895 T RCFIELD (NIL) -9 NIL 2343625 NIL) (-1007 2336751 2337255 2337951 "RCFIELD-" 2338026 NIL RCFIELD- (NIL T) -8 NIL NIL NIL) (-1006 2333067 2334852 2334895 "RCAGG" 2335979 NIL RCAGG (NIL T) -9 NIL 2336444 NIL) (-1005 2332695 2332789 2332952 "RCAGG-" 2332957 NIL RCAGG- (NIL T T) -8 NIL NIL NIL) (-1004 2332030 2332142 2332307 "RATRET" 2332579 NIL RATRET (NIL T) -7 NIL NIL NIL) (-1003 2331583 2331650 2331771 "RATFACT" 2331958 NIL RATFACT (NIL T) -7 NIL NIL NIL) (-1002 2330891 2331011 2331163 "RANDSRC" 2331453 T RANDSRC (NIL) -7 NIL NIL NIL) (-1001 2330625 2330669 2330742 "RADUTIL" 2330840 T RADUTIL (NIL) -7 NIL NIL NIL) (-1000 2323768 2329458 2329768 "RADIX" 2330349 NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-999 2315416 2323612 2323740 "RADFF" 2323745 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-998 2315068 2315143 2315171 "RADCAT" 2315328 T RADCAT (NIL) -9 NIL NIL NIL) (-997 2314853 2314901 2314998 "RADCAT-" 2315003 NIL RADCAT- (NIL T) -8 NIL NIL NIL) (-996 2313004 2314628 2314717 "QUEUE" 2314797 NIL QUEUE (NIL T) -8 NIL NIL NIL) (-995 2309572 2312941 2312986 "QUAT" 2312991 NIL QUAT (NIL T) -8 NIL NIL NIL) (-994 2309210 2309253 2309380 "QUATCT2" 2309523 NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-993 2302949 2306259 2306299 "QUATCAT" 2307079 NIL QUATCAT (NIL T) -9 NIL 2307845 NIL) (-992 2299093 2300130 2301517 "QUATCAT-" 2301611 NIL QUATCAT- (NIL T T) -8 NIL NIL NIL) (-991 2296613 2298177 2298218 "QUAGG" 2298593 NIL QUAGG (NIL T) -9 NIL 2298768 NIL) (-990 2296245 2296438 2296506 "QQUTAST" 2296565 T QQUTAST (NIL) -8 NIL NIL NIL) (-989 2295170 2295643 2295815 "QFORM" 2296117 NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-988 2286374 2291587 2291627 "QFCAT" 2292285 NIL QFCAT (NIL T) -9 NIL 2293286 NIL) (-987 2281946 2283147 2284738 "QFCAT-" 2284832 NIL QFCAT- (NIL T T) -8 NIL NIL NIL) (-986 2281584 2281627 2281754 "QFCAT2" 2281897 NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-985 2281044 2281154 2281284 "QEQUAT" 2281474 T QEQUAT (NIL) -8 NIL NIL NIL) (-984 2274191 2275263 2276447 "QCMPACK" 2279977 NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-983 2271767 2272188 2272616 "QALGSET" 2273846 NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-982 2271012 2271186 2271418 "QALGSET2" 2271587 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-981 2269702 2269926 2270243 "PWFFINTB" 2270785 NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-980 2267884 2268052 2268406 "PUSHVAR" 2269516 NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-979 2263802 2264856 2264897 "PTRANFN" 2266781 NIL PTRANFN (NIL T) -9 NIL NIL NIL) (-978 2262204 2262495 2262817 "PTPACK" 2263513 NIL PTPACK (NIL T) -7 NIL NIL NIL) (-977 2261836 2261893 2262002 "PTFUNC2" 2262141 NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-976 2256363 2260708 2260749 "PTCAT" 2261045 NIL PTCAT (NIL T) -9 NIL 2261198 NIL) (-975 2256021 2256056 2256180 "PSQFR" 2256322 NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-974 2254616 2254914 2255248 "PSEUDLIN" 2255719 NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-973 2241379 2243750 2246074 "PSETPK" 2252376 NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-972 2234423 2237137 2237233 "PSETCAT" 2240254 NIL PSETCAT (NIL T T T T) -9 NIL 2241068 NIL) (-971 2232259 2232893 2233714 "PSETCAT-" 2233719 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL NIL) (-970 2231608 2231773 2231801 "PSCURVE" 2232069 T PSCURVE (NIL) -9 NIL 2232236 NIL) (-969 2227956 2229446 2229511 "PSCAT" 2230355 NIL PSCAT (NIL T T T) -9 NIL 2230595 NIL) (-968 2227019 2227235 2227635 "PSCAT-" 2227640 NIL PSCAT- (NIL T T T T) -8 NIL NIL NIL) (-967 2225751 2226384 2226589 "PRTITION" 2226834 T PRTITION (NIL) -8 NIL NIL NIL) (-966 2225253 2225472 2225564 "PRTDAST" 2225679 T PRTDAST (NIL) -8 NIL NIL NIL) (-965 2214343 2216557 2218745 "PRS" 2223115 NIL PRS (NIL T T) -7 NIL NIL NIL) (-964 2212201 2213693 2213733 "PRQAGG" 2213916 NIL PRQAGG (NIL T) -9 NIL 2214018 NIL) (-963 2211587 2211816 2211844 "PROPLOG" 2212029 T PROPLOG (NIL) -9 NIL 2212151 NIL) (-962 2210095 2210538 2210795 "PROPFRML" 2211363 NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-961 2209564 2209671 2209799 "PROPERTY" 2209987 T PROPERTY (NIL) -8 NIL NIL NIL) (-960 2203649 2207730 2208550 "PRODUCT" 2208790 NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-959 2200954 2203107 2203341 "PR" 2203460 NIL PR (NIL T T) -8 NIL NIL NIL) (-958 2200750 2200782 2200841 "PRINT" 2200915 T PRINT (NIL) -7 NIL NIL NIL) (-957 2200090 2200207 2200359 "PRIMES" 2200630 NIL PRIMES (NIL T) -7 NIL NIL NIL) (-956 2198155 2198556 2199022 "PRIMELT" 2199669 NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-955 2197884 2197933 2197961 "PRIMCAT" 2198085 T PRIMCAT (NIL) -9 NIL NIL NIL) (-954 2194047 2197822 2197867 "PRIMARR" 2197872 NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-953 2193054 2193232 2193460 "PRIMARR2" 2193865 NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-952 2192697 2192753 2192864 "PREASSOC" 2192992 NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-951 2192172 2192305 2192333 "PPCURVE" 2192538 T PPCURVE (NIL) -9 NIL 2192674 NIL) (-950 2191794 2191967 2192050 "PORTNUM" 2192109 T PORTNUM (NIL) -8 NIL NIL NIL) (-949 2189153 2189552 2190144 "POLYROOT" 2191375 NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-948 2183090 2188757 2188917 "POLY" 2189026 NIL POLY (NIL T) -8 NIL NIL NIL) (-947 2182473 2182531 2182765 "POLYLIFT" 2183026 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-946 2178748 2179197 2179826 "POLYCATQ" 2182018 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-945 2165557 2170923 2170988 "POLYCAT" 2174502 NIL POLYCAT (NIL T T T) -9 NIL 2176430 NIL) (-944 2159006 2160868 2163252 "POLYCAT-" 2163257 NIL POLYCAT- (NIL T T T T) -8 NIL NIL NIL) (-943 2158593 2158661 2158781 "POLY2UP" 2158932 NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-942 2158225 2158282 2158391 "POLY2" 2158530 NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-941 2156910 2157149 2157425 "POLUTIL" 2157999 NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-940 2155265 2155542 2155873 "POLTOPOL" 2156632 NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-939 2150780 2155201 2155247 "POINT" 2155252 NIL POINT (NIL T) -8 NIL NIL NIL) (-938 2148967 2149324 2149699 "PNTHEORY" 2150425 T PNTHEORY (NIL) -7 NIL NIL NIL) (-937 2147386 2147683 2148095 "PMTOOLS" 2148665 NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-936 2146979 2147057 2147174 "PMSYM" 2147302 NIL PMSYM (NIL T) -7 NIL NIL NIL) (-935 2146489 2146558 2146732 "PMQFCAT" 2146904 NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-934 2145844 2145954 2146110 "PMPRED" 2146366 NIL PMPRED (NIL T) -7 NIL NIL NIL) (-933 2145240 2145326 2145487 "PMPREDFS" 2145745 NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-932 2143883 2144091 2144476 "PMPLCAT" 2145002 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-931 2143415 2143494 2143646 "PMLSAGG" 2143798 NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-930 2142890 2142966 2143147 "PMKERNEL" 2143333 NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-929 2142507 2142582 2142695 "PMINS" 2142809 NIL PMINS (NIL T) -7 NIL NIL NIL) (-928 2141935 2142004 2142220 "PMFS" 2142432 NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-927 2141163 2141281 2141486 "PMDOWN" 2141812 NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-926 2140330 2140488 2140669 "PMASS" 2141002 T PMASS (NIL) -7 NIL NIL NIL) (-925 2139608 2139718 2139880 "PMASSFS" 2140217 NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-924 2139263 2139331 2139425 "PLOTTOOL" 2139534 T PLOTTOOL (NIL) -7 NIL NIL NIL) (-923 2133870 2135074 2136222 "PLOT" 2138135 T PLOT (NIL) -8 NIL NIL NIL) (-922 2129674 2130718 2131639 "PLOT3D" 2132969 T PLOT3D (NIL) -8 NIL NIL NIL) (-921 2128586 2128763 2128998 "PLOT1" 2129478 NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-920 2103975 2108652 2113503 "PLEQN" 2123852 NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-919 2103293 2103415 2103595 "PINTERP" 2103840 NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-918 2102986 2103033 2103136 "PINTERPA" 2103240 NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-917 2102234 2102755 2102842 "PI" 2102882 T PI (NIL) -8 NIL NIL 2102949) (-916 2100623 2101572 2101600 "PID" 2101782 T PID (NIL) -9 NIL 2101916 NIL) (-915 2100348 2100385 2100473 "PICOERCE" 2100580 NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-914 2099668 2099807 2099983 "PGROEB" 2100204 NIL PGROEB (NIL T) -7 NIL NIL NIL) (-913 2095255 2096069 2096974 "PGE" 2098783 T PGE (NIL) -7 NIL NIL NIL) (-912 2093378 2093625 2093991 "PGCD" 2094972 NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-911 2092716 2092819 2092980 "PFRPAC" 2093262 NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-910 2089384 2091264 2091617 "PFR" 2092395 NIL PFR (NIL T) -8 NIL NIL NIL) (-909 2087773 2088017 2088342 "PFOTOOLS" 2089131 NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-908 2086306 2086545 2086896 "PFOQ" 2087530 NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-907 2084779 2084991 2085354 "PFO" 2086090 NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-906 2081359 2084668 2084737 "PF" 2084742 NIL PF (NIL NIL) -8 NIL NIL NIL) (-905 2078785 2080030 2080058 "PFECAT" 2080643 T PFECAT (NIL) -9 NIL 2081027 NIL) (-904 2078230 2078384 2078598 "PFECAT-" 2078603 NIL PFECAT- (NIL T) -8 NIL NIL NIL) (-903 2076833 2077085 2077386 "PFBRU" 2077979 NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-902 2074698 2075051 2075483 "PFBR" 2076484 NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-901 2070607 2072074 2072750 "PERM" 2074055 NIL PERM (NIL T) -8 NIL NIL NIL) (-900 2065868 2066814 2067684 "PERMGRP" 2069770 NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-899 2064000 2064931 2064972 "PERMCAT" 2065418 NIL PERMCAT (NIL T) -9 NIL 2065723 NIL) (-898 2063653 2063694 2063818 "PERMAN" 2063953 NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-897 2061189 2063318 2063440 "PENDTREE" 2063564 NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-896 2059274 2060016 2060057 "PDRING" 2060714 NIL PDRING (NIL T) -9 NIL 2061000 NIL) (-895 2058377 2058595 2058957 "PDRING-" 2058962 NIL PDRING- (NIL T T) -8 NIL NIL NIL) (-894 2055619 2056370 2057038 "PDEPROB" 2057729 T PDEPROB (NIL) -8 NIL NIL NIL) (-893 2053164 2053668 2054223 "PDEPACK" 2055084 T PDEPACK (NIL) -7 NIL NIL NIL) (-892 2052076 2052266 2052517 "PDECOMP" 2052963 NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-891 2049681 2050498 2050526 "PDECAT" 2051313 T PDECAT (NIL) -9 NIL 2052026 NIL) (-890 2049432 2049465 2049555 "PCOMP" 2049642 NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-889 2047637 2048233 2048530 "PBWLB" 2049161 NIL PBWLB (NIL T) -8 NIL NIL NIL) (-888 2040137 2041710 2043048 "PATTERN" 2046320 NIL PATTERN (NIL T) -8 NIL NIL NIL) (-887 2039769 2039826 2039935 "PATTERN2" 2040074 NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-886 2037526 2037914 2038371 "PATTERN1" 2039358 NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-885 2034921 2035475 2035956 "PATRES" 2037091 NIL PATRES (NIL T T) -8 NIL NIL NIL) (-884 2034485 2034552 2034684 "PATRES2" 2034848 NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-883 2032368 2032773 2033180 "PATMATCH" 2034152 NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-882 2031904 2032087 2032128 "PATMAB" 2032235 NIL PATMAB (NIL T) -9 NIL 2032318 NIL) (-881 2030449 2030758 2031016 "PATLRES" 2031709 NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-880 2029995 2030118 2030159 "PATAB" 2030164 NIL PATAB (NIL T) -9 NIL 2030336 NIL) (-879 2027476 2028008 2028581 "PARTPERM" 2029442 T PARTPERM (NIL) -7 NIL NIL NIL) (-878 2027097 2027160 2027262 "PARSURF" 2027407 NIL PARSURF (NIL T) -8 NIL NIL NIL) (-877 2026729 2026786 2026895 "PARSU2" 2027034 NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-876 2026493 2026533 2026600 "PARSER" 2026682 T PARSER (NIL) -7 NIL NIL NIL) (-875 2026114 2026177 2026279 "PARSCURV" 2026424 NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-874 2025746 2025803 2025912 "PARSC2" 2026051 NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-873 2025385 2025443 2025540 "PARPCURV" 2025682 NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-872 2025017 2025074 2025183 "PARPC2" 2025322 NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-871 2024537 2024623 2024742 "PAN2EXPR" 2024918 T PAN2EXPR (NIL) -7 NIL NIL NIL) (-870 2023341 2023658 2023886 "PALETTE" 2024329 T PALETTE (NIL) -8 NIL NIL NIL) (-869 2021809 2022346 2022706 "PAIR" 2023027 NIL PAIR (NIL T T) -8 NIL NIL NIL) (-868 2015706 2021068 2021262 "PADICRC" 2021664 NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-867 2008962 2015052 2015236 "PADICRAT" 2015554 NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-866 2007304 2008899 2008944 "PADIC" 2008949 NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-865 2004506 2006044 2006084 "PADICCT" 2006665 NIL PADICCT (NIL NIL) -9 NIL 2006947 NIL) (-864 2003463 2003663 2003931 "PADEPAC" 2004293 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-863 2002675 2002808 2003014 "PADE" 2003325 NIL PADE (NIL T T T) -7 NIL NIL NIL) (-862 2001089 2001883 2002163 "OWP" 2002479 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-861 2000609 2000795 2000892 "OVERSET" 2001012 T OVERSET (NIL) -8 NIL NIL NIL) (-860 1999682 2000214 2000386 "OVAR" 2000477 NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-859 1998946 1999067 1999228 "OUT" 1999541 T OUT (NIL) -7 NIL NIL NIL) (-858 1987844 1990055 1992255 "OUTFORM" 1996766 T OUTFORM (NIL) -8 NIL NIL NIL) (-857 1987180 1987441 1987568 "OUTBFILE" 1987737 T OUTBFILE (NIL) -8 NIL NIL NIL) (-856 1986487 1986652 1986680 "OUTBCON" 1986998 T OUTBCON (NIL) -9 NIL 1987164 NIL) (-855 1986088 1986200 1986357 "OUTBCON-" 1986362 NIL OUTBCON- (NIL T) -8 NIL NIL NIL) (-854 1985495 1985817 1985906 "OSI" 1986019 T OSI (NIL) -8 NIL NIL NIL) (-853 1985051 1985363 1985391 "OSGROUP" 1985396 T OSGROUP (NIL) -9 NIL 1985418 NIL) (-852 1983796 1984023 1984308 "ORTHPOL" 1984798 NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-851 1981374 1983631 1983752 "OREUP" 1983757 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-850 1978804 1981065 1981192 "ORESUP" 1981316 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-849 1976332 1976832 1977393 "OREPCTO" 1978293 NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-848 1970148 1972323 1972364 "OREPCAT" 1974712 NIL OREPCAT (NIL T) -9 NIL 1975816 NIL) (-847 1967295 1968077 1969135 "OREPCAT-" 1969140 NIL OREPCAT- (NIL T T) -8 NIL NIL NIL) (-846 1966472 1966744 1966772 "ORDSET" 1967081 T ORDSET (NIL) -9 NIL 1967245 NIL) (-845 1965991 1966113 1966306 "ORDSET-" 1966311 NIL ORDSET- (NIL T) -8 NIL NIL NIL) (-844 1964617 1965382 1965410 "ORDRING" 1965612 T ORDRING (NIL) -9 NIL 1965737 NIL) (-843 1964262 1964356 1964500 "ORDRING-" 1964505 NIL ORDRING- (NIL T) -8 NIL NIL NIL) (-842 1963668 1964105 1964133 "ORDMON" 1964138 T ORDMON (NIL) -9 NIL 1964159 NIL) (-841 1962830 1962977 1963172 "ORDFUNS" 1963517 NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-840 1962194 1962587 1962615 "ORDFIN" 1962680 T ORDFIN (NIL) -9 NIL 1962754 NIL) (-839 1958780 1960780 1961189 "ORDCOMP" 1961818 NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-838 1958046 1958173 1958359 "ORDCOMP2" 1958640 NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-837 1954654 1955537 1956351 "OPTPROB" 1957252 T OPTPROB (NIL) -8 NIL NIL NIL) (-836 1951456 1952095 1952799 "OPTPACK" 1953970 T OPTPACK (NIL) -7 NIL NIL NIL) (-835 1949169 1949909 1949937 "OPTCAT" 1950756 T OPTCAT (NIL) -9 NIL 1951406 NIL) (-834 1948612 1948846 1948951 "OPSIG" 1949084 T OPSIG (NIL) -8 NIL NIL NIL) (-833 1948380 1948419 1948485 "OPQUERY" 1948566 T OPQUERY (NIL) -7 NIL NIL NIL) (-832 1945538 1946691 1947195 "OP" 1947909 NIL OP (NIL T) -8 NIL NIL NIL) (-831 1945073 1945244 1945285 "OPERCAT" 1945420 NIL OPERCAT (NIL T) -9 NIL 1945488 NIL) (-830 1944919 1944946 1945032 "OPERCAT-" 1945037 NIL OPERCAT- (NIL T T) -8 NIL NIL NIL) (-829 1941758 1943716 1944085 "ONECOMP" 1944583 NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-828 1941063 1941178 1941352 "ONECOMP2" 1941630 NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-827 1940482 1940588 1940718 "OMSERVER" 1940953 T OMSERVER (NIL) -7 NIL NIL NIL) (-826 1937370 1939922 1939962 "OMSAGG" 1940023 NIL OMSAGG (NIL T) -9 NIL 1940087 NIL) (-825 1935993 1936256 1936538 "OMPKG" 1937108 T OMPKG (NIL) -7 NIL NIL NIL) (-824 1935423 1935526 1935554 "OM" 1935853 T OM (NIL) -9 NIL NIL NIL) (-823 1933997 1934972 1935141 "OMLO" 1935304 NIL OMLO (NIL T T) -8 NIL NIL NIL) (-822 1932922 1933069 1933296 "OMEXPR" 1933823 NIL OMEXPR (NIL T) -7 NIL NIL NIL) (-821 1932240 1932468 1932604 "OMERR" 1932806 T OMERR (NIL) -8 NIL NIL NIL) (-820 1931418 1931661 1931821 "OMERRK" 1932100 T OMERRK (NIL) -8 NIL NIL NIL) (-819 1930896 1931095 1931203 "OMENC" 1931330 T OMENC (NIL) -8 NIL NIL NIL) (-818 1924791 1925976 1927147 "OMDEV" 1929745 T OMDEV (NIL) -8 NIL NIL NIL) (-817 1923860 1924031 1924225 "OMCONN" 1924617 T OMCONN (NIL) -8 NIL NIL NIL) (-816 1922473 1923423 1923451 "OINTDOM" 1923456 T OINTDOM (NIL) -9 NIL 1923477 NIL) (-815 1918279 1919463 1920179 "OFMONOID" 1921789 NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-814 1917717 1918216 1918261 "ODVAR" 1918266 NIL ODVAR (NIL T) -8 NIL NIL NIL) (-813 1915167 1917462 1917617 "ODR" 1917622 NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-812 1907503 1914943 1915069 "ODPOL" 1915074 NIL ODPOL (NIL T) -8 NIL NIL NIL) (-811 1901373 1907375 1907480 "ODP" 1907485 NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-810 1900139 1900354 1900629 "ODETOOLS" 1901147 NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-809 1897106 1897764 1898480 "ODESYS" 1899472 NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-808 1891988 1892896 1893921 "ODERTRIC" 1896181 NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-807 1891414 1891496 1891690 "ODERED" 1891900 NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-806 1888302 1888850 1889527 "ODERAT" 1890837 NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-805 1885259 1885726 1886323 "ODEPRRIC" 1887831 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-804 1883229 1883798 1884284 "ODEPROB" 1884793 T ODEPROB (NIL) -8 NIL NIL NIL) (-803 1879749 1880234 1880881 "ODEPRIM" 1882708 NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-802 1878998 1879100 1879360 "ODEPAL" 1879641 NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-801 1875160 1875951 1876815 "ODEPACK" 1878154 T ODEPACK (NIL) -7 NIL NIL NIL) (-800 1874193 1874300 1874529 "ODEINT" 1875049 NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-799 1868294 1869719 1871166 "ODEIFTBL" 1872766 T ODEIFTBL (NIL) -8 NIL NIL NIL) (-798 1863629 1864415 1865374 "ODEEF" 1867453 NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-797 1862964 1863053 1863283 "ODECONST" 1863534 NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-796 1861115 1861750 1861778 "ODECAT" 1862383 T ODECAT (NIL) -9 NIL 1862914 NIL) (-795 1858014 1860827 1860946 "OCT" 1861028 NIL OCT (NIL T) -8 NIL NIL NIL) (-794 1857652 1857695 1857822 "OCTCT2" 1857965 NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-793 1852418 1854826 1854866 "OC" 1855963 NIL OC (NIL T) -9 NIL 1856821 NIL) (-792 1849645 1850393 1851383 "OC-" 1851477 NIL OC- (NIL T T) -8 NIL NIL NIL) (-791 1849023 1849465 1849493 "OCAMON" 1849498 T OCAMON (NIL) -9 NIL 1849519 NIL) (-790 1848580 1848895 1848923 "OASGP" 1848928 T OASGP (NIL) -9 NIL 1848948 NIL) (-789 1847867 1848330 1848358 "OAMONS" 1848398 T OAMONS (NIL) -9 NIL 1848441 NIL) (-788 1847307 1847714 1847742 "OAMON" 1847747 T OAMON (NIL) -9 NIL 1847767 NIL) (-787 1846611 1847103 1847131 "OAGROUP" 1847136 T OAGROUP (NIL) -9 NIL 1847156 NIL) (-786 1846301 1846351 1846439 "NUMTUBE" 1846555 NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-785 1839874 1841392 1842928 "NUMQUAD" 1844785 T NUMQUAD (NIL) -7 NIL NIL NIL) (-784 1835630 1836618 1837643 "NUMODE" 1838869 T NUMODE (NIL) -7 NIL NIL NIL) (-783 1833011 1833865 1833893 "NUMINT" 1834816 T NUMINT (NIL) -9 NIL 1835580 NIL) (-782 1831959 1832156 1832374 "NUMFMT" 1832813 T NUMFMT (NIL) -7 NIL NIL NIL) (-781 1818318 1821263 1823795 "NUMERIC" 1829466 NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-780 1812715 1817767 1817862 "NTSCAT" 1817867 NIL NTSCAT (NIL T T T T) -9 NIL 1817906 NIL) (-779 1811909 1812074 1812267 "NTPOLFN" 1812554 NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-778 1799741 1808734 1809546 "NSUP" 1811130 NIL NSUP (NIL T) -8 NIL NIL NIL) (-777 1799373 1799430 1799539 "NSUP2" 1799678 NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-776 1789356 1799147 1799280 "NSMP" 1799285 NIL NSMP (NIL T T) -8 NIL NIL NIL) (-775 1787788 1788089 1788446 "NREP" 1789044 NIL NREP (NIL T) -7 NIL NIL NIL) (-774 1786379 1786631 1786989 "NPCOEF" 1787531 NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-773 1785445 1785560 1785776 "NORMRETR" 1786260 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-772 1783486 1783776 1784185 "NORMPK" 1785153 NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-771 1783171 1783199 1783323 "NORMMA" 1783452 NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-770 1782998 1783128 1783157 "NONE" 1783162 T NONE (NIL) -8 NIL NIL NIL) (-769 1782787 1782816 1782885 "NONE1" 1782962 NIL NONE1 (NIL T) -7 NIL NIL NIL) (-768 1782270 1782332 1782518 "NODE1" 1782719 NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-767 1780540 1781364 1781619 "NNI" 1781966 T NNI (NIL) -8 NIL NIL 1782201) (-766 1778960 1779273 1779637 "NLINSOL" 1780208 NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-765 1775228 1776196 1777095 "NIPROB" 1778081 T NIPROB (NIL) -8 NIL NIL NIL) (-764 1773985 1774219 1774521 "NFINTBAS" 1774990 NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-763 1773159 1773635 1773676 "NETCLT" 1773848 NIL NETCLT (NIL T) -9 NIL 1773930 NIL) (-762 1771867 1772098 1772379 "NCODIV" 1772927 NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-761 1771629 1771666 1771741 "NCNTFRAC" 1771824 NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-760 1769809 1770173 1770593 "NCEP" 1771254 NIL NCEP (NIL T) -7 NIL NIL NIL) (-759 1768706 1769453 1769481 "NASRING" 1769591 T NASRING (NIL) -9 NIL 1769671 NIL) (-758 1768501 1768545 1768639 "NASRING-" 1768644 NIL NASRING- (NIL T) -8 NIL NIL NIL) (-757 1767654 1768153 1768181 "NARNG" 1768298 T NARNG (NIL) -9 NIL 1768389 NIL) (-756 1767346 1767413 1767547 "NARNG-" 1767552 NIL NARNG- (NIL T) -8 NIL NIL NIL) (-755 1766225 1766432 1766667 "NAGSP" 1767131 T NAGSP (NIL) -7 NIL NIL NIL) (-754 1757497 1759181 1760854 "NAGS" 1764572 T NAGS (NIL) -7 NIL NIL NIL) (-753 1756045 1756353 1756684 "NAGF07" 1757186 T NAGF07 (NIL) -7 NIL NIL NIL) (-752 1750583 1751874 1753181 "NAGF04" 1754758 T NAGF04 (NIL) -7 NIL NIL NIL) (-751 1743551 1745165 1746798 "NAGF02" 1748970 T NAGF02 (NIL) -7 NIL NIL NIL) (-750 1738775 1739875 1740992 "NAGF01" 1742454 T NAGF01 (NIL) -7 NIL NIL NIL) (-749 1732403 1733969 1735554 "NAGE04" 1737210 T NAGE04 (NIL) -7 NIL NIL NIL) (-748 1723572 1725693 1727823 "NAGE02" 1730293 T NAGE02 (NIL) -7 NIL NIL NIL) (-747 1719525 1720472 1721436 "NAGE01" 1722628 T NAGE01 (NIL) -7 NIL NIL NIL) (-746 1717320 1717854 1718412 "NAGD03" 1718987 T NAGD03 (NIL) -7 NIL NIL NIL) (-745 1709070 1710998 1712952 "NAGD02" 1715386 T NAGD02 (NIL) -7 NIL NIL NIL) (-744 1702881 1704306 1705746 "NAGD01" 1707650 T NAGD01 (NIL) -7 NIL NIL NIL) (-743 1699090 1699912 1700749 "NAGC06" 1702064 T NAGC06 (NIL) -7 NIL NIL NIL) (-742 1697555 1697887 1698243 "NAGC05" 1698754 T NAGC05 (NIL) -7 NIL NIL NIL) (-741 1696931 1697050 1697194 "NAGC02" 1697431 T NAGC02 (NIL) -7 NIL NIL NIL) (-740 1695991 1696548 1696588 "NAALG" 1696667 NIL NAALG (NIL T) -9 NIL 1696728 NIL) (-739 1695826 1695855 1695945 "NAALG-" 1695950 NIL NAALG- (NIL T T) -8 NIL NIL NIL) (-738 1689776 1690884 1692071 "MULTSQFR" 1694722 NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-737 1689095 1689170 1689354 "MULTFACT" 1689688 NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-736 1682180 1686058 1686111 "MTSCAT" 1687181 NIL MTSCAT (NIL T T) -9 NIL 1687695 NIL) (-735 1681892 1681946 1682038 "MTHING" 1682120 NIL MTHING (NIL T) -7 NIL NIL NIL) (-734 1681684 1681717 1681777 "MSYSCMD" 1681852 T MSYSCMD (NIL) -7 NIL NIL NIL) (-733 1677793 1680439 1680759 "MSET" 1681397 NIL MSET (NIL T) -8 NIL NIL NIL) (-732 1674888 1677354 1677395 "MSETAGG" 1677400 NIL MSETAGG (NIL T) -9 NIL 1677434 NIL) (-731 1670756 1672267 1673012 "MRING" 1674188 NIL MRING (NIL T T) -8 NIL NIL NIL) (-730 1670322 1670389 1670520 "MRF2" 1670683 NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-729 1669940 1669975 1670119 "MRATFAC" 1670281 NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-728 1667552 1667847 1668278 "MPRFF" 1669645 NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-727 1661604 1667406 1667503 "MPOLY" 1667508 NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-726 1661094 1661129 1661337 "MPCPF" 1661563 NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-725 1660608 1660651 1660835 "MPC3" 1661045 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-724 1659803 1659884 1660105 "MPC2" 1660523 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-723 1658104 1658441 1658831 "MONOTOOL" 1659463 NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-722 1657355 1657646 1657674 "MONOID" 1657893 T MONOID (NIL) -9 NIL 1658040 NIL) (-721 1656901 1657020 1657201 "MONOID-" 1657206 NIL MONOID- (NIL T) -8 NIL NIL NIL) (-720 1647752 1653668 1653727 "MONOGEN" 1654401 NIL MONOGEN (NIL T T) -9 NIL 1654857 NIL) (-719 1644970 1645705 1646705 "MONOGEN-" 1646824 NIL MONOGEN- (NIL T T T) -8 NIL NIL NIL) (-718 1643829 1644249 1644277 "MONADWU" 1644669 T MONADWU (NIL) -9 NIL 1644907 NIL) (-717 1643201 1643360 1643608 "MONADWU-" 1643613 NIL MONADWU- (NIL T) -8 NIL NIL NIL) (-716 1642586 1642804 1642832 "MONAD" 1643039 T MONAD (NIL) -9 NIL 1643151 NIL) (-715 1642271 1642349 1642481 "MONAD-" 1642486 NIL MONAD- (NIL T) -8 NIL NIL NIL) (-714 1640587 1641184 1641463 "MOEBIUS" 1642024 NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-713 1639979 1640357 1640397 "MODULE" 1640402 NIL MODULE (NIL T) -9 NIL 1640428 NIL) (-712 1639547 1639643 1639833 "MODULE-" 1639838 NIL MODULE- (NIL T T) -8 NIL NIL NIL) (-711 1637254 1637911 1638238 "MODRING" 1639371 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-710 1634225 1635359 1635880 "MODOP" 1636783 NIL MODOP (NIL T T) -8 NIL NIL NIL) (-709 1632840 1633292 1633569 "MODMONOM" 1634088 NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-708 1622637 1631131 1631545 "MODMON" 1632477 NIL MODMON (NIL T T) -8 NIL NIL NIL) (-707 1619820 1621481 1621757 "MODFIELD" 1622512 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-706 1618824 1619101 1619291 "MMLFORM" 1619650 T MMLFORM (NIL) -8 NIL NIL NIL) (-705 1618350 1618393 1618572 "MMAP" 1618775 NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-704 1616559 1617300 1617341 "MLO" 1617764 NIL MLO (NIL T) -9 NIL 1618006 NIL) (-703 1613925 1614441 1615043 "MLIFT" 1616040 NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-702 1613316 1613400 1613554 "MKUCFUNC" 1613836 NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-701 1612915 1612985 1613108 "MKRECORD" 1613239 NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-700 1611962 1612124 1612352 "MKFUNC" 1612726 NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-699 1611350 1611454 1611610 "MKFLCFN" 1611845 NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-698 1610627 1610729 1610914 "MKBCFUNC" 1611243 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-697 1607361 1610181 1610317 "MINT" 1610511 T MINT (NIL) -8 NIL NIL NIL) (-696 1606173 1606416 1606693 "MHROWRED" 1607116 NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-695 1601580 1604708 1605113 "MFLOAT" 1605788 T MFLOAT (NIL) -8 NIL NIL NIL) (-694 1600937 1601013 1601184 "MFINFACT" 1601492 NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-693 1597252 1598100 1598984 "MESH" 1600073 T MESH (NIL) -7 NIL NIL NIL) (-692 1595642 1595954 1596307 "MDDFACT" 1596939 NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-691 1592484 1594801 1594842 "MDAGG" 1595097 NIL MDAGG (NIL T) -9 NIL 1595240 NIL) (-690 1582254 1591777 1591984 "MCMPLX" 1592297 T MCMPLX (NIL) -8 NIL NIL NIL) (-689 1581395 1581541 1581741 "MCDEN" 1582103 NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-688 1579285 1579555 1579935 "MCALCFN" 1581125 NIL MCALCFN (NIL T T T T) -7 NIL NIL NIL) (-687 1578210 1578450 1578683 "MAYBE" 1579091 NIL MAYBE (NIL T) -8 NIL NIL NIL) (-686 1575822 1576345 1576907 "MATSTOR" 1577681 NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-685 1571827 1575194 1575442 "MATRIX" 1575607 NIL MATRIX (NIL T) -8 NIL NIL NIL) (-684 1567591 1568300 1569036 "MATLIN" 1571184 NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-683 1557745 1560883 1560960 "MATCAT" 1565840 NIL MATCAT (NIL T T T) -9 NIL 1567257 NIL) (-682 1554101 1555122 1556478 "MATCAT-" 1556483 NIL MATCAT- (NIL T T T T) -8 NIL NIL NIL) (-681 1552695 1552848 1553181 "MATCAT2" 1553936 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-680 1550807 1551131 1551515 "MAPPKG3" 1552370 NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-679 1549788 1549961 1550183 "MAPPKG2" 1550631 NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-678 1548287 1548571 1548898 "MAPPKG1" 1549494 NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-677 1547393 1547693 1547870 "MAPPAST" 1548130 T MAPPAST (NIL) -8 NIL NIL NIL) (-676 1547004 1547062 1547185 "MAPHACK3" 1547329 NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-675 1546596 1546657 1546771 "MAPHACK2" 1546936 NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-674 1546033 1546137 1546279 "MAPHACK1" 1546487 NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-673 1544139 1544733 1545037 "MAGMA" 1545761 NIL MAGMA (NIL T) -8 NIL NIL NIL) (-672 1543645 1543863 1543954 "MACROAST" 1544068 T MACROAST (NIL) -8 NIL NIL NIL) (-671 1540111 1541884 1542345 "M3D" 1543217 NIL M3D (NIL T) -8 NIL NIL NIL) (-670 1534265 1538480 1538521 "LZSTAGG" 1539303 NIL LZSTAGG (NIL T) -9 NIL 1539598 NIL) (-669 1530222 1531396 1532853 "LZSTAGG-" 1532858 NIL LZSTAGG- (NIL T T) -8 NIL NIL NIL) (-668 1527336 1528113 1528600 "LWORD" 1529767 NIL LWORD (NIL T) -8 NIL NIL NIL) (-667 1526939 1527140 1527215 "LSTAST" 1527281 T LSTAST (NIL) -8 NIL NIL NIL) (-666 1520132 1526710 1526844 "LSQM" 1526849 NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-665 1519356 1519495 1519723 "LSPP" 1519987 NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-664 1517168 1517469 1517925 "LSMP" 1519045 NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-663 1513947 1514621 1515351 "LSMP1" 1516470 NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-662 1507872 1513114 1513155 "LSAGG" 1513217 NIL LSAGG (NIL T) -9 NIL 1513295 NIL) (-661 1504567 1505491 1506704 "LSAGG-" 1506709 NIL LSAGG- (NIL T T) -8 NIL NIL NIL) (-660 1502193 1503711 1503960 "LPOLY" 1504362 NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-659 1501775 1501860 1501983 "LPEFRAC" 1502102 NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-658 1500122 1500869 1501122 "LO" 1501607 NIL LO (NIL T T T) -8 NIL NIL NIL) (-657 1499774 1499886 1499914 "LOGIC" 1500025 T LOGIC (NIL) -9 NIL 1500106 NIL) (-656 1499636 1499659 1499730 "LOGIC-" 1499735 NIL LOGIC- (NIL T) -8 NIL NIL NIL) (-655 1498829 1498969 1499162 "LODOOPS" 1499492 NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-654 1496279 1498745 1498811 "LODO" 1498816 NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-653 1494817 1495052 1495405 "LODOF" 1496026 NIL LODOF (NIL T T) -7 NIL NIL NIL) (-652 1491165 1493570 1493611 "LODOCAT" 1494049 NIL LODOCAT (NIL T) -9 NIL 1494260 NIL) (-651 1490898 1490956 1491083 "LODOCAT-" 1491088 NIL LODOCAT- (NIL T T) -8 NIL NIL NIL) (-650 1488245 1490739 1490857 "LODO2" 1490862 NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-649 1485707 1488182 1488227 "LODO1" 1488232 NIL LODO1 (NIL T) -8 NIL NIL NIL) (-648 1484567 1484732 1485044 "LODEEF" 1485530 NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-647 1479853 1482697 1482738 "LNAGG" 1483685 NIL LNAGG (NIL T) -9 NIL 1484129 NIL) (-646 1479000 1479214 1479556 "LNAGG-" 1479561 NIL LNAGG- (NIL T T) -8 NIL NIL NIL) (-645 1475163 1475925 1476564 "LMOPS" 1478415 NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-644 1474558 1474920 1474961 "LMODULE" 1475022 NIL LMODULE (NIL T) -9 NIL 1475064 NIL) (-643 1471804 1474203 1474326 "LMDICT" 1474468 NIL LMDICT (NIL T) -8 NIL NIL NIL) (-642 1471530 1471712 1471772 "LITERAL" 1471777 NIL LITERAL (NIL T) -8 NIL NIL NIL) (-641 1464761 1470476 1470774 "LIST" 1471265 NIL LIST (NIL T) -8 NIL NIL NIL) (-640 1464286 1464360 1464499 "LIST3" 1464681 NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-639 1463293 1463471 1463699 "LIST2" 1464104 NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-638 1461427 1461739 1462138 "LIST2MAP" 1462940 NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-637 1460149 1460793 1460834 "LINEXP" 1461089 NIL LINEXP (NIL T) -9 NIL 1461238 NIL) (-636 1458796 1459056 1459353 "LINDEP" 1459901 NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-635 1455563 1456282 1457059 "LIMITRF" 1458051 NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-634 1453838 1454134 1454550 "LIMITPS" 1455258 NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-633 1448293 1453349 1453577 "LIE" 1453659 NIL LIE (NIL T T) -8 NIL NIL NIL) (-632 1447342 1447785 1447825 "LIECAT" 1447965 NIL LIECAT (NIL T) -9 NIL 1448116 NIL) (-631 1447183 1447210 1447298 "LIECAT-" 1447303 NIL LIECAT- (NIL T T) -8 NIL NIL NIL) (-630 1439795 1446632 1446797 "LIB" 1447038 T LIB (NIL) -8 NIL NIL NIL) (-629 1435430 1436313 1437248 "LGROBP" 1438912 NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-628 1433296 1433570 1433932 "LF" 1435151 NIL LF (NIL T T) -7 NIL NIL NIL) (-627 1432136 1432828 1432856 "LFCAT" 1433063 T LFCAT (NIL) -9 NIL 1433202 NIL) (-626 1429038 1429668 1430356 "LEXTRIPK" 1431500 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-625 1425809 1426608 1427111 "LEXP" 1428618 NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-624 1425312 1425530 1425622 "LETAST" 1425737 T LETAST (NIL) -8 NIL NIL NIL) (-623 1423710 1424023 1424424 "LEADCDET" 1424994 NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-622 1422900 1422974 1423203 "LAZM3PK" 1423631 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-621 1417844 1420977 1421515 "LAUPOL" 1422412 NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-620 1417409 1417453 1417621 "LAPLACE" 1417794 NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-619 1415375 1416510 1416761 "LA" 1417242 NIL LA (NIL T T T) -8 NIL NIL NIL) (-618 1414448 1415006 1415047 "LALG" 1415109 NIL LALG (NIL T) -9 NIL 1415168 NIL) (-617 1414162 1414221 1414357 "LALG-" 1414362 NIL LALG- (NIL T T) -8 NIL NIL NIL) (-616 1413997 1414021 1414062 "KVTFROM" 1414124 NIL KVTFROM (NIL T) -9 NIL NIL NIL) (-615 1412797 1413214 1413443 "KTVLOGIC" 1413788 T KTVLOGIC (NIL) -8 NIL NIL NIL) (-614 1412632 1412656 1412697 "KRCFROM" 1412759 NIL KRCFROM (NIL T) -9 NIL NIL NIL) (-613 1411536 1411723 1412022 "KOVACIC" 1412432 NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-612 1411371 1411395 1411436 "KONVERT" 1411498 NIL KONVERT (NIL T) -9 NIL NIL NIL) (-611 1411206 1411230 1411271 "KOERCE" 1411333 NIL KOERCE (NIL T) -9 NIL NIL NIL) (-610 1408939 1409700 1410093 "KERNEL" 1410845 NIL KERNEL (NIL T) -8 NIL NIL NIL) (-609 1408441 1408522 1408652 "KERNEL2" 1408853 NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-608 1402292 1406980 1407034 "KDAGG" 1407411 NIL KDAGG (NIL T T) -9 NIL 1407617 NIL) (-607 1401821 1401945 1402150 "KDAGG-" 1402155 NIL KDAGG- (NIL T T T) -8 NIL NIL NIL) (-606 1394996 1401482 1401637 "KAFILE" 1401699 NIL KAFILE (NIL T) -8 NIL NIL NIL) (-605 1389451 1394507 1394735 "JORDAN" 1394817 NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-604 1388857 1389100 1389221 "JOINAST" 1389350 T JOINAST (NIL) -8 NIL NIL NIL) (-603 1388703 1388762 1388817 "JAVACODE" 1388822 T JAVACODE (NIL) -8 NIL NIL NIL) (-602 1385002 1386908 1386962 "IXAGG" 1387891 NIL IXAGG (NIL T T) -9 NIL 1388350 NIL) (-601 1383921 1384227 1384646 "IXAGG-" 1384651 NIL IXAGG- (NIL T T T) -8 NIL NIL NIL) (-600 1379501 1383843 1383902 "IVECTOR" 1383907 NIL IVECTOR (NIL T NIL) -8 NIL NIL NIL) (-599 1378267 1378504 1378770 "ITUPLE" 1379268 NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-598 1376703 1376880 1377186 "ITRIGMNP" 1378089 NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-597 1375448 1375652 1375935 "ITFUN3" 1376479 NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-596 1375080 1375137 1375246 "ITFUN2" 1375385 NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-595 1372909 1373942 1374241 "ITAYLOR" 1374814 NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-594 1361881 1367046 1368209 "ISUPS" 1371779 NIL ISUPS (NIL T) -8 NIL NIL NIL) (-593 1360985 1361125 1361361 "ISUMP" 1361728 NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-592 1356249 1360786 1360865 "ISTRING" 1360938 NIL ISTRING (NIL NIL) -8 NIL NIL NIL) (-591 1355752 1355970 1356062 "ISAST" 1356177 T ISAST (NIL) -8 NIL NIL NIL) (-590 1354962 1355043 1355259 "IRURPK" 1355666 NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-589 1353898 1354099 1354339 "IRSN" 1354742 T IRSN (NIL) -7 NIL NIL NIL) (-588 1351927 1352282 1352718 "IRRF2F" 1353536 NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-587 1351674 1351712 1351788 "IRREDFFX" 1351883 NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-586 1350289 1350548 1350847 "IROOT" 1351407 NIL IROOT (NIL T) -7 NIL NIL NIL) (-585 1346920 1347973 1348665 "IR" 1349629 NIL IR (NIL T) -8 NIL NIL NIL) (-584 1344533 1345028 1345594 "IR2" 1346398 NIL IR2 (NIL T T) -7 NIL NIL NIL) (-583 1343605 1343718 1343939 "IR2F" 1344416 NIL IR2F (NIL T T) -7 NIL NIL NIL) (-582 1343396 1343430 1343490 "IPRNTPK" 1343565 T IPRNTPK (NIL) -7 NIL NIL NIL) (-581 1340003 1343285 1343354 "IPF" 1343359 NIL IPF (NIL NIL) -8 NIL NIL NIL) (-580 1338357 1339928 1339985 "IPADIC" 1339990 NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-579 1337696 1337917 1338047 "IP4ADDR" 1338247 T IP4ADDR (NIL) -8 NIL NIL NIL) (-578 1337196 1337400 1337510 "IOMODE" 1337606 T IOMODE (NIL) -8 NIL NIL NIL) (-577 1336269 1336793 1336920 "IOBFILE" 1337089 T IOBFILE (NIL) -8 NIL NIL NIL) (-576 1335757 1336173 1336201 "IOBCON" 1336206 T IOBCON (NIL) -9 NIL 1336227 NIL) (-575 1335254 1335312 1335502 "INVLAPLA" 1335693 NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-574 1324902 1327256 1329642 "INTTR" 1332918 NIL INTTR (NIL T T) -7 NIL NIL NIL) (-573 1321246 1321988 1322852 "INTTOOLS" 1324087 NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-572 1320832 1320923 1321040 "INTSLPE" 1321149 T INTSLPE (NIL) -7 NIL NIL NIL) (-571 1318813 1320755 1320814 "INTRVL" 1320819 NIL INTRVL (NIL T) -8 NIL NIL NIL) (-570 1316415 1316927 1317502 "INTRF" 1318298 NIL INTRF (NIL T) -7 NIL NIL NIL) (-569 1315826 1315923 1316065 "INTRET" 1316313 NIL INTRET (NIL T) -7 NIL NIL NIL) (-568 1313823 1314212 1314682 "INTRAT" 1315434 NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-567 1311051 1311634 1312260 "INTPM" 1313308 NIL INTPM (NIL T T) -7 NIL NIL NIL) (-566 1307753 1308353 1309098 "INTPAF" 1310437 NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-565 1302932 1303894 1304945 "INTPACK" 1306722 T INTPACK (NIL) -7 NIL NIL NIL) (-564 1299836 1302661 1302788 "INT" 1302825 T INT (NIL) -8 NIL NIL NIL) (-563 1299088 1299240 1299448 "INTHERTR" 1299678 NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-562 1298527 1298607 1298795 "INTHERAL" 1299002 NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-561 1296373 1296816 1297273 "INTHEORY" 1298090 T INTHEORY (NIL) -7 NIL NIL NIL) (-560 1287681 1289302 1291081 "INTG0" 1294725 NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-559 1268254 1273044 1277854 "INTFTBL" 1282891 T INTFTBL (NIL) -8 NIL NIL NIL) (-558 1267503 1267641 1267814 "INTFACT" 1268113 NIL INTFACT (NIL T) -7 NIL NIL NIL) (-557 1264888 1265334 1265898 "INTEF" 1267057 NIL INTEF (NIL T T) -7 NIL NIL NIL) (-556 1263347 1264060 1264088 "INTDOM" 1264389 T INTDOM (NIL) -9 NIL 1264596 NIL) (-555 1262716 1262890 1263132 "INTDOM-" 1263137 NIL INTDOM- (NIL T) -8 NIL NIL NIL) (-554 1259203 1261100 1261154 "INTCAT" 1261953 NIL INTCAT (NIL T) -9 NIL 1262273 NIL) (-553 1258675 1258778 1258906 "INTBIT" 1259095 T INTBIT (NIL) -7 NIL NIL NIL) (-552 1257346 1257500 1257814 "INTALG" 1258520 NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-551 1256803 1256893 1257063 "INTAF" 1257250 NIL INTAF (NIL T T) -7 NIL NIL NIL) (-550 1250257 1256613 1256753 "INTABL" 1256758 NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-549 1249588 1250027 1250092 "INT8" 1250126 T INT8 (NIL) -8 NIL NIL 1250171) (-548 1248918 1249357 1249422 "INT64" 1249456 T INT64 (NIL) -8 NIL NIL 1249501) (-547 1248248 1248687 1248752 "INT32" 1248786 T INT32 (NIL) -8 NIL NIL 1248831) (-546 1247578 1248017 1248082 "INT16" 1248116 T INT16 (NIL) -8 NIL NIL 1248161) (-545 1242585 1245267 1245295 "INS" 1246229 T INS (NIL) -9 NIL 1246894 NIL) (-544 1239825 1240596 1241570 "INS-" 1241643 NIL INS- (NIL T) -8 NIL NIL NIL) (-543 1238600 1238827 1239125 "INPSIGN" 1239578 NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-542 1237718 1237835 1238032 "INPRODPF" 1238480 NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-541 1236612 1236729 1236966 "INPRODFF" 1237598 NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-540 1235612 1235764 1236024 "INNMFACT" 1236448 NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-539 1234809 1234906 1235094 "INMODGCD" 1235511 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-538 1233317 1233562 1233886 "INFSP" 1234554 NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-537 1232501 1232618 1232801 "INFPROD0" 1233197 NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-536 1229383 1230566 1231081 "INFORM" 1231994 T INFORM (NIL) -8 NIL NIL NIL) (-535 1228993 1229053 1229151 "INFORM1" 1229318 NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-534 1228516 1228605 1228719 "INFINITY" 1228899 T INFINITY (NIL) -7 NIL NIL NIL) (-533 1227692 1228236 1228337 "INETCLTS" 1228435 T INETCLTS (NIL) -8 NIL NIL NIL) (-532 1226308 1226558 1226879 "INEP" 1227440 NIL INEP (NIL T T T) -7 NIL NIL NIL) (-531 1225584 1226205 1226270 "INDE" 1226275 NIL INDE (NIL T) -8 NIL NIL NIL) (-530 1225148 1225216 1225333 "INCRMAPS" 1225511 NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-529 1223966 1224417 1224623 "INBFILE" 1224962 T INBFILE (NIL) -8 NIL NIL NIL) (-528 1219266 1220202 1221146 "INBFF" 1223054 NIL INBFF (NIL T) -7 NIL NIL NIL) (-527 1218174 1218443 1218471 "INBCON" 1218984 T INBCON (NIL) -9 NIL 1219250 NIL) (-526 1217426 1217649 1217925 "INBCON-" 1217930 NIL INBCON- (NIL T) -8 NIL NIL NIL) (-525 1216932 1217150 1217241 "INAST" 1217355 T INAST (NIL) -8 NIL NIL NIL) (-524 1216386 1216611 1216717 "IMPTAST" 1216846 T IMPTAST (NIL) -8 NIL NIL NIL) (-523 1212880 1216230 1216334 "IMATRIX" 1216339 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL NIL) (-522 1211592 1211715 1212030 "IMATQF" 1212736 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-521 1209812 1210039 1210376 "IMATLIN" 1211348 NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-520 1204438 1209736 1209794 "ILIST" 1209799 NIL ILIST (NIL T NIL) -8 NIL NIL NIL) (-519 1202391 1204298 1204411 "IIARRAY2" 1204416 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL NIL) (-518 1197816 1202302 1202366 "IFF" 1202371 NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-517 1197190 1197433 1197549 "IFAST" 1197720 T IFAST (NIL) -8 NIL NIL NIL) (-516 1192233 1196482 1196670 "IFARRAY" 1197047 NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-515 1191440 1192137 1192210 "IFAMON" 1192215 NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-514 1191024 1191089 1191143 "IEVALAB" 1191350 NIL IEVALAB (NIL T T) -9 NIL NIL NIL) (-513 1190699 1190767 1190927 "IEVALAB-" 1190932 NIL IEVALAB- (NIL T T T) -8 NIL NIL NIL) (-512 1190357 1190613 1190676 "IDPO" 1190681 NIL IDPO (NIL T T) -8 NIL NIL NIL) (-511 1189634 1190246 1190321 "IDPOAMS" 1190326 NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-510 1188968 1189523 1189598 "IDPOAM" 1189603 NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-509 1188053 1188303 1188356 "IDPC" 1188769 NIL IDPC (NIL T T) -9 NIL 1188918 NIL) (-508 1187549 1187945 1188018 "IDPAM" 1188023 NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-507 1186952 1187441 1187514 "IDPAG" 1187519 NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-506 1186624 1186788 1186863 "IDENT" 1186897 T IDENT (NIL) -8 NIL NIL NIL) (-505 1182879 1183727 1184622 "IDECOMP" 1185781 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-504 1175743 1176802 1177849 "IDEAL" 1181915 NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-503 1174907 1175019 1175218 "ICDEN" 1175627 NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-502 1174005 1174387 1174534 "ICARD" 1174780 T ICARD (NIL) -8 NIL NIL NIL) (-501 1172065 1172378 1172783 "IBPTOOLS" 1173682 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-500 1167699 1171685 1171798 "IBITS" 1171984 NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-499 1164422 1164998 1165693 "IBATOOL" 1167116 NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-498 1162201 1162663 1163196 "IBACHIN" 1163957 NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-497 1160078 1162047 1162150 "IARRAY2" 1162155 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL NIL) (-496 1156232 1160004 1160061 "IARRAY1" 1160066 NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-495 1150216 1154644 1155125 "IAN" 1155771 T IAN (NIL) -8 NIL NIL NIL) (-494 1149727 1149784 1149957 "IALGFACT" 1150153 NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-493 1149255 1149368 1149396 "HYPCAT" 1149603 T HYPCAT (NIL) -9 NIL NIL NIL) (-492 1148793 1148910 1149096 "HYPCAT-" 1149101 NIL HYPCAT- (NIL T) -8 NIL NIL NIL) (-491 1148415 1148588 1148671 "HOSTNAME" 1148730 T HOSTNAME (NIL) -8 NIL NIL NIL) (-490 1148260 1148297 1148338 "HOMOTOP" 1148343 NIL HOMOTOP (NIL T) -9 NIL 1148376 NIL) (-489 1144939 1146270 1146311 "HOAGG" 1147292 NIL HOAGG (NIL T) -9 NIL 1147971 NIL) (-488 1143533 1143932 1144458 "HOAGG-" 1144463 NIL HOAGG- (NIL T T) -8 NIL NIL NIL) (-487 1137564 1143128 1143277 "HEXADEC" 1143404 T HEXADEC (NIL) -8 NIL NIL NIL) (-486 1136312 1136534 1136797 "HEUGCD" 1137341 NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-485 1135415 1136149 1136279 "HELLFDIV" 1136284 NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-484 1133642 1135192 1135280 "HEAP" 1135359 NIL HEAP (NIL T) -8 NIL NIL NIL) (-483 1132932 1133194 1133328 "HEADAST" 1133528 T HEADAST (NIL) -8 NIL NIL NIL) (-482 1126846 1132847 1132909 "HDP" 1132914 NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-481 1120589 1126481 1126633 "HDMP" 1126747 NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-480 1119913 1120053 1120217 "HB" 1120445 T HB (NIL) -7 NIL NIL NIL) (-479 1113410 1119759 1119863 "HASHTBL" 1119868 NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-478 1112913 1113131 1113223 "HASAST" 1113338 T HASAST (NIL) -8 NIL NIL NIL) (-477 1110718 1112535 1112717 "HACKPI" 1112751 T HACKPI (NIL) -8 NIL NIL NIL) (-476 1106413 1110571 1110684 "GTSET" 1110689 NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-475 1099939 1106291 1106389 "GSTBL" 1106394 NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-474 1092244 1098970 1099235 "GSERIES" 1099730 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-473 1091411 1091802 1091830 "GROUP" 1092033 T GROUP (NIL) -9 NIL 1092167 NIL) (-472 1090777 1090936 1091187 "GROUP-" 1091192 NIL GROUP- (NIL T) -8 NIL NIL NIL) (-471 1089144 1089465 1089852 "GROEBSOL" 1090454 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-470 1088084 1088346 1088397 "GRMOD" 1088926 NIL GRMOD (NIL T T) -9 NIL 1089094 NIL) (-469 1087852 1087888 1088016 "GRMOD-" 1088021 NIL GRMOD- (NIL T T T) -8 NIL NIL NIL) (-468 1083169 1084206 1085206 "GRIMAGE" 1086872 T GRIMAGE (NIL) -8 NIL NIL NIL) (-467 1081635 1081896 1082220 "GRDEF" 1082865 T GRDEF (NIL) -7 NIL NIL NIL) (-466 1081079 1081195 1081336 "GRAY" 1081514 T GRAY (NIL) -7 NIL NIL NIL) (-465 1080292 1080672 1080723 "GRALG" 1080876 NIL GRALG (NIL T T) -9 NIL 1080969 NIL) (-464 1079953 1080026 1080189 "GRALG-" 1080194 NIL GRALG- (NIL T T T) -8 NIL NIL NIL) (-463 1076757 1079538 1079716 "GPOLSET" 1079860 NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-462 1076111 1076168 1076426 "GOSPER" 1076694 NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-461 1071870 1072549 1073075 "GMODPOL" 1075810 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-460 1070875 1071059 1071297 "GHENSEL" 1071682 NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-459 1064926 1065769 1066796 "GENUPS" 1069959 NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-458 1064623 1064674 1064763 "GENUFACT" 1064869 NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-457 1064035 1064112 1064277 "GENPGCD" 1064541 NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-456 1063509 1063544 1063757 "GENMFACT" 1063994 NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-455 1062075 1062332 1062639 "GENEEZ" 1063252 NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-454 1055976 1061686 1061848 "GDMP" 1061998 NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-453 1045345 1049747 1050853 "GCNAALG" 1054959 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-452 1043764 1044600 1044628 "GCDDOM" 1044883 T GCDDOM (NIL) -9 NIL 1045040 NIL) (-451 1043234 1043361 1043576 "GCDDOM-" 1043581 NIL GCDDOM- (NIL T) -8 NIL NIL NIL) (-450 1041906 1042091 1042395 "GB" 1043013 NIL GB (NIL T T T T) -7 NIL NIL NIL) (-449 1030522 1032852 1035244 "GBINTERN" 1039597 NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-448 1028359 1028651 1029072 "GBF" 1030197 NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-447 1027140 1027305 1027572 "GBEUCLID" 1028175 NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-446 1026489 1026614 1026763 "GAUSSFAC" 1027011 T GAUSSFAC (NIL) -7 NIL NIL NIL) (-445 1024856 1025158 1025472 "GALUTIL" 1026208 NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-444 1023164 1023438 1023762 "GALPOLYU" 1024583 NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-443 1020529 1020819 1021226 "GALFACTU" 1022861 NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-442 1012335 1013834 1015442 "GALFACT" 1018961 NIL GALFACT (NIL T) -7 NIL NIL NIL) (-441 1009723 1010381 1010409 "FVFUN" 1011565 T FVFUN (NIL) -9 NIL 1012285 NIL) (-440 1008989 1009171 1009199 "FVC" 1009490 T FVC (NIL) -9 NIL 1009673 NIL) (-439 1008659 1008814 1008882 "FUNDESC" 1008941 T FUNDESC (NIL) -8 NIL NIL NIL) (-438 1008301 1008456 1008537 "FUNCTION" 1008611 NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-437 1006072 1006623 1007089 "FT" 1007855 T FT (NIL) -8 NIL NIL NIL) (-436 1004890 1005373 1005576 "FTEM" 1005889 T FTEM (NIL) -8 NIL NIL NIL) (-435 1003146 1003435 1003839 "FSUPFACT" 1004581 NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-434 1001543 1001832 1002164 "FST" 1002834 T FST (NIL) -8 NIL NIL NIL) (-433 1000714 1000820 1001015 "FSRED" 1001425 NIL FSRED (NIL T T) -7 NIL NIL NIL) (-432 999392 999648 1000002 "FSPRMELT" 1000429 NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-431 996477 996915 997414 "FSPECF" 998955 NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-430 978531 986980 987020 "FS" 990868 NIL FS (NIL T) -9 NIL 993157 NIL) (-429 967178 970171 974227 "FS-" 974524 NIL FS- (NIL T T) -8 NIL NIL NIL) (-428 966692 966746 966923 "FSINT" 967119 NIL FSINT (NIL T T) -7 NIL NIL NIL) (-427 965011 965685 965988 "FSERIES" 966471 NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-426 964025 964141 964372 "FSCINT" 964891 NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-425 960259 962969 963010 "FSAGG" 963380 NIL FSAGG (NIL T) -9 NIL 963639 NIL) (-424 958021 958622 959418 "FSAGG-" 959513 NIL FSAGG- (NIL T T) -8 NIL NIL NIL) (-423 957063 957206 957433 "FSAGG2" 957874 NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-422 954717 954997 955551 "FS2UPS" 956781 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-421 954299 954342 954497 "FS2" 954668 NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-420 953156 953327 953636 "FS2EXPXP" 954124 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-419 952582 952697 952849 "FRUTIL" 953036 NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-418 944022 948077 949435 "FR" 951256 NIL FR (NIL T) -8 NIL NIL NIL) (-417 939097 941740 941780 "FRNAALG" 943176 NIL FRNAALG (NIL T) -9 NIL 943783 NIL) (-416 934770 935846 937121 "FRNAALG-" 937871 NIL FRNAALG- (NIL T T) -8 NIL NIL NIL) (-415 934408 934451 934578 "FRNAAF2" 934721 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-414 932815 933262 933557 "FRMOD" 934220 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-413 930593 931198 931515 "FRIDEAL" 932606 NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-412 929788 929875 930164 "FRIDEAL2" 930500 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-411 928921 929335 929376 "FRETRCT" 929381 NIL FRETRCT (NIL T) -9 NIL 929557 NIL) (-410 928033 928264 928615 "FRETRCT-" 928620 NIL FRETRCT- (NIL T T) -8 NIL NIL NIL) (-409 925237 926421 926480 "FRAMALG" 927362 NIL FRAMALG (NIL T T) -9 NIL 927654 NIL) (-408 923371 923826 924456 "FRAMALG-" 924679 NIL FRAMALG- (NIL T T T) -8 NIL NIL NIL) (-407 917319 922846 923122 "FRAC" 923127 NIL FRAC (NIL T) -8 NIL NIL NIL) (-406 916955 917012 917119 "FRAC2" 917256 NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-405 916591 916648 916755 "FR2" 916892 NIL FR2 (NIL T T) -7 NIL NIL NIL) (-404 911256 914116 914144 "FPS" 915263 T FPS (NIL) -9 NIL 915820 NIL) (-403 910705 910814 910978 "FPS-" 911124 NIL FPS- (NIL T) -8 NIL NIL NIL) (-402 908151 909794 909822 "FPC" 910047 T FPC (NIL) -9 NIL 910189 NIL) (-401 907944 907984 908081 "FPC-" 908086 NIL FPC- (NIL T) -8 NIL NIL NIL) (-400 906822 907432 907473 "FPATMAB" 907478 NIL FPATMAB (NIL T) -9 NIL 907630 NIL) (-399 904522 904998 905424 "FPARFRAC" 906459 NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-398 899915 900414 901096 "FORTRAN" 903954 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL NIL) (-397 897631 898131 898670 "FORT" 899396 T FORT (NIL) -7 NIL NIL NIL) (-396 895307 895869 895897 "FORTFN" 896957 T FORTFN (NIL) -9 NIL 897581 NIL) (-395 895071 895121 895149 "FORTCAT" 895208 T FORTCAT (NIL) -9 NIL 895270 NIL) (-394 893204 893687 894077 "FORMULA" 894701 T FORMULA (NIL) -8 NIL NIL NIL) (-393 892992 893022 893091 "FORMULA1" 893168 NIL FORMULA1 (NIL T) -7 NIL NIL NIL) (-392 892515 892567 892740 "FORDER" 892934 NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-391 891611 891775 891968 "FOP" 892342 T FOP (NIL) -7 NIL NIL NIL) (-390 890219 890891 891065 "FNLA" 891493 NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-389 888974 889363 889391 "FNCAT" 889851 T FNCAT (NIL) -9 NIL 890111 NIL) (-388 888540 888933 888961 "FNAME" 888966 T FNAME (NIL) -8 NIL NIL NIL) (-387 887195 888132 888160 "FMTC" 888165 T FMTC (NIL) -9 NIL 888201 NIL) (-386 883555 884718 885347 "FMONOID" 886599 NIL FMONOID (NIL T) -8 NIL NIL NIL) (-385 882774 883297 883446 "FM" 883451 NIL FM (NIL T T) -8 NIL NIL NIL) (-384 880198 880844 880872 "FMFUN" 882016 T FMFUN (NIL) -9 NIL 882724 NIL) (-383 879467 879648 879676 "FMC" 879966 T FMC (NIL) -9 NIL 880148 NIL) (-382 876661 877495 877549 "FMCAT" 878744 NIL FMCAT (NIL T T) -9 NIL 879239 NIL) (-381 875554 876427 876527 "FM1" 876606 NIL FM1 (NIL T T) -8 NIL NIL NIL) (-380 873328 873744 874238 "FLOATRP" 875105 NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-379 866929 871057 871678 "FLOAT" 872727 T FLOAT (NIL) -8 NIL NIL NIL) (-378 864367 864867 865445 "FLOATCP" 866396 NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-377 863168 863980 864021 "FLINEXP" 864026 NIL FLINEXP (NIL T) -9 NIL 864119 NIL) (-376 862322 862557 862885 "FLINEXP-" 862890 NIL FLINEXP- (NIL T T) -8 NIL NIL NIL) (-375 861398 861542 861766 "FLASORT" 862174 NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-374 858615 859457 859509 "FLALG" 860736 NIL FLALG (NIL T T) -9 NIL 861203 NIL) (-373 852399 856101 856142 "FLAGG" 857404 NIL FLAGG (NIL T) -9 NIL 858056 NIL) (-372 851125 851464 851954 "FLAGG-" 851959 NIL FLAGG- (NIL T T) -8 NIL NIL NIL) (-371 850167 850310 850537 "FLAGG2" 850978 NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-370 847134 848116 848175 "FINRALG" 849303 NIL FINRALG (NIL T T) -9 NIL 849811 NIL) (-369 846294 846523 846862 "FINRALG-" 846867 NIL FINRALG- (NIL T T T) -8 NIL NIL NIL) (-368 845700 845913 845941 "FINITE" 846137 T FINITE (NIL) -9 NIL 846244 NIL) (-367 838158 840319 840359 "FINAALG" 844026 NIL FINAALG (NIL T) -9 NIL 845479 NIL) (-366 833490 834540 835684 "FINAALG-" 837063 NIL FINAALG- (NIL T T) -8 NIL NIL NIL) (-365 832885 833245 833348 "FILE" 833420 NIL FILE (NIL T) -8 NIL NIL NIL) (-364 831569 831881 831935 "FILECAT" 832619 NIL FILECAT (NIL T T) -9 NIL 832835 NIL) (-363 829429 830931 830959 "FIELD" 830999 T FIELD (NIL) -9 NIL 831079 NIL) (-362 828049 828434 828945 "FIELD-" 828950 NIL FIELD- (NIL T) -8 NIL NIL NIL) (-361 825926 826684 827031 "FGROUP" 827735 NIL FGROUP (NIL T) -8 NIL NIL NIL) (-360 825016 825180 825400 "FGLMICPK" 825758 NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-359 820875 824941 824998 "FFX" 825003 NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-358 820476 820537 820672 "FFSLPE" 820808 NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-357 816465 817248 818044 "FFPOLY" 819712 NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-356 815969 816005 816214 "FFPOLY2" 816423 NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-355 811839 815888 815951 "FFP" 815956 NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-354 807264 811750 811814 "FF" 811819 NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-353 802417 806607 806797 "FFNBX" 807118 NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-352 797373 801552 801810 "FFNBP" 802271 NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-351 792033 796657 796868 "FFNB" 797206 NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-350 790865 791063 791378 "FFINTBAS" 791830 NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-349 787085 789272 789300 "FFIELDC" 789920 T FFIELDC (NIL) -9 NIL 790296 NIL) (-348 785747 786118 786615 "FFIELDC-" 786620 NIL FFIELDC- (NIL T) -8 NIL NIL NIL) (-347 785316 785362 785486 "FFHOM" 785689 NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-346 783011 783498 784015 "FFF" 784831 NIL FFF (NIL T) -7 NIL NIL NIL) (-345 778656 782753 782854 "FFCGX" 782954 NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-344 774304 778388 778495 "FFCGP" 778599 NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-343 769514 774031 774139 "FFCG" 774240 NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-342 751339 760385 760471 "FFCAT" 765636 NIL FFCAT (NIL T T T) -9 NIL 767087 NIL) (-341 746537 747584 748898 "FFCAT-" 750128 NIL FFCAT- (NIL T T T T) -8 NIL NIL NIL) (-340 745948 745991 746226 "FFCAT2" 746488 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-339 735145 738920 740140 "FEXPR" 744800 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL NIL) (-338 734145 734580 734621 "FEVALAB" 734705 NIL FEVALAB (NIL T) -9 NIL 734966 NIL) (-337 733304 733514 733852 "FEVALAB-" 733857 NIL FEVALAB- (NIL T T) -8 NIL NIL NIL) (-336 731897 732687 732890 "FDIV" 733203 NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-335 728963 729678 729793 "FDIVCAT" 731361 NIL FDIVCAT (NIL T T T T) -9 NIL 731798 NIL) (-334 728725 728752 728922 "FDIVCAT-" 728927 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL NIL) (-333 727945 728032 728309 "FDIV2" 728632 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-332 726631 726890 727179 "FCPAK1" 727676 T FCPAK1 (NIL) -7 NIL NIL NIL) (-331 725757 726131 726272 "FCOMP" 726522 NIL FCOMP (NIL T) -8 NIL NIL NIL) (-330 709486 712907 716445 "FC" 722239 T FC (NIL) -8 NIL NIL NIL) (-329 702057 706050 706090 "FAXF" 707892 NIL FAXF (NIL T) -9 NIL 708584 NIL) (-328 699333 699991 700816 "FAXF-" 701281 NIL FAXF- (NIL T T) -8 NIL NIL NIL) (-327 694433 698709 698885 "FARRAY" 699190 NIL FARRAY (NIL T) -8 NIL NIL NIL) (-326 689678 691718 691771 "FAMR" 692794 NIL FAMR (NIL T T) -9 NIL 693254 NIL) (-325 688568 688870 689305 "FAMR-" 689310 NIL FAMR- (NIL T T T) -8 NIL NIL NIL) (-324 687764 688490 688543 "FAMONOID" 688548 NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-323 685576 686260 686313 "FAMONC" 687254 NIL FAMONC (NIL T T) -9 NIL 687640 NIL) (-322 684268 685330 685467 "FAGROUP" 685472 NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-321 682063 682382 682785 "FACUTIL" 683949 NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-320 681162 681347 681569 "FACTFUNC" 681873 NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-319 673559 680413 680625 "EXPUPXS" 681018 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-318 671042 671582 672168 "EXPRTUBE" 672993 T EXPRTUBE (NIL) -7 NIL NIL NIL) (-317 667236 667828 668565 "EXPRODE" 670381 NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-316 652602 665891 666319 "EXPR" 666840 NIL EXPR (NIL T) -8 NIL NIL NIL) (-315 647009 647596 648409 "EXPR2UPS" 651900 NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-314 646645 646702 646809 "EXPR2" 646946 NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-313 638042 645777 646074 "EXPEXPAN" 646482 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-312 637869 637999 638028 "EXIT" 638033 T EXIT (NIL) -8 NIL NIL NIL) (-311 637376 637593 637684 "EXITAST" 637798 T EXITAST (NIL) -8 NIL NIL NIL) (-310 637003 637065 637178 "EVALCYC" 637308 NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-309 636544 636662 636703 "EVALAB" 636873 NIL EVALAB (NIL T) -9 NIL 636977 NIL) (-308 636025 636147 636368 "EVALAB-" 636373 NIL EVALAB- (NIL T T) -8 NIL NIL NIL) (-307 633485 634761 634789 "EUCDOM" 635344 T EUCDOM (NIL) -9 NIL 635694 NIL) (-306 631890 632332 632922 "EUCDOM-" 632927 NIL EUCDOM- (NIL T) -8 NIL NIL NIL) (-305 619428 622188 624938 "ESTOOLS" 629160 T ESTOOLS (NIL) -7 NIL NIL NIL) (-304 619060 619117 619226 "ESTOOLS2" 619365 NIL ESTOOLS2 (NIL T T) -7 NIL NIL NIL) (-303 618811 618853 618933 "ESTOOLS1" 619012 NIL ESTOOLS1 (NIL T) -7 NIL NIL NIL) (-302 612716 614444 614472 "ES" 617240 T ES (NIL) -9 NIL 618649 NIL) (-301 607663 608950 610767 "ES-" 610931 NIL ES- (NIL T) -8 NIL NIL NIL) (-300 604037 604798 605578 "ESCONT" 606903 T ESCONT (NIL) -7 NIL NIL NIL) (-299 603782 603814 603896 "ESCONT1" 603999 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL NIL) (-298 603457 603507 603607 "ES2" 603726 NIL ES2 (NIL T T) -7 NIL NIL NIL) (-297 603087 603145 603254 "ES1" 603393 NIL ES1 (NIL T T) -7 NIL NIL NIL) (-296 602303 602432 602608 "ERROR" 602931 T ERROR (NIL) -7 NIL NIL NIL) (-295 595806 602162 602253 "EQTBL" 602258 NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-294 588357 591120 592569 "EQ" 594390 NIL -2045 (NIL T) -8 NIL NIL NIL) (-293 587989 588046 588155 "EQ2" 588294 NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-292 583278 584327 585420 "EP" 586928 NIL EP (NIL T) -7 NIL NIL NIL) (-291 581878 582169 582475 "ENV" 582992 T ENV (NIL) -8 NIL NIL NIL) (-290 581049 581577 581605 "ENTIRER" 581610 T ENTIRER (NIL) -9 NIL 581656 NIL) (-289 577543 579004 579374 "EMR" 580848 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-288 576687 576872 576926 "ELTAGG" 577306 NIL ELTAGG (NIL T T) -9 NIL 577517 NIL) (-287 576406 576468 576609 "ELTAGG-" 576614 NIL ELTAGG- (NIL T T T) -8 NIL NIL NIL) (-286 576195 576224 576278 "ELTAB" 576362 NIL ELTAB (NIL T T) -9 NIL NIL NIL) (-285 575321 575467 575666 "ELFUTS" 576046 NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-284 575063 575119 575147 "ELEMFUN" 575252 T ELEMFUN (NIL) -9 NIL NIL NIL) (-283 574933 574954 575022 "ELEMFUN-" 575027 NIL ELEMFUN- (NIL T) -8 NIL NIL NIL) (-282 569824 573033 573074 "ELAGG" 574014 NIL ELAGG (NIL T) -9 NIL 574477 NIL) (-281 568109 568543 569206 "ELAGG-" 569211 NIL ELAGG- (NIL T T) -8 NIL NIL NIL) (-280 566774 567052 567345 "ELABEXPR" 567836 T ELABEXPR (NIL) -8 NIL NIL NIL) (-279 559638 561441 562268 "EFUPXS" 566050 NIL EFUPXS (NIL T T T T) -8 NIL NIL NIL) (-278 553088 554889 555699 "EFULS" 558914 NIL EFULS (NIL T T T) -8 NIL NIL NIL) (-277 550510 550868 551347 "EFSTRUC" 552720 NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-276 539581 541147 542707 "EF" 549025 NIL EF (NIL T T) -7 NIL NIL NIL) (-275 538682 539066 539215 "EAB" 539452 T EAB (NIL) -8 NIL NIL NIL) (-274 537891 538641 538669 "E04UCFA" 538674 T E04UCFA (NIL) -8 NIL NIL NIL) (-273 537100 537850 537878 "E04NAFA" 537883 T E04NAFA (NIL) -8 NIL NIL NIL) (-272 536309 537059 537087 "E04MBFA" 537092 T E04MBFA (NIL) -8 NIL NIL NIL) (-271 535518 536268 536296 "E04JAFA" 536301 T E04JAFA (NIL) -8 NIL NIL NIL) (-270 534729 535477 535505 "E04GCFA" 535510 T E04GCFA (NIL) -8 NIL NIL NIL) (-269 533940 534688 534716 "E04FDFA" 534721 T E04FDFA (NIL) -8 NIL NIL NIL) (-268 533149 533899 533927 "E04DGFA" 533932 T E04DGFA (NIL) -8 NIL NIL NIL) (-267 527322 528674 530038 "E04AGNT" 531805 T E04AGNT (NIL) -7 NIL NIL NIL) (-266 526028 526508 526548 "DVARCAT" 527023 NIL DVARCAT (NIL T) -9 NIL 527222 NIL) (-265 525232 525444 525758 "DVARCAT-" 525763 NIL DVARCAT- (NIL T T) -8 NIL NIL NIL) (-264 518124 525031 525160 "DSMP" 525165 NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-263 512933 514069 515137 "DROPT" 517076 T DROPT (NIL) -8 NIL NIL NIL) (-262 512598 512657 512755 "DROPT1" 512868 NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-261 507713 508839 509976 "DROPT0" 511481 T DROPT0 (NIL) -7 NIL NIL NIL) (-260 506058 506383 506769 "DRAWPT" 507347 T DRAWPT (NIL) -7 NIL NIL NIL) (-259 500645 501568 502647 "DRAW" 505032 NIL DRAW (NIL T) -7 NIL NIL NIL) (-258 500278 500331 500449 "DRAWHACK" 500586 NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-257 499009 499278 499569 "DRAWCX" 500007 T DRAWCX (NIL) -7 NIL NIL NIL) (-256 498524 498593 498744 "DRAWCURV" 498935 NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-255 488992 490954 493069 "DRAWCFUN" 496429 T DRAWCFUN (NIL) -7 NIL NIL NIL) (-254 485805 487687 487728 "DQAGG" 488357 NIL DQAGG (NIL T) -9 NIL 488630 NIL) (-253 474076 480783 480866 "DPOLCAT" 482718 NIL DPOLCAT (NIL T T T T) -9 NIL 483263 NIL) (-252 468912 470261 472219 "DPOLCAT-" 472224 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL NIL) (-251 462061 468773 468871 "DPMO" 468876 NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-250 455113 461841 462008 "DPMM" 462013 NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-249 454745 455032 455080 "DOMCTOR" 455085 T DOMCTOR (NIL) -8 NIL NIL NIL) (-248 454040 454267 454404 "DOMAIN" 454628 T DOMAIN (NIL) -8 NIL NIL NIL) (-247 447783 453675 453827 "DMP" 453941 NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-246 447383 447439 447583 "DLP" 447721 NIL DLP (NIL T) -7 NIL NIL NIL) (-245 441253 446710 446900 "DLIST" 447225 NIL DLIST (NIL T) -8 NIL NIL NIL) (-244 438097 440106 440147 "DLAGG" 440697 NIL DLAGG (NIL T) -9 NIL 440927 NIL) (-243 436902 437540 437568 "DIVRING" 437660 T DIVRING (NIL) -9 NIL 437743 NIL) (-242 436139 436329 436629 "DIVRING-" 436634 NIL DIVRING- (NIL T) -8 NIL NIL NIL) (-241 434241 434598 435004 "DISPLAY" 435753 T DISPLAY (NIL) -7 NIL NIL NIL) (-240 428177 434155 434218 "DIRPROD" 434223 NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-239 427025 427228 427493 "DIRPROD2" 427970 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-238 416282 422240 422293 "DIRPCAT" 422703 NIL DIRPCAT (NIL NIL T) -9 NIL 423543 NIL) (-237 413608 414250 415131 "DIRPCAT-" 415468 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL NIL) (-236 412895 413055 413241 "DIOSP" 413442 T DIOSP (NIL) -7 NIL NIL NIL) (-235 409597 411807 411848 "DIOPS" 412282 NIL DIOPS (NIL T) -9 NIL 412511 NIL) (-234 409146 409260 409451 "DIOPS-" 409456 NIL DIOPS- (NIL T T) -8 NIL NIL NIL) (-233 408030 408632 408660 "DIFRING" 408847 T DIFRING (NIL) -9 NIL 408957 NIL) (-232 407676 407753 407905 "DIFRING-" 407910 NIL DIFRING- (NIL T) -8 NIL NIL NIL) (-231 405473 406719 406760 "DIFEXT" 407123 NIL DIFEXT (NIL T) -9 NIL 407417 NIL) (-230 403758 404186 404852 "DIFEXT-" 404857 NIL DIFEXT- (NIL T T) -8 NIL NIL NIL) (-229 401080 403290 403331 "DIAGG" 403336 NIL DIAGG (NIL T) -9 NIL 403356 NIL) (-228 400464 400621 400873 "DIAGG-" 400878 NIL DIAGG- (NIL T T) -8 NIL NIL NIL) (-227 395929 399423 399700 "DHMATRIX" 400233 NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-226 391541 392450 393460 "DFSFUN" 394939 T DFSFUN (NIL) -7 NIL NIL NIL) (-225 386646 390472 390784 "DFLOAT" 391249 T DFLOAT (NIL) -8 NIL NIL NIL) (-224 384874 385155 385551 "DFINTTLS" 386354 NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-223 381930 382895 383295 "DERHAM" 384540 NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-222 379779 381705 381794 "DEQUEUE" 381874 NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-221 378994 379127 379323 "DEGRED" 379641 NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-220 375389 376134 376987 "DEFINTRF" 378222 NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-219 372916 373385 373984 "DEFINTEF" 374908 NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-218 372293 372536 372651 "DEFAST" 372821 T DEFAST (NIL) -8 NIL NIL NIL) (-217 366324 371888 372037 "DECIMAL" 372164 T DECIMAL (NIL) -8 NIL NIL NIL) (-216 363834 364294 364800 "DDFACT" 365868 NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-215 363430 363473 363624 "DBLRESP" 363785 NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-214 361329 361663 362023 "DBASE" 363197 NIL DBASE (NIL T) -8 NIL NIL NIL) (-213 360598 360809 360955 "DATAARY" 361228 NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-212 359731 360557 360585 "D03FAFA" 360590 T D03FAFA (NIL) -8 NIL NIL NIL) (-211 358865 359690 359718 "D03EEFA" 359723 T D03EEFA (NIL) -8 NIL NIL NIL) (-210 356815 357281 357770 "D03AGNT" 358396 T D03AGNT (NIL) -7 NIL NIL NIL) (-209 356131 356774 356802 "D02EJFA" 356807 T D02EJFA (NIL) -8 NIL NIL NIL) (-208 355447 356090 356118 "D02CJFA" 356123 T D02CJFA (NIL) -8 NIL NIL NIL) (-207 354763 355406 355434 "D02BHFA" 355439 T D02BHFA (NIL) -8 NIL NIL NIL) (-206 354079 354722 354750 "D02BBFA" 354755 T D02BBFA (NIL) -8 NIL NIL NIL) (-205 347276 348865 350471 "D02AGNT" 352493 T D02AGNT (NIL) -7 NIL NIL NIL) (-204 345044 345567 346113 "D01WGTS" 346750 T D01WGTS (NIL) -7 NIL NIL NIL) (-203 344138 345003 345031 "D01TRNS" 345036 T D01TRNS (NIL) -8 NIL NIL NIL) (-202 343233 344097 344125 "D01GBFA" 344130 T D01GBFA (NIL) -8 NIL NIL NIL) (-201 342328 343192 343220 "D01FCFA" 343225 T D01FCFA (NIL) -8 NIL NIL NIL) (-200 341423 342287 342315 "D01ASFA" 342320 T D01ASFA (NIL) -8 NIL NIL NIL) (-199 340518 341382 341410 "D01AQFA" 341415 T D01AQFA (NIL) -8 NIL NIL NIL) (-198 339613 340477 340505 "D01APFA" 340510 T D01APFA (NIL) -8 NIL NIL NIL) (-197 338708 339572 339600 "D01ANFA" 339605 T D01ANFA (NIL) -8 NIL NIL NIL) (-196 337803 338667 338695 "D01AMFA" 338700 T D01AMFA (NIL) -8 NIL NIL NIL) (-195 336898 337762 337790 "D01ALFA" 337795 T D01ALFA (NIL) -8 NIL NIL NIL) (-194 335993 336857 336885 "D01AKFA" 336890 T D01AKFA (NIL) -8 NIL NIL NIL) (-193 335088 335952 335980 "D01AJFA" 335985 T D01AJFA (NIL) -8 NIL NIL NIL) (-192 328383 329936 331497 "D01AGNT" 333547 T D01AGNT (NIL) -7 NIL NIL NIL) (-191 327720 327848 328000 "CYCLOTOM" 328251 T CYCLOTOM (NIL) -7 NIL NIL NIL) (-190 324455 325168 325895 "CYCLES" 327013 T CYCLES (NIL) -7 NIL NIL NIL) (-189 323767 323901 324072 "CVMP" 324316 NIL CVMP (NIL T) -7 NIL NIL NIL) (-188 321538 321796 322172 "CTRIGMNP" 323495 NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-187 321033 321332 321405 "CTOR" 321485 T CTOR (NIL) -8 NIL NIL NIL) (-186 320569 320764 320865 "CTORKIND" 320952 T CTORKIND (NIL) -8 NIL NIL NIL) (-185 319917 320176 320204 "CTORCAT" 320386 T CTORCAT (NIL) -9 NIL 320499 NIL) (-184 319515 319626 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NIL NIL) (-133 221496 221697 221772 "CAPSLAST" 221838 T CAPSLAST (NIL) -8 NIL NIL NIL) (-132 220868 221196 221224 "CACHSET" 221356 T CACHSET (NIL) -9 NIL 221433 NIL) (-131 220364 220660 220688 "CABMON" 220738 T CABMON (NIL) -9 NIL 220794 NIL) (-130 219864 220068 220178 "BYTEORD" 220274 T BYTEORD (NIL) -8 NIL NIL NIL) (-129 218867 219398 219540 "BYTE" 219703 T BYTE (NIL) -8 NIL NIL 219825) (-128 214267 218372 218544 "BYTEBUF" 218715 T BYTEBUF (NIL) -8 NIL NIL NIL) (-127 211824 213959 214066 "BTREE" 214193 NIL BTREE (NIL T) -8 NIL NIL NIL) (-126 209321 211472 211594 "BTOURN" 211734 NIL BTOURN (NIL T) -8 NIL NIL NIL) (-125 206738 208791 208832 "BTCAT" 208900 NIL BTCAT (NIL T) -9 NIL 208977 NIL) (-124 206405 206485 206634 "BTCAT-" 206639 NIL BTCAT- (NIL T T) -8 NIL NIL NIL) (-123 201697 205548 205576 "BTAGG" 205798 T BTAGG (NIL) -9 NIL 205959 NIL) (-122 201187 201312 201518 "BTAGG-" 201523 NIL BTAGG- (NIL T) -8 NIL NIL NIL) (-121 198230 200465 200680 "BSTREE" 201004 NIL BSTREE (NIL T) -8 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18418 26347 26398 "ACFS" 27109 NIL ACFS (NIL T) -9 NIL 27348 NIL) (-28 16432 16922 17697 "ACFS-" 17702 NIL ACFS- (NIL T T) -8 NIL NIL NIL) (-27 12697 14599 14625 "ACF" 15504 T ACF (NIL) -9 NIL 15916 NIL) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL NIL) (-25 10999 11168 11194 "ABELSG" 11286 T ABELSG (NIL) -9 NIL 11351 NIL) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL NIL) (-23 10235 10496 10522 "ABELMON" 10692 T ABELMON (NIL) -9 NIL 10804 NIL) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL NIL) (-21 9233 9579 9605 "ABELGRP" 9730 T ABELGRP (NIL) -9 NIL 9812 NIL) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119 NIL) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 9e37ad01..07bdf710 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,89 +1,124 @@ -(735605 . 3451461728) -(((*1 *2) (-12 (-5 *2 (-1152)) (-5 *1 (-1179))))) +(735605 . 3451578538) +(((*1 *2 *1 *1) + (-12 (-4 *3 (-556)) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *2 (-641 *1)) (-4 *1 (-1059 *3 *4 *5))))) +(((*1 *2 *1) (-12 (-4 *1 (-670 *3)) (-4 *3 (-1209)) (-5 *2 (-112))))) (((*1 *2 *3) (-12 (-5 *2 (-564)) (-5 *1 (-569 *3)) (-4 *3 (-1034 *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1097 *3 *4 *2 *5 *6)) (-4 *3 (-1094)) (-4 *4 (-1094)) (-4 *5 (-1094)) (-4 *6 (-1094)) (-4 *2 (-1094))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1166 *6)) (-4 *6 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *2 (-1166 *7)) (-5 *1 (-321 *4 *5 *6 *7)) + (-4 *7 (-945 *6 *4 *5))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 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(-38 (-407 (-564)))) - (-5 *1 (-1155 *3)))) - ((*1 *2 *2) - (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) - (-5 *1 (-1156 *3))))) + (|partial| -12 (-4 *4 (-13 (-556) (-147))) + (-5 *2 (-2 (|:| -4242 *3) (|:| -4251 *3))) (-5 *1 (-1229 *4 *3)) + (-4 *3 (-1235 *4))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) (((*1 *2 *3) (-12 (-4 *5 (-13 (-612 *2) (-172))) (-5 *2 (-888 *4)) (-5 *1 (-170 *4 *5 *3)) (-4 *4 (-1094)) (-4 *3 (-166 *5)))) @@ -5693,9 +368,9 @@ (-12 (-5 *2 (-948 *3)) (-4 *3 (-1045)) (-4 *1 (-1059 *3 *4 *5)) (-4 *5 (-612 (-1170))) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *1 *2) - (-2797 + (-2750 (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) - (-12 (-2352 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) + (-12 (-2356 (-4 *3 (-38 (-407 (-564))))) (-4 *3 (-38 (-564))) (-4 *5 (-612 (-1170)))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846))) (-12 (-5 *2 (-948 (-564))) (-4 *1 (-1059 *3 *4 *5)) @@ -5706,12 +381,12 @@ (-4 *3 (-38 (-407 (-564)))) (-4 *5 (-612 (-1170))) (-4 *3 (-1045)) (-4 *4 (-789)) (-4 *5 (-846)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -2265 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3461 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1065 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1152)) (-5 *1 (-1063 *4 *5 *6 *7 *8)))) ((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -2265 *8))) + (-12 (-5 *3 (-2 (|:| |val| (-641 *7)) (|:| -3461 *8))) (-4 *7 (-1059 *4 *5 *6)) (-4 *8 (-1103 *4 *5 *6 *7)) (-4 *4 (-452)) (-4 *5 (-789)) (-4 *6 (-846)) (-5 *2 (-1152)) (-5 *1 (-1139 *4 *5 *6 *7 *8)))) @@ -5743,48 +418,51 @@ (-4 *4 (-13 (-844) (-307) (-147) (-1018))) (-14 *6 (-641 (-1170))) (-5 *2 (-641 (-776 *4 (-860 *6)))) (-5 *1 (-1285 *4 *5 *6)) (-14 *5 (-641 (-1170)))))) -(((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1152)) (-5 *4 (-564)) (-5 *5 (-685 (-225))) - (-5 *2 (-1031)) (-5 *1 (-753))))) -(((*1 *1 *1 *2) (-12 (-4 *1 (-1138)) (-5 *2 (-141)))) - ((*1 *1 *1 *2) (-12 (-4 *1 (-1138)) (-5 *2 (-144))))) -(((*1 *1 *2 *1) (-12 (-5 *2 (-109)) (-5 *1 (-1079))))) -(((*1 *2 *1) (-12 (-5 *2 (-1264)) (-5 *1 (-817))))) -(((*1 *2 *1) - (-12 (-4 *4 (-1094)) (-5 *2 (-885 *3 *5)) (-5 *1 (-881 *3 *4 *5)) - (-4 *3 (-1094)) (-4 *5 (-662 *4))))) -(((*1 *1 *1) (-4 *1 (-627))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-628 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998) (-1194)))))) -(((*1 *2 *1) - (-12 (-4 *1 (-166 *3)) (-4 *3 (-172)) (-4 *3 (-545)) - (-5 *2 (-407 (-564))))) - ((*1 *2 *1) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-418 *3)) (-4 *3 (-545)) - (-4 *3 (-556)))) - ((*1 *2 *1) (-12 (-4 *1 (-545)) (-5 *2 (-407 (-564))))) - ((*1 *2 *1) - (-12 (-4 *1 (-793 *3)) (-4 *3 (-172)) (-4 *3 (-545)) - (-5 *2 (-407 (-564))))) - ((*1 *2 *1) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-829 *3)) (-4 *3 (-545)) - (-4 *3 (-1094)))) - ((*1 *2 *1) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-839 *3)) (-4 *3 (-545)) - (-4 *3 (-1094)))) - ((*1 *2 *1) - (-12 (-4 *1 (-993 *3)) (-4 *3 (-172)) (-4 *3 (-545)) - (-5 *2 (-407 (-564))))) - ((*1 *2 *3) - (-12 (-5 *2 (-407 (-564))) (-5 *1 (-1004 *3)) (-4 *3 (-1034 *2))))) -(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-1190))))) +(((*1 *1 *2) + (-12 (-5 *2 (-1166 *3)) (-4 *3 (-1045)) (-4 *1 (-1235 *3))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-972 *4 *5 *3 *6)) (-4 *4 (-1045)) (-4 *5 (-789)) + (-4 *3 (-846)) (-4 *6 (-1059 *4 *5 *3)) (-5 *2 (-112))))) (((*1 *2 *3) - (-12 (-4 *4 (-1235 (-407 *2))) (-5 *2 (-564)) (-5 *1 (-909 *4 *3)) - (-4 *3 (-1235 (-407 *4)))))) -(((*1 *2 *2 *2) (-12 (-5 *2 (-379)) (-5 *1 (-205)))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-641 (-379))) (-5 *2 (-379)) (-5 *1 (-205))))) + (-12 + (-5 *3 + (-641 + (-2 (|:| -2828 (-767)) + (|:| |eqns| + (-641 + (-2 (|:| |det| *7) (|:| |rows| (-641 (-564))) + (|:| |cols| (-641 (-564)))))) + (|:| |fgb| (-641 *7))))) + (-4 *7 (-945 *4 *6 *5)) (-4 *4 (-13 (-307) (-147))) + (-4 *5 (-13 (-846) (-612 (-1170)))) (-4 *6 (-789)) (-5 *2 (-767)) + (-5 *1 (-920 *4 *5 *6 *7))))) +(((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-641 (-948 (-564)))) (-5 *4 (-641 (-1170))) + (-5 *2 (-641 (-641 (-379)))) (-5 *1 (-1019)) (-5 *5 (-379)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1042 *4 *5)) (-4 *4 (-13 (-844) (-307) (-147) (-1018))) + (-14 *5 (-641 (-1170))) (-5 *2 (-641 (-641 (-1020 (-407 *4))))) + (-5 *1 (-1285 *4 *5 *6)) (-14 *6 (-641 (-1170))))) + ((*1 *2 *3 *4 *4 *4) + (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-844) (-307) (-147) (-1018))) + (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) + (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) + ((*1 *2 *3 *4 *4) + (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-844) (-307) (-147) (-1018))) + (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) + (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-641 (-948 *5))) (-5 *4 (-112)) + (-4 *5 (-13 (-844) (-307) (-147) (-1018))) + (-5 *2 (-641 (-641 (-1020 (-407 *5))))) (-5 *1 (-1285 *5 *6 *7)) + (-14 *6 (-641 (-1170))) (-14 *7 (-641 (-1170))))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-948 *4))) + (-4 *4 (-13 (-844) (-307) (-147) (-1018))) + (-5 *2 (-641 (-641 (-1020 (-407 *4))))) (-5 *1 (-1285 *4 *5 *6)) + (-14 *5 (-641 (-1170))) (-14 *6 (-641 (-1170)))))) (((*1 *1 *1) (-4 *1 (-95))) ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) @@ -5795,12 +473,22 @@ ((*1 *2 *2) (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1219 *3)) (-5 *1 (-279 *3 *4 *2 *5)) (-4 *2 (-1242 *3 *4)) (-4 *5 (-979 *4)))) + ((*1 *1 *1) + (-12 (-5 *1 (-339 *2 *3 *4)) (-14 *2 (-641 (-1170))) + (-14 *3 (-641 (-1170))) (-4 *4 (-387)))) ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1155 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) (-5 *1 (-1156 *3))))) +(((*1 *2) (-12 (-5 *2 (-1170)) (-5 *1 (-1173))))) +(((*1 *2 *2) (-12 (-5 *2 (-225)) (-5 *1 (-226)))) + ((*1 *2 *2) (-12 (-5 *2 (-169 (-225))) (-5 *1 (-226)))) + ((*1 *2 *2) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-431 *3 *2)) + (-4 *2 (-430 *3)))) + ((*1 *1 *1) (-4 *1 (-1133)))) (((*1 *2 *1) (-12 (-4 *1 (-254 *3)) (-4 *3 (-1209)) (-5 *2 (-767)))) ((*1 *2 *1) (-12 (-4 *1 (-302)) (-5 *2 (-767)))) ((*1 *2 *3) @@ -5810,31 +498,24 @@ ((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-610 *3)) (-4 *3 (-846)))) ((*1 *2) (-12 (-5 *2 (-564)) (-5 *1 (-858)))) ((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-858))))) -(((*1 *1 *2) - (-12 (-5 *2 (-685 *5)) (-4 *5 (-1045)) (-5 *1 (-1049 *3 *4 *5)) - (-14 *3 (-767)) (-14 *4 (-767))))) -(((*1 *2 *3 *3 *3 *3 *4 *3 *5 *5 *5 *3) - (-12 (-5 *3 (-564)) (-5 *5 (-685 (-225))) (-5 *4 (-225)) - (-5 *2 (-1031)) (-5 *1 (-746))))) -(((*1 *2 *3 *3) - (-12 (-4 *4 (-556)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -2810 *4))) - (-5 *1 (-965 *4 *3)) (-4 *3 (-1235 *4))))) -(((*1 *2 *2 *3) - (|partial| -12 (-5 *2 (-407 (-948 *4))) (-5 *3 (-1170)) - (-4 *4 (-13 (-556) (-1034 (-564)) (-147))) (-5 *1 (-570 *4))))) -(((*1 *1 *1) - (-12 (-5 *1 (-594 *2)) (-4 *2 (-38 (-407 (-564)))) (-4 *2 (-1045))))) -(((*1 *2 *3) - (-12 (-5 *2 (-112)) (-5 *1 (-442 *3)) (-4 *3 (-1235 (-564)))))) -(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-858))))) -(((*1 *2 *3 *4) - (-12 (-4 *5 (-1094)) (-4 *3 (-896 *5)) (-5 *2 (-685 *3)) - (-5 *1 (-688 *5 *3 *6 *4)) (-4 *6 (-373 *3)) - (-4 *4 (-13 (-373 *5) (-10 -7 (-6 -4406))))))) -(((*1 *2 *2 *2) - (-12 (-4 *3 (-1045)) (-5 *1 (-1231 *3 *2)) (-4 *2 (-1235 *3))))) -(((*1 *1 *1) (-4 *1 (-95))) - ((*1 *2 *2) +(((*1 *2 *1 *3 *3 *2) + (-12 (-5 *3 (-564)) (-4 *1 (-57 *2 *4 *5)) (-4 *2 (-1209)) + (-4 *4 (-373 *2)) (-4 *5 (-373 *2)))) + ((*1 *2 *1 *3 *2) + (-12 (|has| *1 (-6 -4407)) (-4 *1 (-288 *3 *2)) (-4 *3 (-1094)) + (-4 *2 (-1209))))) +(((*1 *1 *2 *1) (-12 (-5 *1 (-121 *2)) (-4 *2 (-846))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-114))))) +(((*1 *2 *2 *2 *3) + (-12 (-5 *3 (-767)) (-4 *4 (-556)) (-5 *1 (-965 *4 *2)) + (-4 *2 (-1235 *4))))) +(((*1 *2) (-12 (-5 *2 (-379)) (-5 *1 (-1036))))) +(((*1 *2 *1) (-12 (-5 *2 (-767)) (-5 *1 (-418 *3)) (-4 *3 (-556)))) + ((*1 *2 *3) + (-12 (-5 *3 (-641 (-2 (|:| -3595 *4) (|:| -2762 (-564))))) + (-4 *4 (-1235 (-564))) (-5 *2 (-767)) (-5 *1 (-442 *4))))) +(((*1 *2 *2) (-12 (-5 *2 (-564)) (-5 *1 (-923))))) +(((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) ((*1 *2 *2) @@ -5848,36 +529,50 @@ (-5 *1 (-1155 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) - (-5 *1 (-1156 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1152)) (-5 *1 (-1190))))) + (-5 *1 (-1156 *3)))) + ((*1 *1 *1) (-4 *1 (-1197)))) +(((*1 *2 *3) + (-12 (-5 *3 (-917)) (-5 *2 (-1166 *4)) (-5 *1 (-587 *4)) + (-4 *4 (-349))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-57 *3 *4 *5)) (-4 *3 (-1209)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 *3)) (|has| *1 (-6 -4407)) (-4 *1 (-489 *3)) + (-4 *3 (-1209))))) (((*1 *2 *1) - (|partial| -12 (-5 *2 (-1170)) (-5 *1 (-610 *3)) (-4 *3 (-846))))) -(((*1 *2 *1 *2) - (-12 (|has| *1 (-6 -4407)) (-4 *1 (-1247 *2)) (-4 *2 (-1209))))) + (-12 (-4 *1 (-326 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)) + (-5 *2 (-641 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-382 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-1094)) + (-5 *2 (-641 *3)))) + ((*1 *2 *1) + (-12 (-5 *2 (-1150 *3)) (-5 *1 (-595 *3)) (-4 *3 (-1045)))) + ((*1 *2 *1) + (-12 (-5 *2 (-641 *3)) (-5 *1 (-731 *3 *4)) (-4 *3 (-1045)) + (-4 *4 (-722)))) + ((*1 *2 *1) (-12 (-4 *1 (-848 *3)) (-4 *3 (-1045)) (-5 *2 (-641 *3)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1250 *3)) (-4 *3 (-1045)) (-5 *2 (-1150 *3))))) +(((*1 *2 *3 *3 *4 *5 *5 *5 *4 *4 *4 *3 *4 *4 *6) + (-12 (-5 *3 (-685 (-225))) (-5 *4 (-564)) (-5 *5 (-225)) + (-5 *6 (-3 (|:| |fn| (-388)) (|:| |fp| (-86 FCN)))) (-5 *2 (-1031)) + (-5 *1 (-745))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-147)) + (-4 *3 (-307)) (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) + (-5 *1 (-973 *3 *4 *5 *6))))) +(((*1 *1 *2) (-12 (-5 *2 (-641 (-858))) (-5 *1 (-330))))) +(((*1 *1 *1 *2) + (-12 (-5 *2 (-1226 (-564))) (-4 *1 (-282 *3)) (-4 *3 (-1209)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-282 *3)) (-4 *3 (-1209))))) +(((*1 *1 *1 *2 *2 *1) + (-12 (-5 *2 (-564)) (-4 *1 (-683 *3 *4 *5)) (-4 *3 (-1045)) + (-4 *4 (-373 *3)) (-4 *5 (-373 *3))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-452))) (-5 *1 (-1200 *3 *2)) - (-4 *2 (-13 (-430 *3) (-1194)))))) -(((*1 *1) (-12 (-4 *1 (-166 *2)) (-4 *2 (-172))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-641 *3)) (-4 *3 (-1235 *5)) (-4 *5 (-307)) - (-5 *2 (-767)) (-5 *1 (-455 *5 *3))))) -(((*1 *2 *1 *1) - (-12 (-5 *2 (-641 (-294 *4))) (-5 *1 (-625 *3 *4 *5)) (-4 *3 (-846)) - (-4 *4 (-13 (-172) (-713 (-407 (-564))))) (-14 *5 (-917))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) - (|:| |relerr| (-225)))) - (-5 *2 (-379)) (-5 *1 (-192))))) -(((*1 *1 *2 *2 *2 *2 *2 *2 *2 *2) - (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)))) - ((*1 *1 *2 *2) - (-12 (-5 *2 (-995 *3)) (-4 *3 (-172)) (-5 *1 (-795 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-1098)) (-5 *1 (-52))))) -(((*1 *1 *1) (-4 *1 (-95))) - ((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) ((*1 *2 *2) @@ -5891,37 +586,32 @@ (-5 *1 (-1155 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) - (-5 *1 (-1156 *3))))) -(((*1 *2 *1) (-12 (-5 *2 (-564)) (-5 *1 (-870)))) - ((*1 *2 *3) (-12 (-5 *3 (-939 *2)) (-5 *1 (-978 *2)) (-4 *2 (-1045))))) -(((*1 *2) - (-12 (-4 *4 (-172)) (-5 *2 (-112)) (-5 *1 (-366 *3 *4)) - (-4 *3 (-367 *4)))) - ((*1 *2) (-12 (-4 *1 (-367 *3)) (-4 *3 (-172)) (-5 *2 (-112))))) -(((*1 *1 *1 *1) - (-12 (-4 *1 (-683 *2 *3 *4)) (-4 *2 (-1045)) (-4 *3 (-373 *2)) - (-4 *4 (-373 *2))))) + (-5 *1 (-1156 *3)))) + ((*1 *1 *1) (-4 *1 (-1197)))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-373 *2)) (-4 *2 (-1209)) (-4 *2 (-846)))) + ((*1 *1 *2 *1 *1) + (-12 (-5 *2 (-1 (-112) *3 *3)) (-4 *1 (-373 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(-1065 *6 *7 *8 *3)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-452)) (-4 *6 (-789)) (-4 *7 (-846)) - (-4 *3 (-1059 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-641 *4)) - (|:| |todo| (-641 (-2 (|:| |val| (-641 *3)) (|:| -2265 *4)))))) - (-5 *1 (-1139 *5 *6 *7 *3 *4)) (-4 *4 (-1103 *5 *6 *7 *3))))) + (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-192)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-300)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1088 (-839 (-225)))) (-5 *2 (-225)) (-5 *1 (-305))))) +(((*1 *2 *1) (-12 (-4 *1 (-865 *3)) (-5 *2 (-564))))) +(((*1 *2 *2) + (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) + (-4 *2 (-13 (-430 *3) (-998)))))) (((*1 *2 *3 *1) (-12 (-5 *3 (-1283 *4 *2)) (-4 *1 (-374 *4 *2)) (-4 *4 (-846)) (-4 *2 (-172)))) @@ -5932,22 +622,17 @@ (-4 *2 (-1045)))) ((*1 *2 *1 *3) (-12 (-4 *2 (-1045)) (-5 *1 (-1282 *2 *3)) (-4 *3 (-842))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-564)) (-5 *2 (-641 (-2 (|:| -2400 *3) (|:| -1595 *4)))) - (-5 *1 (-692 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(-536)))) - (-5 *2 (-52)) (-5 *1 (-317 *7 *3))))) -(((*1 *2 *2 *2 *2) - (-12 (-5 *2 (-407 (-1166 (-316 *3)))) (-4 *3 (-13 (-556) (-846))) - (-5 *1 (-1124 *3))))) -(((*1 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-945 *3 *4 *5)) (-4 *3 (-452)) - (-4 *4 (-789)) (-4 *5 (-846)) (-5 *1 (-449 *3 *4 *5 *6))))) + (-641 + (-2 (|:| |det| *8) (|:| |rows| (-641 (-564))) + (|:| |cols| (-641 (-564)))))) + (-5 *1 (-920 *5 *6 *7 *8))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-979 *2)) (-4 *2 (-1194))))) (((*1 *2 *2) (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) - (-4 *2 (-13 (-430 *3) (-998)))))) -(((*1 *1 *1) (-4 *1 (-95))) - ((*1 *2 *2) - (-12 (-4 *3 (-13 (-846) (-556))) (-5 *1 (-276 *3 *2)) (-4 *2 (-13 (-430 *3) (-998))))) ((*1 *2 *2) (-12 (-4 *3 (-38 (-407 (-564)))) (-4 *4 (-1250 *3)) @@ -6053,7 +755,19 @@ (-5 *1 (-1155 *3)))) ((*1 *2 *2) (-12 (-5 *2 (-1150 *3)) (-4 *3 (-38 (-407 (-564)))) - (-5 *1 (-1156 *3))))) + (-5 *1 (-1156 *3)))) + ((*1 *1 *1) (-4 *1 (-1197)))) +(((*1 *2 *1) (-12 (-4 *1 (-793 *2)) (-4 *2 (-172)))) + ((*1 *2 *1) (-12 (-4 *1 (-993 *2)) (-4 *2 (-172))))) +(((*1 *2 *1) (-12 (-4 *1 (-951)) (-5 *2 (-1088 (-225))))) + ((*1 *2 *1) (-12 (-4 *1 (-970)) (-5 *2 (-1088 (-225)))))) +(((*1 *2 *1) + (-12 (-5 *2 (-641 (-2 (|:| |integrand| *3) (|:| |intvar| *3)))) + (-5 *1 (-585 *3)) (-4 *3 (-363))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *6 (-917)) (-4 *5 (-307)) (-4 *3 (-1235 *5)) + (-5 *2 (-2 (|:| |plist| (-641 *3)) (|:| |modulo| *5))) + (-5 *1 (-460 *5 *3)) (-5 *4 (-641 *3))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1045)) (-4 *4 (-788)))) @@ -6161,9 +875,9 @@ (-4 *6 (-363)) (-5 *2 (-585 *6)) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -1886 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2656 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-363)) (-4 *6 (-363)) - (-5 *2 (-2 (|:| -1886 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2656 *6) (|:| |coeff| *6))) (-5 *1 (-584 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -6282,7 +996,7 @@ (-4 *8 (-1045)) (-4 *6 (-789)) (-4 *2 (-13 (-1094) - (-10 -8 (-15 -3008 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) + (-10 -8 (-15 -2980 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-767)))))) (-5 *1 (-947 *6 *7 *8 *5 *2)) (-4 *5 (-945 *8 *6 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-954 *5)) (-4 *5 (-1209)) @@ -6295,8 +1009,8 @@ (-4 *2 (-945 (-948 *4) *5 *6)) (-4 *5 (-789)) (-4 *6 (-13 (-846) - (-10 -8 (-15 -3193 ((-1170) $)) - (-15 -3282 ((-3 $ "failed") (-1170)))))) + (-10 -8 (-15 -4344 ((-1170) $)) + (-15 -3257 ((-3 $ "failed") (-1170)))))) (-5 *1 (-980 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-556)) (-4 *6 (-556)) @@ -6383,32 +1097,15 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1045)) (-5 *1 (-1282 *3 *4)) (-4 *4 (-842))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-641 *6)) (-4 *6 (-1059 *3 *4 *5)) (-4 *3 (-452)) - (-4 *3 (-556)) (-4 *4 (-789)) (-4 *5 (-846)) - (-5 *1 (-973 *3 *4 *5 *6))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1170)) (-5 *2 (-379)) (-5 *1 (-1057))))) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1 (-3 *5 "failed") *8)) - (-5 *4 (-685 (-1166 *8))) (-4 *5 (-1045)) (-4 *8 (-1045)) - (-4 *6 (-1235 *5)) (-5 *2 (-685 *6)) (-5 *1 (-501 *5 *6 *7 *8)) - (-4 *7 (-1235 *6))))) -(((*1 *2 *3) - (-12 (-4 *4 (-1045)) (-4 *3 (-1235 *4)) (-4 *2 (-1250 *4)) - (-5 *1 (-1253 *4 *3 *5 *2)) (-4 *5 (-652 *3))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-3 - (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -2760 (-641 (-225))) - (|:| |lb| (-641 (-839 (-225)))) - (|:| |cf| (-641 (-316 (-225)))) - (|:| |ub| (-641 (-839 (-225)))))) - (|:| |lsa| - (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -2760 (-641 (-225))))))) - (-5 *2 (-641 (-1152))) (-5 *1 (-267))))) + (-12 (-5 *3 (-641 *6)) (-5 *4 (-641 (-1170))) (-4 *6 (-363)) + (-5 *2 (-641 (-294 (-948 *6)))) (-5 *1 (-538 *5 *6 *7)) + (-4 *5 (-452)) (-4 *7 (-13 (-363) (-844)))))) +(((*1 *2) + (-12 (-4 *3 (-556)) (-5 *2 (-641 *4)) (-5 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|particular| (-3 *4 "failed")) (|:| -2510 (-641 *4)))) + (-2 (|:| |particular| (-3 *4 "failed")) (|:| -3776 (-641 *4)))) (-5 *1 (-664 *5 *6 *4 *3)) (-4 *3 (-683 *5 *6 *4)))) ((*1 *2 *3 *4) (-12 (-4 *5 (-363)) (-4 *6 (-13 (-373 *5) (-10 -7 (-6 -4407)))) (-4 *7 (-13 (-373 *5) (-10 -7 (-6 -4407)))) (-5 *2 (-641 - (-2 (|:| |particular| (-3 *7 "failed")) (|:| -2510 (-641 *7))))) + (-2 (|:| |particular| (-3 *7 "failed")) (|:| -3776 (-641 *7))))) (-5 *1 (-664 *5 *6 *7 *3)) (-5 *4 (-641 *7)) (-4 *3 (-683 *5 *6 *7)))) ((*1 *2 *3 *4) @@ -10094,7 +8544,7 @@ (-4 *7 (-13 (-29 *6) (-1194) (-955))) (-4 *6 (-13 (-846) (-307) (-1034 (-564)) (-637 (-564)) (-147))) (-5 *2 - (-2 (|:| |particular| (-1259 *7)) (|:| -2510 (-641 (-1259 *7))))) + (-2 (|:| |particular| (-1259 *7)) (|:| -3776 (-641 (-1259 *7))))) (-5 *1 (-798 *6 *7)) (-5 *4 (-1259 *7)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-685 *6)) (-5 *4 (-1170)) @@ -10106,27 +8556,27 @@ (-5 *5 (-1170)) (-4 *7 (-13 (-29 *6) (-1194) (-955))) (-4 *6 (-13 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|fst| (-434)) (|:| -1829 "void"))) (-14 *5 (-641 (-1170))) (-14 *6 (-1174)))) ((*1 *1 *2) (-12 (-5 *2 (-331 *4)) (-4 *4 (-13 (-846) (-21))) @@ -11895,14 +12204,14 @@ ((*1 *1 *2) (-12 (-5 *2 (-434)) (-5 *1 (-437)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3094 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3063 (-641 (-330))))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 (-5 *2 (-1259 (-695))) (-4 *1 (-440)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3094 (-641 (-330))))) + (-5 *2 (-2 (|:| |localSymbols| (-1174)) (|:| -3063 (-641 (-330))))) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-330)) (-4 *1 (-441)))) ((*1 *1 *2) (-12 (-5 *2 (-641 (-330))) (-4 *1 (-441)))) @@ -11971,7 +12280,7 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-641 (-2 (|:| -3154 *3) (|:| -1970 *4)))) + (-12 (-5 *2 (-641 (-2 (|:| -4311 *3) (|:| -3144 *4)))) (-4 *3 (-1045)) (-4 *4 (-722)) (-5 *1 (-731 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-564)) (-4 *1 (-759)))) ((*1 *1 *2) @@ -11980,25 +12289,25 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (|:| |mdnia| (-2 (|:| |fn| (-316 (-225))) - (|:| -1953 (-641 (-1088 (-839 (-225))))) + (|:| -2029 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-316 (-225))) - (|:| -1953 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) + (|:| -2029 (-641 (-1088 (-839 (-225))))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1170)) (|:| |fn| (-316 (-225))) - (|:| -1953 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) + (|:| -2029 (-1088 (-839 (-225)))) (|:| |abserr| (-225)) (|:| |relerr| (-225)))) (-5 *1 (-765)))) ((*1 *2 *3) (-12 (-5 *2 (-770)) (-5 *1 (-769 *3)) (-4 *3 (-1209)))) @@ -12016,23 +12325,23 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-316 (-225))) (|:| -2760 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3978 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (|:| |lsa| (-2 (|:| |lfn| (-641 (-316 (-225)))) - (|:| -2760 (-641 (-225))))))) + (|:| -3978 (-641 (-225))))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -2760 (-641 (-225))))) + (-2 (|:| |lfn| (-641 (-316 (-225)))) (|:| -3978 (-641 (-225))))) (-5 *1 (-837)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-316 (-225))) (|:| -2760 (-641 (-225))) + (-2 (|:| |fn| (-316 (-225))) (|:| -3978 (-641 (-225))) (|:| |lb| (-641 (-839 (-225)))) (|:| |cf| (-641 (-316 (-225)))) (|:| |ub| (-641 (-839 (-225)))))) (-5 *1 (-837)))) @@ -12133,47 +12442,46 @@ ((*1 *1 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\ No newline at end of file |